Prediction, optimization and monitoring of chromatographic processes

Abstract

This disclosure provides methods for simulating chromatographic processes, methods for monitoring chromatographic processes, methods for controlling chromatographic processes, and related systems and products that use a global flow mass balance model solved by numerical integration over one or more discrete volume elements along a chromatographic unit. The model is an ordinary differential equation model including binding and diffusion terms, each parameterized by a single corresponding parameter predicted by a machine learning model.

Description

Technical Field

[0001] This disclosure relates to computer-implemented methods, computer programs, and systems for simulating, optimizing, monitoring, and controlling chromatographic processes. Specific methods, programs, and systems of this disclosure use machine learning-parameterized mass balance models within differential volume elements to predict the state of the chromatographic process. Background Technology

[0002] Process chromatography is a critical step in purifying most high-value products from biological processes, including biotherapeutic agents. In the context of biotherapeutic agents, the specificity of the chromatographic purification steps is essential for producing safe and effective products. To achieve the required specificity, the chromatographic columns used in these steps possess complex chemical and physical properties and require precise manufacturing. Consequently, chromatographic columns are expensive, accounting for up to 30% of the manufacturing cost of biotherapeutic agents in some processes. Furthermore, due to the stringent specification requirements, these columns have a limited lifespan. Therefore, optimizing the performance of chromatographic steps is a major driving force in the process development and manufacturing stages of bioproduct production.

[0003] Traditionally, optimizing chromatographic steps during process development involves starting with small-scale (i.e., 5 ml column bed volume) laboratory experiments and gradually scaling up to production volumes. During this process, the feed concentration of the target product, buffer conditions, and flow rate can be optimized to maximize product recovery (traditionally measured in milligrams of product per liter of chromatographic resin). Throughout the design process, simple summary statistics, such as the column's "dynamic binding capacity" (the maximum amount of target product (e.g., target protein) that can be loaded onto the column under a specific set of process conditions), are typically calculated based on experimental results. These are then used to aid in the design of subsequent experiments. While dynamic binding capacity is a useful design tool due to its simplicity, it is difficult to predict how its value will change when the flow rate or feed concentration is altered.

[0004] To predict chromatographic performance under varying feedstock, flow rate, and physical size conditions, various first-principles (physics-based) chromatographic models have been proposed. These models, also known as “mechanical” models, involve detailed modeling of the physicochemical processes occurring during chromatography. Typically, these models are mathematically described by partial differential equations (PDEs) because the chromatographic column is dynamically evolving in both spatial and temporal dimensions. For example, the universal rate model is a detailed mechanical model that describes the transport of solute molecules through the interstitial column volume via convective flow, mass transfer resistance through the stagnant membrane surrounding the beads, diffusion through the pores (and surfaces) of the porous beads, and adsorption onto the inner bead surface. Different forms of universal rate models for different chromatographic conditions / configurations have been extensively studied (see, for example, Shekhawat and Rathore, 2019).

[0005] While these models can serve as powerful predictive tools, they have some drawbacks when used in practical applications. To mathematically describe all the physical effects occurring within the column, these models require a relatively large number of complex nonlinear terms and numerous coefficients. These coefficients must be uniquely determined through careful experimentation. For typical applications, identifying these coefficients can take approximately one to two months of experimental time. Furthermore, building a model using this first-principles approach requires the modeler to understand and correctly characterize every physical interaction within the column. Factors such as competitive binding and complex diffusion must be explicitly described. Therefore, building a good model requires substantial prior experience. Additionally, with the advancement of chromatographic techniques, the physical properties of state-of-the-art columns have become increasingly complex and difficult to model using first-principles methods. For example, membrane columns may have complex pore structures that may be difficult, or even impossible, to fully characterize. For these reasons, building a general rate model to describe a real column is a nontrivial task typically performed by modeling experts.

[0006] Therefore, new methods are needed to model chromatographic processes. Summary of the Invention

[0007] The inventors of this invention recognized that current state-of-the-art chromatographic process simulation methods (e.g., chromatographic process optimization, monitoring, scale-up, etc.) suffer from numerous shortcomings related to the complexity of phenomena that need to be considered to obtain reliable simulations. They hypothesized that some of this complexity could be circumvented by providing a unique novel hybrid model that combines a simple physics-based model that captures only the overall flow (i.e., mass balance) with a machine learning model trained to capture binding and diffusion. Specifically, the machine learning model predicts the parameters of the mass balance model for dynamically capturing all binding and diffusion phenomena within the column. These can be viewed as phenomenological parameters directly substituted into a simple mass balance equation, thus eliminating the need for detailed models of all aspects of binding and diffusion of the captured products within the individual compartments of the column. Furthermore, since the mass balance model does not explicitly model the diffusion geometry but instead uses differential volume elements, the same machine learning model can be used regardless of the column geometry, and the same architecture can be used regardless of the type of stationary phase (e.g., resin, membrane, or monolithic column). Therefore, this represents a universal chromatographic model that is easy to parameterize, stable, and computationally efficient.

[0008] According to a first aspect of this disclosure, a computer-implemented method for simulating a chromatographic process is provided, wherein a feed stream comprising one or more products passes through a chromatographic unit comprising a stationary phase, the one or more products interacting with the stationary phase, the method comprising: The overall flow mass balance model is solved by numerical integration over one or more discrete volume elements along the chromatographic unit. The overall flow mass balance model is an ordinary differential equation model, which represents the concentration changes of bound and unbound fractions of one or more products in a discrete volume element. The ordinary differential equation model includes binding terms and diffusion terms, wherein the binding term captures the binding of the product to the stationary phase, and the diffusion term captures the diffusion of the bound product. The binding term and diffusion term are each parameterized by a single corresponding parameter predicted by a machine learning model trained to take inputs including the concentrations of bound fractions and unbound fractions of one or more products in a discrete volume element, and to produce predicted parameters of the binding term and diffusion term as outputs.

[0009] This aspect also provides a method for simulating a chromatographic process, wherein a feed stream comprising one or more products passes through a chromatographic unit comprising a stationary phase, the one or more products interacting with the stationary phase, the method comprising: Using a mass balance module implemented in the processor, a global flow mass balance model representing the concentration changes of bound and unbound fractions of one or more products in one or more discrete volume elements along a chromatographic unit is solved, where the solution uses a numerical integration module. The overall flow mass balance model is an ordinary differential equation model that includes binding and diffusion terms. The binding term captures the binding of products with the stationary phase, and the diffusion term captures the diffusion of the bound products. Both the binding and diffusion terms are parameterized by individual corresponding parameters. The solution involves using a machine learning module implemented in the processor to predict the value of the parameter. This machine learning module uses a trained machine learning model to predict the value of the parameter using inputs including the concentrations of bound fractions and unbound fractions of one or more products in a discrete volume element.

[0010] Therefore, the method of the present invention advantageously utilizes a very simple physics-based model that represents the overall flow and the effects of binding and diffusion on the overall flow solely through phenomenological terms (i.e., terms that do not explicitly model the detailed physicochemical phenomena under the kinetics of product binding and the diffusion of bound products), combined with a data-driven phenomenological parameterization model to provide holistic-level phenomenological parameters representing diffusion and binding. Unmodeled phenomena occur along multiple dimensions in different compartments of the chromatographic unit, such as in pores and on films on surfaces, and involve physicochemical processes that are not necessarily well characterized. The method of the present invention advantageously bypasses all of these by using machine learning algorithms to identify all dynamic behavioral components of the system that are difficult to explain by first principles.

[0011] Advantageously, the approach, which relies on differential volume elements and includes simple diffusion and binding terms captured as ordinary differential equations (ODEs), means that the model has the same architecture regardless of the geometry of the chromatographic unit. In other words, the model does not explicitly represent the diffusion geometry, and the same model can be used for columns with different geometries, thus enabling direct application to computer simulations scaled up experiments. Furthermore, using ODEs on discrete volume elements means that simulations can be run without the need for adaptive step-size partial differential equation solvers. Therefore, the simulations are more stable and computationally efficient than existing methods.

[0012] The method of the first aspect may have any one or any combination of the following optional features.

[0013] The overall flow mass balance model may include a linear term representing the flow of unbound compounds (products and optional inert substances) into and out of discrete volume elements, as well as a binding term and a diffusion term, wherein the binding term captures the nonlinearity of the adsorption process of unbound products on the static phase by pre-setting the corresponding parameters of the term in the machine learning model at each iteration of the numerical integration. The overall flow mass balance model may include the following equations (1) and (2) and optional equation (3):

[0014] Where f k It is the feed flow rate, and ΔV is the discrete volume element. n volume, It is the concentration vector of unbound products in the discrete volume element n. Discrete volume element n Concentration vector of the bound product, Discrete volume element n The concentration vector of unbound products in the previous discrete volume element, where the discrete volume elements are labeled sequentially from the input to the output of the chromatographic unit. Discrete volume element n The concentration vector of one or more inert substances. Discrete volume element n The concentration vector of inert material in the previous discrete volume element, and It is an element-wise product. This system of equations represents only three macroscopic phenomena along the discrete volume of a chromatographic unit: the flow of unbound products into and out of the volume (and optionally, the flow of inert substances), the diffusion of bound products, and the binding of unbound products to the stationary phase. The latter two are represented by vectors. and The "overall" parameters are parameterized and calculated as the output of the machine learning model.

[0015] The overall flow mass balance model can be solved on N discrete volume elements, where N is at least 2, where N is between 5 and 20, where N is between 5 and 15, where N is selected from 8, 9, 10, 11, 12, or where N is 10. The discrete volume elements can include multiple discrete volume elements along the chromatographic unit where binding and diffusion occur, preceding a discrete volume element in which no binding or diffusion occurs (inlet dead volume) and following a discrete volume element in which no binding or diffusion occurs (outlet dead volume).

[0016] The machine learning model input can also include the feed flow rate. Advantageously, this means that the model (combining the mass balance model and the machine learning model) can capture the effect of flow rate on the dynamics of binding and diffusion (via the machine learning model), thus allowing the same model to be used to simulate columns with different flow rates. In fact, the hydrodynamic binding and diffusion effects can be learned from experimental data generated at different flow rates, making the resulting trained model applicable to at least any range of flow rates for which the training data (or training data with similar flow rates) is available. Furthermore, due to the flow rate variable f... k This variable is not used in the equations derived from first principles by the machine learning model, and therefore can be "transformed" by the user before being passed to the machine learning model. For example, while a mass balance model uses volumetric flow rate, the flow rate can be converted to linear velocity or residence time before being provided as input to the machine learning model. This is expected to make the model less scale-dependent. This property is particularly advantageous for applications that wish to identify models from experiments conducted in small columns and use these models to make predictions for larger-scale (commercial manufacturing-related) columns. Therefore, in an implementation, the method includes obtaining the volumetric feed flow rate, converting the volumetric feed flow rate to linear velocity or residence time, and providing the converted feed flow rate as input to the machine learning model.

[0017] In the implementation scheme, the machine learning model will also take parameters indicating the service life of the chromatographic unit as input. For example, the machine learning model can take as input the number of cycles the chromatographic unit has run, the total unit volume that has passed through the unit, or any other value derived therefrom (e.g., the percentage of the estimated lifetime as the number of cycles used by the chromatographic unit relative to the expected number of cycles in the column lifetime). This advantageously enables the machine learning model to accurately capture the effect of aging columns on the kinetics of the chromatographic process.

[0018] The overall flow mass balance model can also represent the concentration changes of one or more inert substances in a discrete volume element (e.g., using equation (3)), and the machine learning model input can also include the concentration of one or more inert substances in the discrete volume element.

[0019] The machine learning model can be a recurrent machine learning model, which is a machine learning model that considers one or more predictions made in one or more previous iterations of the numerical integral when making a prediction at the current iteration of the numerical integral. The machine learning model can also include the current iteration... k and discrete volume element n A cyclic state vector of one or more state values As input, and to produce an updated loop state vector The output is used in subsequent iterations. The machine learning model can include a parameter prediction sub-model and a recurrent state sub-model, wherein the recurrent state sub-model is configured to predict updated recurrent state vectors based on the input of the machine learning model. This is for use in subsequent iterations, and the parameter prediction sub-model is configured to predict the parameters of the binding and diffusion terms based on the input of the machine learning model. The cyclic state vector can be cascaded with other input variables (concentrations of bound and unbound products, feed rate, and concentration of inert substances, if used). Before being used as input to the machine learning model, the cyclic state vector can be transformed using any function (such as the tanh or sigmoid function) configured to produce bounded values ​​from unbounded values. This advantageously ensures that the state values ​​do not increase to dominate other input variables. In embodiments that include both the parameter prediction sub-model and the cyclic state sub-model, the cascaded input can be fed into both. The machine learning model can include both the cyclic state sub-model and the parameter prediction sub-model parameterized by corresponding weights learned simultaneously. Thus, the trained machine learning model can be associated with the same learned weights for each iteration of each discrete volume element and numerical integral.

[0020] The machine learning model can be a non-linear regression model. The machine learning model can include a neural network, optionally wherein the neural network is a fully connected neural network, a neural network including at least 2 hidden layers, a neural network including 1 to 4 hidden layers, a neural network including 2 or 3 hidden layers, and / or a neural network including 8 to 60 nodes in each hidden layer.

[0021] The method may further include training a machine learning model using training data comprising feed concentration data and effluent concentration data from multiple chromatographic processes, and / or wherein the machine learning model has been trained using training data comprising feed concentration data and effluent concentration data from multiple chromatographic processes, wherein the feed concentration data is data indicating the inlet product concentration and the effluent concentration data is data indicating the outlet product concentration, optionally wherein the training data comprises feed concentration data and effluent concentration data respectively associated with corresponding discrete time points during the chromatographic process and / or feed concentration data and effluent concentration data associated with a time range during the chromatographic process, such as data collected using a fraction collector.

[0022] Training a machine learning model can involve iteratively updating the model's weights in the following ways: For each of one or more training datasets, each including feed concentration data, effluent concentration data, and feed flow rate data corresponding to multiple time points during the chromatographic process, the overall flow mass balance model is solved using the values ​​of the parameters of the combination and diffusion terms predicted by the machine learning model at the previous iteration of training within discrete time intervals corresponding to multiple time points from the training datasets, where the feed rate trajectory corresponds to the feed flow rate data and feed concentration data from the training datasets, thereby obtaining simulated data corresponding to each of the one or more training datasets; A loss function that evaluates the difference between quantized simulated data and one or more corresponding training datasets; and Optionally, a gradient descent procedure can be used to update the weights of the machine learning model based on the weights and the value of the loss function at the current iteration, until one or more predetermined stopping criteria are met.

[0023] Training a machine learning model may include: during the first iteration of the iterative training, setting the weights of the machine learning model to initial weights corresponding to predetermined values ​​of the parameters of the combination and diffusion terms. Setting the weights of the machine learning model to the initial weights may include: obtaining the predetermined values ​​of the parameters of the combination and diffusion terms, setting the weights of the machine learning model to default values, and pre-training the machine learning model, wherein the pre-training includes iteratively updating the weights of the machine learning model in the following manner: Using a machine learning model, the values ​​of the parameters for the combination and diffusion terms are predicted using inputs from the machine learning model sampled from the training data. A loss function is used to evaluate the difference between the predicted values ​​and predetermined values ​​of the parameters of the quantification combination and diffusion terms; and The weights of the machine learning model are updated based on the weights and the value of the loss function at the current pre-training iteration.

[0024] Training a machine learning model may involve determining predetermined values ​​for the parameters of the combination and diffusion terms by performing one or both of the following: (a) Set the values ​​of the parameters of the diffusion term and the parameters of the binding term, or the corresponding parameters associated with the corresponding nonlinear binding term, to their respective default values. The overall flow mass balance model is solved by numerical integration using default values ​​for the parameters of the diffusion and binding terms, along with predetermined feed concentration and feed rate data. Optionally, the predetermined feed concentration and feed rate data are selected as the maximum values ​​of feed rate and feed concentration observed in the training data. Determine whether numerical integration failed to compute any solutions to the model, and When numerical integration fails to compute any solution to the model, the default values ​​of the parameters of the combination and diffusion terms are updated by decreasing the default values ​​by a predetermined factor. The above steps are repeated until the numerical integration can compute all the solutions of the model in an iteration, and the values ​​of the parameters of the combination term and the diffusion term are selected as those used in the iteration. (b) Set the values ​​of the parameters of the diffusion term and the parameters of the binding term, or the corresponding parameters associated with the corresponding nonlinear binding term, to their respective default values, optionally wherein the default values ​​are obtained using the method of step (a). For each of one or more training datasets, each including feed concentration data, effluent concentration data, and feed flow rate data corresponding to multiple time points during the chromatographic process, the overall flow mass balance model is solved using the default values ​​of the parameters of the combination term and the diffusion term, thereby obtaining simulation data corresponding to each of the one or more training datasets. A loss function that evaluates the difference between quantized simulated data and one or more corresponding training datasets; and Optionally, a gradient descent procedure can be used to update the default values ​​of the parameters of the combination and diffusion terms based on the value of the loss function. The above steps are repeated until one or more predetermined stopping criteria are met.

[0025] Solving the overall flow mass balance model may involve iteratively integrating the model over multiple discrete time intervals of a predetermined duration. At each iteration, a machine learning model and a current state vector are used to obtain predictions of the parameters for the binding and diffusion terms in each discrete volume element. This current state vector includes the concentration of bound products, the concentration of unbound products, and optionally the concentration of inert substances and the optional feed rate in each discrete volume element at the most recent iteration. The overall flow mass balance model, parameterized using the predictions, is used to identify the discrete state-space model. The updated state vector corresponding to the current iteration time interval is determined using the values ​​of the current state vector and the coefficients of the discrete state-space model.

[0026] Solving the overall flow mass balance model along one or more discrete volume elements of a chromatographic unit by numerical integration may include integrating the model over each of the one or more discrete volume elements at multiple discrete time points to obtain simulated data including the concentration of the product in the effluent of the chromatographic unit at multiple discrete time points. The method may also include using the simulated data to determine one or more of the following: effluent product concentration, product adsorption rate, product desorption rate, total product capture, dynamic binding capacity of the chromatographic process with respect to the product, product binding capacity per cycle, product recovery percentage, maximum breakthrough concentration of the product, maximum breakthrough percentage of the product, and cost associated with the simulated chromatographic process.

[0027] According to a second aspect, a computer-implemented method is provided for obtaining a training model for simulating a chromatographic process, wherein a feed stream containing one or more products passes through a chromatographic unit containing a stationary phase, the one or more products interacting with the stationary phase, the method comprising: Training data was obtained, including feed concentration data and effluent concentration data from multiple chromatographic processes, where the feed concentration data indicates the inlet product concentration and the effluent concentration data indicates the outlet product concentration; and The machine learning model is trained to take inputs including the concentrations of bound fractions and unbound fractions of one or more products in a discrete volume element, and outputs predicted parameters of the bound and diffuse terms of the overall flow mass balance model of the chromatographic unit. The training mentioned above involves solving a global flow mass balance model by numerical integration over one or more discrete volume elements along the chromatographic cell; The overall flow mass balance model is an ordinary differential equation model, which represents the concentration changes of bound and unbound fractions of one or more products in a discrete volume element. The ordinary differential equation model includes binding terms and diffusion terms, where the binding term captures the binding of the product with the stationary phase, and the diffusion term captures the diffusion of the bound product.

[0028] The method in this aspect may have any of the features described in the first aspect.

[0029] According to a third aspect, a computer-implemented method for designing a chromatographic process is provided, the method comprising: using the method of any embodiment of the first aspect, simulating the chromatographic process using multiple candidate sets of process parameters, each including at least a feed product concentration and a feed flow rate, thereby obtaining a simulated effluent concentration for each candidate set of process parameters; and comparing the simulated effluent concentrations or one or more indices derived therefrom to select a set of process parameters from the set of candidate process parameters.

[0030] The candidate set of process parameters can include different stationary phases, and simulating the chromatographic process can include using corresponding machine learning models trained with corresponding training data obtained using the respective stationary phases. The candidate set of process parameters can include columns with different numbers of tandem connections. Such methods can be used in many different scenarios. For example, these methods can be used for scenarios involving the design of multi-column chromatographic processes. The methods disclosed herein are particularly advantageous in such cases because the same model applies to both single-column and multi-column settings, and these models can run efficiently (i.e., rapidly) on many different sets of process parameters. Furthermore, the methods disclosed herein are particularly advantageous in that multi-column processes can be simulated using models that have been specifically or primarily trained on batch (i.e., single-column) training data. Again, these methods can be used for scenarios involving scaled-up process design, such as for predicting large-scale binding capacities from small-scale experiments. In fact, the methods disclosed herein are particularly advantageous in that they are scale-independent, i.e., large-scale processes can be simulated using models that have been trained on training data from different scales.

[0031] According to another aspect, a method for monitoring a chromatographic process is provided, the method comprising: simulating the chromatographic process using the method of any embodiment of the first aspect and feed concentration data and feed flow rate data corresponding to the measured or planned feed concentration and feed flow rate of the chromatographic process, thereby obtaining a simulated effluent concentration corresponding to the effluent concentration of the chromatographic process; and comparing the simulated effluent concentration or one or more indicators derived therefrom with an observed effluent concentration or an indicator derived therefrom, wherein the comparison indicates the presence of a malfunction or aging condition of the chromatographic unit.

[0032] According to another aspect, a method for controlling a chromatographic process is provided, the method comprising: (a) simulating the chromatographic process using the method of any embodiment of the first aspect and feed concentration data and feed flow rate data corresponding to the measured or planned feed concentration and feed flow rate of the chromatographic process, thereby obtaining a simulated effluent concentration corresponding to the effluent concentration of the chromatographic process; and comparing the simulated effluent concentration or one or more indicators derived therefrom with an observed effluent concentration or indicators derived therefrom, and determining, based on the result of the comparison, whether to repack the chromatographic unit or whether to switch the feed to a different column in a multi-column chromatography process; and / or (b) using the method of the embodiment of the first aspect, simulating the chromatographic process using a plurality of candidate sets of process parameters, each including at least a feed product concentration and a feed flow rate, thereby obtaining a simulated effluent concentration for each candidate set of process parameters, and comparing the simulated effluent concentration or one or more indicators derived therefrom to select a set of process parameters from the set of candidate process parameters for operating the chromatographic process, optionally wherein the candidate set of process parameters includes a desired feed product concentration or feed flow rate.

[0033] Unless the context otherwise requires, all steps of the methods described herein are computer-implemented. Specifically, any step of this method may be implemented by a computing device that optionally communicates operatively with one or more sensors, one or more chromatographic processes (e.g., each single-column or multi-column chromatographic unit), other computing devices, and / or a user interface.

[0034] According to another aspect, a system is provided, comprising: at least one processor; and at least one non-transitory computer-readable medium containing instructions that, when executed by the at least one processor, cause the at least one processor to perform operations including steps of any of the methods described in the first, second, and / or third aspects. Specifically, the at least one non-transitory computer-readable medium may contain instructions that, when executed by the at least one processor, cause the at least one processor to perform operations including any of the operations described in relation to the first, second, and / or third aspects. The system may also include one or more of the following: a chromatographic unit, one or more sensors, and a user interface.

[0035] According to another aspect, a non-transitory computer-readable medium comprising instructions that, when executed by at least one processor, cause at least one processor to perform any embodiment of any aspect described herein.

[0036] According to another aspect, a method is provided that includes a computer program with code, which, when executed on a computer, causes the computer to perform any implementation of any aspect described herein. Attached Figure Description

[0037] Embodiments of this disclosure will now be described by way of example with reference to the accompanying drawings, wherein: Figure 1 A simplified process diagram of a system in which embodiments of the present disclosure can be used is shown.

[0038] Figure 2 schematically illustrates (A) a method for simulating a chromatographic process according to an embodiment of the present disclosure, and (B) a method for obtaining a trained machine learning model according to an embodiment of the present disclosure.

[0039] Figure 3 The components used in the simulated chromatography process and / or the method for obtaining a trained machine learning model according to the present disclosure are illustrated schematically.

[0040] Figure 4 Methods for monitoring a chromatographic process, optimizing a chromatographic process, and controlling a chromatographic process according to embodiments of the present disclosure are illustrated schematically.

[0041] Figure 5 A system according to an embodiment of this disclosure is illustrated schematically.

[0042] Figure 6 A discretization scheme for describing a chromatographic process according to an embodiment of the present disclosure is illustrated schematically.

[0043] Figure 7 A machine learning model structure for parameterizing a quality balance model according to an embodiment of the present disclosure is illustrated schematically.

[0044] Figure 8A -B schematically illustrates a method for training a machine learning model according to an embodiment of the present disclosure.

[0045] Figure 9A -B schematically illustrates a method for simulating a chromatographic process according to an embodiment of the present disclosure (A: a flowchart illustrating the process used, and B: the mass balance model equations used—note that each of B-1 to B-3 shows the same set of equations at the top, where the state of the system is in vector form, and the terms of matrices A and B are expanded for the state vectors corresponding to the concentrations of unbound products (B-1), bound products (B-2), and inert substances (B-3) along differential volume elements 1 to n; B-4 combines the information from B-1 to B-3).

[0046] Figure 10A-D shows simulation results of the chromatographic process using the method described herein, with different flow rate values ​​for the chromatographic process (A: flow rate = 20 ml / min, B: flow rate = 13.9 ml / min, C: flow rate = 5.9 ml / min, D: flow rate = 1.8 ml / min). The left side of each subplot shows the calculated adsorption rate for different binding phase concentrations and mobile phase concentrations, and the right side shows the calculated desorption rate for different binding phase concentrations and mobile phase concentrations. The data shown simulates the binding phase of the chromatographic process, which is why the differences are primarily reflected in the calculated adsorption rate. However, the method described herein is equally applicable to the simulation of the elution phase of the chromatographic process, where differences between operating settings will be more pronounced in the calculated desorption rate.

[0047] Figure 11 The figure shows representative model prediction performance using training data (i.e., data used to identify model parameters) and validation data not seen by the training algorithm. The scatter points (solid circles) in the figure represent experimental measurements of product concentration at column outlet (monoclonal antibody titer, in mg / ml), while the solid lines represent the corresponding model predictions. Examples of three different feed flow rates used as training data and two feed flow rates used as validation cases are shown.

[0048] Figure 12 An example of a user interface for accessing the methods of this disclosure is shown.

[0049] Figure 13 shows example results of the simulation method of this disclosure applied to protein A purification, using the same operating parameters (feed rate = 2.5 ml / min, feed concentration = 1 mg / ml, simulation duration = 200 min, breakthrough threshold % = 5), but using two different protein A chromatography systems: (AB) MabSelect™ SuRe chromatography resin from Cytiva (calculated breakthrough time = 53.77 min, calculated dynamic binding capacity = 134.42 mg / ml) and (CD) Sartobind from Sartorius Stedim Biotech GmbH. ® Rapid A membrane (calculated breakthrough time = 24.10 min, calculated dynamic binding capacity = 50.20 mg / ml); A and C show the simulation results, and B and D show the model validation data (from experiments with different feed rates and feed concentrations to demonstrate the effectiveness of the model predictions) and the correlation R between the predicted (continuous line) and the observed (point) breakthrough curves. 2 And RMSE; each model uses the corresponding substrate and column, and is trained using real data (4 breakthrough curves obtained from experiments); each graph shows the breakthrough curve, i.e. the change of product concentration (mg / ml) in the effluent over time (minutes).

[0050] Figure 14 illustrates an example of economic modeling and / or optimization of a chromatographic process using the methods described herein; the heatmap shows the results compared to using MabSelect™ (A) or Sartobind. ® The Rapid A membrane (B) column is run at a specified titer value and flow rate to generate the chromatographic process associated with the model (used to generate the results in Figure 13).

[0051] Figure 15 An example of column amplification prediction using the method described in this paper is shown.

[0052] Figure 16 shows the results of robustness evaluations of the method described in this paper; AC. Results evaluating the impact of the number of loop states on model performance. These figures show the simulated capture (A), simulated dynamic assemblage capacity (B), and validation loss (C) as a function of the number of nodes per layer of the neural network used to predict the assemblage and diffusion coefficients when using 1 or 2 loop states. DF. Evaluation results of prediction stability as a function of the number of nodes in the neural network for two independent iterations of training a neural network with different random initializations of neural network weights. These figures show the simulated capture (D), simulated dynamic assemblage capacity (E), and validation loss (F) as a function of the number of nodes in the neural network over two iterations of the method. GI. Evaluation results of prediction stability as a function of the number of nodes in the neural network when using 1, 2, or 4 layers. These figures show the simulated capture (G), simulated dynamic assemblage capacity (H), and validation loss (I) as a function of the number of nodes in the neural network when using a network with 1, 2, or 4 layers.

[0053] Figure 17 illustrates the setup for a detailed evaluation of the method of this disclosure using data generated from a general rate model with numerical evaluation. A. Example of fully synthesized data from the general rate model, showing the target mobile phase concentration at the inlet (red dashed line), the target mobile phase concentration at the outlet (red solid line), the regulator mobile phase concentration at the inlet (black dashed line), and the regulator mobile phase concentration at the outlet (black solid line), where the target indicates the concentration of the target molecule we want to separate in the mobile phase, and the regulator is the concentration of a buffer solution that counteracts the binding of the target molecule to the solid phase, thereby eluting the target molecule. B shows how the data in A was used to generate synthetic fractional measurements of the target mobile phase concentration (black squares) by integrating over time periods of the synthesized data. C. Simulated data (points) from the general rate model used for training and validating the model of this disclosure, and corresponding predictions from the trained model of this disclosure. For each experiment, the model was trained on four time series and validated on the final series. This figure shows a set of example training and validation data (CADET simulated breakthrough curves) from one experiment.

[0054] Figure 18 shows the results of the evaluation described with reference to Figure 17. A. Histograms of the average loss on the validation and training datasets for each of the 180 experiments (see Example 4) (top left and top right, respectively), and the distribution of the average loss on the validation and training datasets (bottom left and bottom right, respectively), illustrated as box plots (thick black line = median, bins extending to the interquartile range, whiskers indicating the interquartile range of 1.5, dots indicating the lowest data point above Q1-1.5*(Q3-Q1) and the highest data point below Q3+1.5*(Q3-Q1), where Q1 and Q3 are the first and third quartiles). BE shows instances with errors higher than the median in A (i.e., these are exceptions to the selection with particularly poor performance, which should be analyzed to gain insight into situations where the model does not perform well; it should be noted that most instances, by definition, have lower errors than those shown in BD). B. Exemplary results with validation loss = 0.1. C. Exemplary results with validation loss = 0.01. D. Exemplary result with validation loss = 0.01. E. Exemplary result with validation loss = 4.4 × 10⁻³ (median recall 4.3 × 10⁻³).

[0055] In the accompanying drawings, embodiments of the invention are illustrated, but these should not be construed as limiting the scope of the invention. Where appropriate, the same reference numerals will be used in different drawings to denote the same structural features illustrating the embodiments. Detailed Implementation

[0056] Specific embodiments of the present invention will now be described with reference to the accompanying drawings.

[0057] This disclosure describes novel methods for simulating chromatographic processes and methods for process design, control, monitoring, and optimization using such simulations.

[0058] A “chromatographic process” refers to any process utilizing liquid chromatography, particularly in the case of purifying one or more products present in a feed solution. Chromatographic processes are typically performed in a chromatographic unit comprising one or more individual columns. Each column contains a stationary phase (e.g., resin, membrane, monolithic column) and a mobile phase. The methods disclosed herein are not limited in any way by regard to the geometry of the columns, the organization of multiple columns (e.g., multiple columns connected in series), or the type of stationary or mobile phase. Liquid chromatography is commonly used to purify one or more target molecules, compounds, or particles (referring to the fact that chromatography is commonly used to purify products of biological processes, collectively referred to as “products” or “biological products”). Products can be proteins or particles, such as viral particles. Purification of products is performed by loading the product onto the column by passing a feed liquid containing the product through the column, where the product interacts with and is immobilized on the stationary phase (where they are referred to as “bound products”). Once the column has been loaded with product, it is typically washed, and then a buffer solution is passed through the column during an elution phase, where a buffer of choice is used to reduce the affinity of the product for the stationary phase and elute the product from the column. The effluent from a chromatographic column can be referred to as "eluent," whether in the loading or elution phase. The methods described herein are applicable to simulating any part of a chromatographic process, provided that a machine learning model is trained using training data for the corresponding phase, as further described below. For example, the methods described herein can be used to simulate the loading phase of a chromatographic process (e.g., to obtain simulated breakthrough curves and indices derived therefrom) using a machine learning model trained with training data that includes loading phase data (e.g., breakthrough curves). As another example, the methods described herein can be used to simulate the loading and elution phases of a chromatographic process using corresponding machine learning models trained with training data that includes loading phase data and elution phase data, respectively. The washing phase can be omitted, or it can also be simulated using a machine learning model trained with training data that includes washing phase data. Note that the same machine learning model can be used to simulate multiple phases (such as a complete cycle including loading, washing, elution, and regeneration, or a portion thereof, such as a loading-washing-elution process only), provided that the machine learning model is trained with training data that includes the multiple phases being modeled.

[0059] Figure 1 A simplified process diagram of a system in which embodiments of the present disclosure can be used is shown. The bioprocess includes an upstream process 10 in which a product is being produced, illustrated herein as a bioreactor 10. In an embodiment where the bioreactor operates as a perfusion process, as illustrated, at a flow rate f... H Permeate is obtained from the bioreactor (also known as "harvest stream" or "harvest feed stream"). Bioreactor 10 can also be used at a flow rate f. FFeed. The permeate is typically the primary output of the upstream process, containing one or more target products. The permeate typically contains a large volume of culture that has undergone a cell separation step. In such embodiments, the output of upstream process 10 can be processed continuously in downstream process 12. In other embodiments, the process can be operated as a batch process, with no continuous harvest stream, and the product of the upstream process is processed after the upstream process is complete. The methods of this disclosure are independent of how the upstream process operates, or even the type of upstream process used. The illustrated embodiments are provided only to provide background for typical applications of chromatographic processes where the methods of this disclosure can be deployed. Downstream process 12 includes a chromatographic unit, illustrated herein as a single column, but in practice multiple columns can be used in parallel or in series. The chromatographic unit may include one or more columns and a flow control system. The chromatographic unit receives a flow rate f... k The input feed. The chromatography unit produces a flow rate f. k The output feed contains one or more target products at different concentrations. The input feed can be obtained directly from the upstream process; that is, in the case of a perfusion process, the input feed of the chromatographic unit can be directly connected to (or equal to) the harvest stream of the upstream process.

[0060] As used herein, the term "bioprocess" (also referred to herein as "biomanufacturing process") refers to a process of maintaining biological components (such as cells, parts thereof such as organelles, or multicellular structures such as organoids or spheroids) in a liquid culture medium in an artificial environment (such as a bioreactor). In the context of this disclosure, a bioprocess generally refers to cell culture. Bioprocesses typically produce products that may include biomass and / or one or more compounds resulting from the activity of the biological components. For example, live cells may be cultured to a desired cell density and then used in a fermentation process to produce one or more desired products in a bioreactor. This is generally referred to as an "upstream process" (USP). One or more desired products may be extracted from the cells or culture medium in a downstream process (DSP). The downstream process may include one or more steps, such as separation and / or purification steps. A bioreactor may be a single-use or reusable container that may contain a liquid culture medium suitable for carrying out the bioprocess. For example, a bioreactor may be selected from: multiple parallel single-use bioreactors (e.g., Ambr from The Automation Partnership Ltd.). ® 250 or Ambr ® 15. Bioreactors), disposable bag bioreactors (e.g., Biostat from Sartorius Stedim Biotech GmbH) ®STR bioreactors, with capacities ranging from 50 to 2000 L, are available for use from process development to commercial manufacturing; stainless steel bioreactors (e.g., biostatistics with capacities ranging from 10 to 200 L). ® D-DCU bioreactors or biostats with a capacity of 5 to 30 L ® Cplus bioreactors, all from Sartorius Stedim Systems GmbH, and benchtop systems (e.g., Biostat from Sartorius Stedim Systems GmbH) ® B and Biostat ® B-DCU supports 2L disposable rigid-walled containers or 1, 2, 5, and 10L glass containers, such as the 2L Univssel. ® SU and Univssel with capacities of 2 to 10L ® Glass (all from SartoriusStedim Biotech GmbH, etc.). This invention is applicable to downstream processes associated with upstream processes in any type of bioreactor, particularly bioreactors of any scale from any supplier and ranging from benchtop systems to manufacturing-scale systems.

[0061] Cell culture is a biological process of maintaining living cells in an artificial environment such as a bioreactor. The methods, tools, and systems described herein are applicable to biological processes using any type of cell that can be maintained in culture, whether eukaryotic or prokaryotic. This invention is particularly useful for monitoring and / or controlling biological processes using cell types, including but not limited to mammalian cells (such as Chinese hamster ovary (CHO) cells, human embryonic kidney (HEK) cells, Vero cells, etc.), non-mammalian cells (e.g., chicken embryonic fibroblast (CEF) cells), and insect cells (e.g., Drosophila melanogaster cells). D. melanogaster Cells, silkworms (B. mori) Animal cells of any cell type (e.g., induced pluripotent stem cells (iPSCs), stem cells such as mesenchymal stem cells, immune cells such as T cells and natural killer cells), and bacterial cells (e.g., Escherichia coli). E. coli ) cells), fungal (e.g., yeast) cells (e.g., Saccharomyces cerevisiae) S. cerevisiae ) cells) and plant cells (e.g., Arabidopsis thaliana) A. thaliana(Cells). Biological processes typically result in the production of products, which can be the cells themselves (e.g., cell populations used for further biological processes, cell populations used in cell therapy, cell populations used as products such as probiotics, raw materials, etc.), macromolecules or macromolecular structures such as proteins, peptides, nucleic acids, or viral particles (e.g., monoclonal antibodies, immunogenic proteins or peptides, viral or non-viral vectors used in gene therapy, enzymes, for example, used in the food industry, for environmental applications such as water purification, decontamination, etc.), or small molecules (e.g., alcohols, sugars, amino acids, etc.).

[0062] When the product contains macromolecules or macromolecular structures (such as proteins, peptides, nucleic acids, or viral particles), downstream processes typically include at least one chromatographic separation step, i.e., a chromatographic process. This disclosure provides methods suitable for such processes. The methods of this disclosure are applicable to any chromatographic process, including chromatographic processes performed on single-column and multi-column platforms of any scale (including, but not limited to, Resolute from Sartorius Stedim Chromatography Systems Ltd.). ® BioSC platform and Resolute ® The BioSMB platform, chromatographic processes using any chromatographic stationary phase known in the art (such as resins, membranes, and monolithic columns), and chromatographic processes for separating any type of analyte (including proteins (e.g., protein A, antibodies and their fragments, including, for example, monoclonal antibodies, enzymes), viral particles, small molecules (e.g., metabolites), etc.).

[0063] Products of a biological process (also referred to herein as “biomaterials” or “target bioproducts”) may include metabolites, cells, desired proteins, antibodies, immunoglobulins, toxins, one or more byproducts, target molecules, or any other type of molecule manufactured using the biological process. More than one target biomaterial (product) may be present. Products of a biological process may have one or more critical quality attributes (CQAs). As used herein, a “critical quality attribute” is any property of a product that can be defined and measured to characterize the quality of the product (particularly including any chemical, physical, biological, and microbiological properties). Quality characteristics of the product (in terms of the value of one or more CQAs) can be defined to ensure that the safety and efficacy of the product are maintained within predetermined boundaries. The term “metabolite” refers to any molecule consumed or produced by cells during a biological process. Metabolites specifically include: nutrients, such as glucose, amino acids, etc.; byproducts, such as lactate and ammonia; desired products, such as recombinant proteins or peptides; complex molecules involved in biomass production, such as lipids and nucleic acids; and any other molecules consumed or produced by cells, such as oxygen (O2). Depending on the specific circumstances, the same molecule can be considered a nutrient, a byproduct, or a desired product, and this can even change as biological processes are manipulated. However, all molecules involved in cellular metabolism (whether as inputs or outputs of reactions carried out by cellular machinery) are referred to herein as “metabolites.” Specifically, metabolites may include any suitable analytes, including but not limited to: amino acids (e.g., alanine, arginine, aspartic acid, asparagine, cysteine, glutamic acid, glutamine, glycine, histidine, hydroxyproline, isoleucine, leucine, lysine, methionine, phenylalanine, proline, serine, threonine, tryptophan, tyrosine, valine, etc.), carbohydrates (e.g., fucose, galactose, glucose, glucose-1-phosphate, lactose, mannose, raffinose, sucrose, xylose, etc.), organic acids (e.g., acetic acid, butyric acid and 2-hydroxy-butyric acid, 3-hydroxy-butyric acid, citric acid, formic acid, fumaric acid, isovaleric acid, lactic acid, maleic acid, propionic acid, pyruvic acid, succinic acid, etc.), and other organic compounds (e.g., acetone, ethanol, pyroglutamic acid, etc.).

[0064] Figure 2 schematically illustrates (A) a method for simulating a chromatographic process according to an embodiment of the present disclosure, and (B) a method for obtaining a trained machine learning model according to an embodiment of the present disclosure. Figure 3 Components used in methods for simulating chromatographic processes and / or training machine learning models according to this disclosure are illustrated. In an embodiment, the reference is performed. Figure 2A Described steps and references Figure 2B The steps described are both.

[0065] The method disclosed herein utilizes a hybrid physics-based chromatographic model, comprising a simple physics-based model of the mass balance equations confined to the overall flow of the liquid phase, and a machine learning model trained to predict the values ​​of phenomenological parameters of the physics-based model, which capture all binding kinetic details, diffusion effects, and any other interactions (e.g., all resin / membrane interactions, competitive binding, etc.).

[0066] As described above, chromatography is a process in which a feed stream containing one or more products passes through a chromatographic unit containing a stationary phase, which interacts with the stationary phase. The overall flow mass balance model is also referred to herein as a "mass balance model" or "column model." Figure 3As illustrated, solving the overall flow mass balance model along one or more discrete volumes of a chromatographic unit by numerical integration can be achieved through a mass balance module 20 implemented by a processor, which stores or accesses the mass balance model 20A and uses the numerical integration module 20B. Therefore, a method for simulating such a chromatographic process may include step 214 of solving (e.g., using the mass balance module 20B of the mass balance module) the overall flow mass balance model along one or more discrete volume elements of a chromatographic unit by numerical integration (e.g., using the mass balance module 200 implemented in the processor) (e.g., implemented in the mass balance model 20A stored in the mass balance module 20). The overall flow mass balance model is an ordinary differential equation model that represents the concentration changes of bound and unbound fractions of one or more products in the discrete volume elements. The ordinary differential equation model includes binding terms and diffusion terms, wherein the binding term captures the binding of the product with the stationary phase, and the diffusion term captures the diffusion of the bound product. These binding and diffusion terms are each parameterized by a single corresponding parameter, which is predicted by a machine learning model trained to take inputs including the concentrations of bound and unbound fractions of one or more products in a discrete volume element, and to produce predicted parameters for the binding and diffusion terms as outputs. Therefore, solving the overall flow mass balance model may include, at step 214A, using the machine learning module 22 implemented in the processor, storing or accessing the trained machine learning model, and using the trained machine learning model to predict the values ​​of the parameters for the diffusion and binding terms using inputs including the concentrations of bound and unbound fractions of one or more products in a discrete volume element. Solving the overall flow mass balance model may include using the machine learning module 22 implemented in the processor, storing or accessing the trained machine learning model, and using the trained machine learning model to predict the values ​​of the parameters for the diffusion and binding terms using inputs including the concentrations of bound and unbound fractions of one or more products in a discrete volume element. As will be understood by those skilled in the art, numerical integration is an iterative process, whereby the model integrates over subsequent discrete time intervals.

[0067] The above method advantageously utilizes a very simple physics-based model that represents the overall flow and the effects of binding and diffusion on the overall flow solely through phenomenological terms (i.e., terms that do not explicitly model the detailed physicochemical phenomena under the kinetics of product binding and the diffusion of bound products), combined with a data-driven phenomenological parameterized model to provide overall-level phenomenological parameters representing diffusion and binding. Unmodeled phenomena occur along multiple dimensions in different compartments of the chromatographic unit, such as in pores and on films on surfaces, and involve physicochemical processes that are not necessarily well characterized. The method of the present invention advantageously bypasses all of these, using machine learning algorithms to identify all dynamic behavioral components of the system that are difficult to explain by first principles. Advantageously, the method, which relies on differential volume elements and includes simple diffusion and binding terms as ODE captures, means that the model has the same architecture regardless of the geometry of the chromatographic unit. In other words, the model does not explicitly represent the diffusion geometry, and the same model can be used for columns with different geometries, thus enabling direct application to computer simulations for scale-up experiments. Furthermore, using ODEs on discrete volume elements means that simulations can be run without the need for adaptive step-size partial differential equation solvers. Therefore, the simulation is more stable and computationally efficient than existing methods. As those skilled in the art will understand, numerical integration is an iterative process, in which the model is integrated over subsequent discrete time intervals. Thus, solving the model may include iteratively evaluating (step 214B) the model over all discrete volumes at corresponding time intervals using the solution from the previous iteration, wherein the binding and diffusion parameters are evaluated at each iteration using a machine learning model and the concentration in the corresponding discrete volume element from the previous iteration. This can be achieved at each time point using the initial conditions of the first discrete volume of the column set by the observed concentration of the product (inert material, if used) received at step 210 and the known feed rate value (used in the model defined below) also received at step 210.

[0068] A chromatographic unit may include a single column. A chromatographic unit may include multiple columns connected in series, and simulating a chromatographic process may include connecting multiple instances of a global flow mass balance model, each instance corresponding to a corresponding column, such that the outlet concentration obtained by solving the global flow mass balance model of the first column among the multiple columns is used to set the inlet concentration for solving the global flow mass balance model of the second column among the multiple columns connected in series with the first column.

[0069] The overall flow mass balance model may include a linear term representing the flow of unbound compounds (products and optional inert substances) into and out of each discrete volume element, as well as a binding term and a diffusion term, wherein the binding term captures the nonlinearity of the adsorption process of unbound products on the static phase by the corresponding parameters of the term pre-defined by a machine learning model at each iteration of the numerical integration. The overall flow mass balance model may include the following equations (1) and (2) and optional equation (3):

[0070] Where f k It is the feed flow rate, and ΔV is the discrete volume element. n volume, It is the concentration vector of unbound products in the discrete volume element n. Discrete volume element n Concentration vector of the bound product, Discrete volume element n The concentration vector of unbound products in the previous discrete volume element, where the discrete volume elements are labeled sequentially from the input to the output of the chromatographic unit. Discrete volume element n The concentration vector of one or more inert substances. Discrete volume element n The concentration vector of inert material in the previous discrete volume element, and It is an element-wise product. In these equations, and This describes the overall effect of binding and diffusion on the overall concentration of each non-inert substance in a discrete volume at any given sampling time. Therefore, the overall flow mass balance model can also represent the concentration changes of one or more inert substances in a discrete volume element. In such implementations, the machine learning model input also includes the concentration of one or more inert substances in the discrete volume. The equations represent only three macroscopic phenomena along the discrete volume of the chromatographic unit: the flow of unbound products into and out of the volume (and optionally, the flow of inert substances into and out of the volume), the diffusion of bound products, and the binding of unbound products with the stationary phase. The latter two are represented by vectors. and The "overall" parameters are parameterized and computed as the output of the machine learning model. The overall flow mass balance model can be solved on N discrete volumetric elements (N is an integer), where N is a parameter of the chromatographic process simulation method, representing the granularity of modeling the chromatographic unit. N is at least 2, and can be between 5 and 20, between 5 and 15, or selected from 8, 9, 10, 11, and 12. The inventors have found that a value of N equal to approximately 10 provides good simulation accuracy, stability, and computational efficiency. The discrete volumetric elements can include multiple discrete volumetric elements along the chromatographic unit in which binding and diffusion occur, preceding a discrete volumetric element in which no binding or diffusion occurs (inlet dead volume) and following a discrete volumetric element in which no binding or diffusion occurs (outlet dead volume). Figure 6 An implementation scheme for this model is illustrated.

[0071] Therefore, more specifically, solving the overall flow mass balance model at step 214 may include iteratively integrating the modulus over multiple discrete time intervals of a predetermined duration, wherein at each iteration, predictions of the parameters of the binding and diffusion terms for each discrete volume element are obtained using a machine learning model (step 214A) and the current state vector, which includes the concentration of bound products in each discrete volume element at the most recent iteration, the concentration of unbound products in each discrete volume element at the most recent iteration, and optionally, the concentration of inert substances in each discrete volume element (if used) at the most recent iteration. The predictions of the parameters of the binding and diffusion terms may also use the feed rate (which may also be provided as input to the machine learning model), and any other input provided to the machine learning model, such as parameters indicating the service life of the column. At each iteration, at step 214B, the discrete state-space model is identified by using the overall flow mass balance model parameterized with the predictions, and an updated state vector corresponding to the time interval of the current iteration is determined using the values ​​of the current state vector and the coefficients of the discrete state-space model; these predictions are used to evaluate the mass balance model over the discrete volumes. For example, solving the overall flow mass balance model can include obtaining parameters from a machine learning model. and parameters The estimated value is used to revolve around the current state (by...) , , , (Definition) Linearize equations (1)-(3), use equation (4) to compute the discrete state-space model, and use the following equation (5) to update the state of one or more intervals: .

[0072] Calculating a discrete state-space model may include using equation (4) to calculate matrix A. d and B d In the implementation scheme, calculating the discrete state-space model may include reusing the discrete state-space model (e.g., A) calculated in the previous iteration when the difference between the coefficients of the linearized overall flow mass balance model in the current iteration and the coefficients of the linearized overall flow mass balance model in the previous iteration is within a predetermined range. d and B d The coefficients of ) can be used to improve the computational efficiency of this method by eliminating the need to recalculate the discrete state-space model at each iteration when the dynamics of the system do not change significantly between subsequent iterations.

[0073] Machine learning models can also measure feed flow rate f k As input, this advantageously means that the model (combining the mass balance model and the machine learning model) can capture the effect of flow velocity on the dynamics of binding and diffusion (via the machine learning model), thus allowing the same model to be used to simulate columns with different flow velocities. In fact, the hydrodynamic binding and diffusion effects can be learned from experimental data generated at different flow velocities, making the resulting trained model applicable to at least any range of flow velocities for which the training data (or training data with similar flow velocities) is available. Furthermore, due to the flow velocity variable f... k This variable is not used in the equations derived from first principles by the machine learning model, and therefore can be "transformed" by the user before being passed to the machine learning model. Thus, the method may optionally include obtaining the volumetric feed rate at step 210, converting the feed rate to linear velocity or residence time at step 212, and providing the converted feed rate as input to the machine learning model at step 214A. For example, while the mass balance model uses the volumetric flow rate, the flow rate can be converted to linear velocity or residence time before being provided as input to the machine learning model. This is expected to make the model less scale-dependent. This property is particularly advantageous for applications that wish to identify models from experiments conducted in small columns and use these models to make predictions for larger-scale (commercial manufacturing-related) columns.

[0074] In the implementation scheme, the machine learning model will also take parameters indicating the service life of the chromatographic unit as input. For example, the machine learning model can take as input the number of cycles the chromatographic unit has run, the total unit volume that has passed through the unit, or any other value derived therefrom (e.g., the percentage of the estimated lifetime as the number of cycles used by the chromatographic unit relative to the expected number of cycles in the column lifetime). This advantageously enables the machine learning model to accurately capture the effect of aging columns on the kinetics of the chromatographic process.

[0075] The machine learning model can be a recurrent machine learning model, which is a machine learning model that is able to consider one or more predictions made in one or more previous iterations of the numerical integral when making a prediction at the current iteration of the numerical integral. For example, the machine learning model can be one that further includes the current iteration. k and discrete volume element n A cyclic state vector of one or more state values As input, and to produce an updated loop state vector This output is used in subsequent iterations. The inventors have discovered that a single state value for each discrete volume element is sufficient for a machine learning model to capture the kinetics of binding and diffusion during chromatography. Therefore, the cyclic state vector... It can include the current iteration k Each discrete volume element n A single state value. For example... Figure 3 As illustrated, the machine learning model may include a parameter prediction sub-model 22B and a recurrent state sub-model 22A (both of which can be executed by the machine learning module). The recurrent state sub-model is configured (i.e. trained) to predict updated recurrent state vectors based on the inputs to the machine learning model. For use in subsequent iterations, the parameter prediction submodel is configured (i.e., trained) to predict the parameters of the binding and diffusion terms based on the input of the machine learning model. The cyclic state vector can be cascaded with other input variables (concentrations of bound and unbound products, feed rate, and concentration of inert substances, if used). Before being used as input to the machine learning model, the cyclic state vector can be transformed using any function (such as a tanh or sigmoid function) configured to produce bounded values ​​from unbounded values. This advantageously ensures that the state values ​​do not dominate other input variables. In embodiments including both the parameter prediction submodel and the cyclic state submodel, cascaded inputs can be fed into both. The parameter prediction submodel 22B is configured (i.e., trained) to provide vectors. and Predictions, so that in the current iteration k Used for concentration , , Flow velocity f k and the current state vector Each associated volume n (Right now and At each iteration, the concentration , , By applying the model provided by equations (1)-(3) (which itself uses the previous iteration from the machine learning model) and The predicted parameters are obtained by integration. Furthermore, at each iteration, the machine learning model, as illustrated, outputs an updated state vector for use in the next iteration.

[0076] The recurrent state submodel and the parameter prediction submodel can be parameterized using corresponding weights learned simultaneously. The trained machine learning model can be associated with the same learned weights for each iteration of each discrete volume element and numerical integral. The recurrent state submodel 22A may include a first branch and a second branch, the first branch including taking the cascaded input and applying the learned weight vector. The first activation function node, and the second branch includes taking the cascaded input and applying the learned weight vector. The node contains the second activation function. Both activation functions can be functions configured to produce bounded outputs from unbounded inputs. The first activation function (in the first branch) can be configured to produce an output (α) limited to between 0 and 1. For example, the first activation function could be the sigmoid function. The first branch may also include a node that stores the loop state vector of the current iteration of the numerical integration. The output of the first activation function is used as input, and a loop state vector based on the output of the first activation function is generated. The first activation function produces a weighted output (e.g., weighted by 1-α). The second activation function produces an output that can be interpreted as a new proposed value for the recurrent state vector. The first activation function produces an output that can be interpreted as a "forgetting factor." The second branch may also include nodes that take the outputs of the first and second activation functions as inputs and produce an output that weights the output of the second activation function based on the output of the first activation function (e.g., weighted by α). The outputs of the first and second branches can be summed to produce the output of the recurrent state submodel. This output can be interpreted as a recurrent state vector. The current value and the loop state vector The weighted average of the new suggested values, where the current value and the new suggested value are weighted by (1-α) and α respectively (i.e., based on the forgetting factor). Figure 7 An implementation scheme for this machine learning model is illustrated.

[0077] The machine learning model can be a nonlinear regression model. The machine learning model can include a neural network, which can be fully connected and can include any number of layers. In embodiments, the neural network includes at least two hidden layers, one to four hidden layers, or two or three hidden layers. In embodiments, the neural network includes eight to 60 nodes in each hidden layer. For example, the neural network can include one to four hidden layers, each with eight to 60 nodes, such as two or three hidden layers, each with at least 10 nodes. For example, the neural network can include two hidden layers, each with approximately 20 nodes. The neural network can additionally include multiple input nodes (one for each input) and multiple output nodes (one for each output). Each output node can each include an activation function, which is a function configured to produce a bounded output from an unbounded input, such as a tanh or sigmoid function. This function can be a smoothing function (e.g., not a step function). The neural network can consist of the input nodes, output nodes, and hidden layers described above. Note that trained machine learning models are typically specific to a particular stationary phase and product (and inert substance, if used), but are applicable to any column size, configuration, product concentration (and inert substance concentration, if used), and feed rate (although it is advantageous for the product / inert substance concentration and feed rate used for simulation to be within the range of values ​​available in the training data, or at a certain distance from those values, such as within 50% of those values, as this may improve the accuracy of the resulting predictions).

[0078] As those skilled in the art will understand, solving the overall flow mass balance model along one or more discrete volume elements of a chromatographic unit by numerical integration involves integrating the model over each of the one or more discrete volume elements at multiple discrete time points to obtain simulation data (also known as a trajectory), which includes the concentration of the product in the effluent of the chromatographic unit at multiple discrete time points. In embodiments, the method may further include, at step 216, using the simulation data to determine one or more of the following: effluent product concentrations, product adsorption rates, product desorption rates, total product capture, dynamic binding capacity of the chromatographic process with respect to the product, product binding capacity per cycle, product recovery percentage, maximum breakthrough concentration of the product, maximum breakthrough percentage of the product, and costs associated with the simulated chromatographic process. Specifically, the method may include using simulation data of the chromatographic process to determine costs associated with the process using an economic model that considers one or more of the following: costs associated with regeneration of the chromatographic unit, costs associated with buffer solutions consumed during the chromatographic process, costs of waste generated during the chromatographic process, and benefits associated with the amount of product recovered. This method may include providing any values ​​obtained at steps 214 or 216 to a user, for example, through a user interface, or to a controller or computing device associated with the chromatographic unit or an upstream process that supplies feed to the chromatographic unit. The method may include (e.g., at step 216) determining the effluent product concentrations of multiple simulated fractions using simulation data and a predetermined fractionation scheme. This can be used when deploying methods for simulation and when training machine learning models using simulations when the training data includes concentration data associated with a time range during the chromatographic process (i.e., data collected using a fraction collector and a known fractionation scheme).

[0079] A method for providing a trained machine learning model (which may be performed prior to step 214) may include step 411 of obtaining training data, and step 413 of training the machine learning model using the training data, which includes feed concentration data and effluent concentration data from multiple chromatographic processes. Alternatively, see reference to Figure 2AThe described method may include receiving a previously trained model, wherein the machine learning model has been trained using training data including feed concentration data and effluent concentration data from multiple chromatographic processes. Feed concentration data is data indicating the inlet product concentration, and effluent concentration data is data indicating the outlet product concentration. Training data may include feed concentration data and effluent concentration data, each associated with a corresponding discrete time point during the chromatographic process and / or feed concentration data and effluent concentration data associated with a time range during the chromatographic process, such as data collected using a fraction collector. Training data also includes feed flow rate data. This may be volumetric flow rate, linear velocity, or residence time, and conversion between any of these (e.g., providing a volumetric flow rate for use by a mass balance model and any selected rate for use by a machine learning model) may also be performed at optional step 212, as per [reference to step 212]. Figure 2AAs explained in step 212. Training data may include data indicating the concentration of one or more products (and optionally one or more inert substances) in the effluent of the chromatographic unit. This may be referred to as effluent concentration data or effluent concentration data. This data may include time-resolved concentrations (e.g., from an online sensor) and fractionated effluent concentrations. Training data may include data indicating the concentration of one or more products (and optionally one or more inert substances) in the feed of the chromatographic unit. This may be referred to as inlet concentration data or feed concentration data. Each such data is typically in the form of multiple concentrations or information indicating concentration changes over time. Therefore, they may also be referred to as trajectories. Data indicating the concentration of one or more products in the effluent of the chromatographic unit may be in the form of one or more breakthrough curves, which include time-resolved concentrations of the products in the effluent of the chromatographic unit, i.e., a dataset of product concentration changes in the effluent over time. Training data may include data collected using the same stationary phase for the same product, optionally the same buffer (i.e., the same mobile phase), at multiple sets of process parameters including feed flow rate and feed concentration. Training data may include data collected at multiple feed flow rates. Training data may include multiple replicates of at least one set of process parameters. Training data may include fractional concentration data, i.e., effluent concentration data points, each associated with a corresponding time range during a chromatographic process. In such cases, effluent concentration data may include multiple effluent concentration data points for each chromatographic process in the training data. For example, for each chromatographic process, the training data may include at least five, ten, or more effluent concentration data points associated with a corresponding time point or time range. As understood by those skilled in the art, in embodiments where the machine learning model takes feed flow rate and / or any other input (such as a parameter indicating the service life of the chromatographic unit) as input, this data is typically also part of the training data for each set of concentration data determined by each experiment. Therefore, the method may include, at step 213, using a processor-implemented training module 28 to train a machine learning model using training data including effluent product concentration data from multiple chromatographic processes. Training module 28 may obtain training data from data storage device 26 and use the training data to train a machine learning model (e.g., including a cyclic state sub-model 22A and a parameter prediction sub-model 22B) stored in machine learning module 22. At step 411, training data may be obtained from sensor 24 or from a user interface. Training module 28 can communicate with mass balancing module 20 to solve mass balancing model 20A using predictions from machine learning module 22 via numerical integration module 20B. Simulation data obtained through this process can be used by training module 28 to update the weights of machine learning model 22 using simulation data obtained from data source 26 and corresponding training data.

[0080] Training the machine learning model may include, at step 213B, solving the overall flow mass balance model using the values ​​of the parameters of the binding and diffusion terms predicted by the machine learning model at the previous iteration of training over discrete time intervals corresponding to the multiple time points from the training dataset, for each of one or more training datasets, each including feed concentration data, effluent concentration data, and feed flow rate data corresponding to multiple time points during the chromatographic process. This is done for each of the one or more training datasets, where the feed rate trajectory corresponds to the feed flow rate data and feed concentration data from the training datasets, thereby obtaining simulated data corresponding to each of the one or more training datasets. This can be as described above regarding... Figure 2A The process can be performed as explained in step 214. Training the machine learning model may include, at step 213C, evaluating a loss function that quantifies the difference between the simulated data and one or more corresponding training datasets. Training the machine learning model may also include, at step 213D, optionally using a gradient descent procedure to update the weights of the machine learning model based on the weights of the machine learning model at the current iteration and the value of the loss function, until one or more predetermined stopping criteria are met. One or more predetermined stopping criteria may be applied to the number of iterations, the value of the loss function, and / or the difference between the updated weights and the weights of the current iteration. The iterative training process may begin with default weights, random weights, weights from a previously trained model (e.g., for similar chromatographic processes, such as similar products, inert substances, and / or mobile phases), or weights initialized using a “warm-start” procedure, as will now be described.

[0081] The “warm start” procedure, also known as “pre-training,” sets the weights of the machine learning model to promising starting values ​​for training the model, thereby improving the computational efficiency of the training process and increasing the likelihood that the training process will converge to a suitable solution. In an implementation, training the machine learning model may include: during the first iteration of the iterative training, setting the weights of the machine learning model (step 213A) to initial weights corresponding to predetermined values ​​of the parameters of the combination and diffusion terms. Setting the weights of the machine learning model to the initial weights may include: obtaining the predetermined values ​​of the parameters of the combination and diffusion terms (step 213A-1), setting the weights of the machine learning model to default values ​​(step 213A-2), and pre-training the machine learning model (step 413A-3) using a loss function based on the difference between the predicted values ​​from the model and the predetermined values ​​of the parameters of the combination and diffusion terms. Specifically, the pre-training may include iteratively updating the weights of the machine learning model by: using the machine learning model, using inputs from the machine learning model sampled from the training data to predict the values ​​of the parameters of the combination and diffusion terms, evaluating a loss function that quantifies the difference between the predicted values ​​of the parameters of the combination and diffusion terms and their predetermined values; and updating the weights of the machine learning model based on the weights of the machine learning model and the values ​​of the loss function at the current pre-training iteration. Advantageously, this method increases the chance of model training convergence compared to random weights or other uninformative weight initialization procedures. This is particularly important in the current context because machine learning models capture complex dynamic phenomena, and improper parameterization can lead to instability in the solution of the mass balancing module, which in some cases can prevent the entire training method from converging.

[0082] Step 213A-1, which obtains predetermined values ​​for the parameters of the binding and diffusion terms, may include one or both of the following processes. In a first process, the predetermined values ​​may be obtained by: (i) setting the values ​​of the parameters of the diffusion and binding terms, or the corresponding parameters associated with the corresponding nonlinear binding terms, to their respective default values; (ii) using these default values, along with predetermined feed concentration and feed rate data, to solve the overall flow mass balance model by numerical integration, optionally wherein the predetermined feed concentration and feed rate data are selected as the maximum values ​​of feed rate and feed concentration observed in the training data; (iii) determining whether the numerical integration has failed to compute any solution to the model; and (iv) when the numerical integration has failed to compute any solution to the model, updating the default values ​​for the parameters of the binding and diffusion terms by reducing the default values ​​by a predetermined factor. The above steps may be repeated until an iteration of numerical integration is able to compute all solutions to the model, and the values ​​of the parameters of the binding and diffusion terms are selected as those values ​​used in the iteration. In a second process, which may be performed after or in place of the first process, predetermined values ​​may be obtained by: (i) setting the values ​​of the parameters of the diffusion term and the parameters of the binding term, or the corresponding parameters associated with the corresponding nonlinear binding term, to their respective default values ​​(e.g., using the default values ​​obtained in the first process described above); (ii) for each of one or more training datasets, each comprising feed concentration data, effluent concentration data, and feed flow rate data corresponding to multiple time points during the chromatographic process, solving the overall flow mass balance model using the default values ​​of the parameters of the binding and diffusion terms, thereby obtaining simulated data corresponding to each of the one or more training datasets; (iii) evaluating a loss function that quantifies the difference between the simulated data and the corresponding one or more training datasets; and (iv) optionally using a gradient descent procedure to update the default values ​​of the parameters of the binding and diffusion terms based on the value of the loss function. The above steps may be repeated until one or more predetermined stopping criteria are met. Advantageously, each of the first and second processes described above increases the chance of convergence of the training process. Specifically, the first process ensures that the pre-training of the model is based on the values ​​of the parameters of the binding and diffusion terms that are unlikely to cause numerical instability when solving the overall flow mass balance model. The second process ensures that the model's pre-training is based on the parameter values ​​of the combination and diffusion terms, provided by the data during computationally efficient training, before initiating the more computationally demanding training of the machine learning model. The parameters of the diffusion term can be represented as... And it can be a corresponding parameter. The linearized version is calculated as ,in These are the corresponding parameters associated with the corresponding nonlinear associative terms (where the corresponding nonlinear associative terms are...). ),and This is the total associative capacity of the columns (also known as the static associative capacity of the columns). Therefore, the corresponding linear associative term is... The value can also be set to a default value, which can be identified using the same process explained above. As understood by those skilled in the art, references to "diffusion term," "binding term," and "flow term" refer to multiple terms because a separate equation is evaluated for each discrete volume element n, and because multiple products and optionally multiple inert substances can exist. However, for a single product in a single discrete volume element, there will typically be a single diffusion term, a single binding term, and a single flow term (although the same binding term may appear with different signs in the equations for the bound and unbound fractions of the product).

[0083] Figure 4 Methods for monitoring a chromatographic process, optimizing a chromatographic process, and controlling a chromatographic process according to embodiments of the present disclosure are illustrated schematically.

[0084] Methods for monitoring chromatographic processes may include step 400, using methods as described herein (e.g., via a reference). Figure 2A The method simulates the chromatographic process by using feed concentration data and feed flow rate data corresponding to the measured or planned feed concentration and feed flow rate of the chromatographic process, thereby obtaining a simulated effluent concentration corresponding to the effluent concentration of the chromatographic process. This method may also include step 402, comparing the simulated effluent concentration or one or more indicators derived therefrom with the observed effluent concentration or corresponding indicators derived therefrom, wherein the comparison indicates the presence of a malfunction or aging condition of the chromatographic unit. Therefore, at optional step 404, the result of the comparison can be used to determine whether a malfunction or aging condition exists, for example, when the simulated effluent concentration or one or more indicators derived therefrom differ from the observed effluent concentration or corresponding indicator derived therefrom by more than a predetermined threshold, or when the difference increases by more than a predetermined threshold within a predetermined time period. At optional step 406, control actions can be implemented based on the determined result. For example, when a malfunction or aging condition is determined to exist, the chromatographic process can be interrupted or the feed can be redirected to another column.

[0085] Methods for controlling a chromatographic process may include step 400, using methods as described herein (e.g., by reference). Figure 2AThe method simulates the chromatographic process by using feed concentration data and feed flow rate data corresponding to the measured or planned feed concentration and feed flow rate of the chromatographic process, thereby obtaining a simulated effluent concentration corresponding to the effluent concentration of the chromatographic process. This method may also include step 402, comparing the simulated effluent concentration or one or more indicators derived therefrom with the observed effluent concentration or its derived counterpart, and step 414, determining, based on the comparison result, whether to repack the chromatographic unit or whether to switch the feed to a different column in a multi-column chromatography process. For example, when the simulated effluent concentration or one or more indicators derived therefrom differ from the observed effluent concentration or its corresponding derived indicator by more than a predetermined threshold, or when the difference increases by more than a predetermined threshold within a predetermined time period, the method may determine that the column (e.g., a single-column chromatographic unit) should be repacked or the feed should be switched to another column (e.g., a multi-column chromatographic unit). This method may also include optional step 416, implementing the identified control action (e.g., repacking the column or switching the feed to another column).

[0086] Methods for controlling a chromatographic process may include step 400, using methods as described herein (e.g., by reference). Figure 2A The method simulates a chromatographic process using multiple candidate sets of process parameters, each including at least a feed product concentration and a feed flow rate, to obtain simulated effluent concentrations for each candidate set of process parameters. This method may further include step 422, comparing the simulated effluent concentrations or one or more indices derived therefrom to select a set of process parameters from the set of candidate process parameters for operating the chromatographic process. The candidate set of process parameters may include expected feed product concentrations or feed flows (e.g., which may be anticipated based on current operating plans or current or planned operations of upstream processes supplying feed to the chromatographic process). The method may further include step 424, selecting one set of candidate process parameters based on the comparison results (e.g., an optimal set using one or more optimality criteria applied to simulated effluent data or indices derived therefrom). The method may further include operating the chromatographic unit with the selected set of parameters at step 426. Note that simulating a chromatographic process can include using different sets of candidate parameters to simulate the chromatographic process, including using models associated with different chromatographic units (e.g., units with different stationary phases, buffers, physical configurations, etc.), and therefore, selecting / operating a chromatographic unit with a selected set of parameters can include operating different chromatographic units according to the selected set of parameters.

[0087] The methods disclosed herein can be applied to a wide range of scenarios, including process development, column health modeling, and advanced control. For example, in process development, these methods can be used to design transitions from batch to continuous chromatography with a lower experimental burden than previously possible (e.g., computer-simulated formulation design for multi-column operations from batch breakthrough experiments, and robustness testing for connected continuous processes). As another example, these methods can be used to scale up processes, for instance, by enabling the prediction of large-scale binding capacities from small-scale trials and enabling formulation design for large-scale continuous chromatography based on development-scale equipment. In production, these methods can be used for column health modeling, enabling the comparison of digital twin predictions with real-time performance and labeling deviations from expectations, and capturing and quantifying inter-column variations during / after column changes. Still in production, these methods can enable advanced control by automatically adapting multi-column processes to changes in feedstock (predicted or measured), and, particularly, real-time economic optimization of column use in multi-column setups.

[0088] Figure 5 An embodiment of a system for implementing the methods of this disclosure is shown. The system includes a computing device 1, which includes a processor 101 and a computer-readable storage 102. In the illustrated embodiment, the computing device 1 also includes a user interface 103, exemplified as a screen, but may include any other means of conveying information to the user, for example, by printing or emitting auditory or visual signals. The computing device 1 may be operatively connected, for example, via a network 6 or a wired connection, to one or more sensors 3 (e.g., sensors associated with the feed flow or effluent of a chromatography unit) and / or to a chromatography unit 2 (e.g., such as...). Figure 1 One or more effectors 4 (e.g., flow control systems) associated with the illustrated unit 12). The computing device 1 may be a smartphone, tablet, personal computer, or other computing device. The computing device 1 is configured to implement methods for simulating chromatographic processes and / or for training chromatographic process simulation models and / or for monitoring chromatographic processes, as described herein. In alternative embodiments, the computing device 1 is configured to implement a portion of the methods for simulating or monitoring chromatographic processes and / or training models as described herein, and to communicate with a remote computing device (not shown) to implement other portions of the methods for simulating or monitoring chromatographic processes and / or training models as described herein. For example, the computing device 1 may be a distributed control unit and may be associated with implementing... Figure 3The illustrated mass balance module 20, machine learning module 22, and training module 28 communicate with a remote computing device. Communication between the computing device 1 and the remote computing device can be via a wired or wireless connection, and can be via a local or public network (e.g., via the public Internet). Each of the sensor 3 and optional effector 4 can be wired to the computing device 1 (or the remote computing device, if present), or can communicate wirelessly (i.e., via network 6), such as via WiFi, as illustrated. The connection between the computing device 1 and the effector 4 and sensor 3 can be direct or indirect (e.g., via a remote computer). One or more sensors 3 can each be an online sensor (sometimes also called a "built-in sensor") that automatically and continuously measures the properties of the chromatographic effluent, or an offline sensor (for offline sensors, a sample of the effluent, also called a "fraction," is obtained manually or automatically and subsequently processed to obtain a measurement). Each measurement from the sensor (or a quantity derived from such a measurement) represents a data point associated with a time value (or a time range for fractions). One or more sensors typically include one or more sensors that measure the concentration of one or more biological products in the effluent (including, for example, target products, biological products that are contaminants for the production of biological products but are referred to as products in the context of chromatographic modeling because they also interact with the chromatographic stationary phase, and biological products that are contaminants for the production of biological products but are referred to as inert substances in the context of chromatographic modeling because they do not interact with the chromatographic stationary phase). Examples of such sensors are known in the art and include NMR spectrometers, mass spectrometers, enzyme-based sensors, spectrophotometric sensors, etc.

[0089] As used herein, sensor 3 can also refer to a system that estimates the concentration of metabolites or the amount of biomass based on one or more measured variables (e.g., provided by other sensors). For example, a metabolite sensor may be implemented in practice as a processor (e.g., processor 101) that receives information from one or more sensors (e.g., measuring the physical / chemical properties of the system) and uses one or more mathematical models to estimate the concentration of bioproducts based on that information. For example, a product sensor may be implemented as a processor that receives spectra from a near-infrared spectrometer and estimates the concentration of one or more products based on those spectra. Such sensors may be referred to as “soft sensors” (by referring to their “measurements” obtained using software rather than by direct measurement). One or more sensors 3 may also include one or more sensors that measure other process conditions (such as pH, flow rate, temperature, etc.). Such sensors are known in the art. Measurements from sensor 3 are transmitted to computing device 1, which may store the data permanently or temporarily in memory 102. Computing device memory 102 may store one or more training models as described herein. Processor 101 may execute instructions to train the models, thereby using these models and data from one or more sensors 3 to simulate chromatographic processes as described herein. Note that this does not require direct interaction with sensor 3, chromatographic unit 3, or effector 4. Instead, data from these components may have been previously collected (including data that may have been collected at different times using different sensors, chromatographic units, and effectors) and stored in any memory, then acquired by computing device 1 and stored in memory 102 for model training by processor 102. Processor 101 can execute instructions to simulate the chromatographic process using the previously trained model. Processor 101 can also execute instructions to compare the simulation results with measurements received from sensor 3 to identify malfunctions or aging of the chromatographic unit. In such embodiments, processor 101 can receive data from sensor 3 in a continuous or periodic manner.

[0090] As used herein, the term "computer system" includes hardware, software, and data storage devices for embodying a system or performing methods according to the embodiments described above. For example, a computer system may include one or more processing units (processors), such as a central processing unit (CPU) and / or a graphics processing unit (GPU), input devices, output devices, and data storage devices, which may be embodied as one or more connected computing devices. Preferably, the computer system has a display or includes a computing device with a display to provide visual output display (e.g., in the design of business processes). Data storage devices may include RAM, disk drives, or other computer-readable media. A computer system may include multiple computing devices connected via a network and capable of communicating with each other through the network. For example, a computer system may be implemented as a cloud computer. Therefore, the processor may be a network server.

[0091] The methods described herein may be provided as a computer program, a computer program product, or a computer-readable medium carrying a computer program configured to perform the methods described herein when run on a computer. The term "computer-readable medium" includes, but is not limited to, any one or more non-transitory media that can be directly read and accessed by a computer or computer system. Media may include, but is not limited to, magnetic storage media such as floppy disks, hard disk storage media, and magnetic tape; optical storage media such as optical discs or CD-ROMs; electrical storage media such as memory, including RAM, ROM, and flash memory; and mixtures and combinations of the foregoing, such as magnetic / optical storage media.

[0092] The methods and systems described in this paper offer numerous advantages. They do not require a detailed understanding of the physicochemical mechanisms influencing the behavior of chromatographic processes. These are often difficult to obtain at best (requiring expertise and extensive experimentation), and sometimes impossible. For example, it is often unclear how to model the effects of impurity profiles on column performance (e.g., host cell proteins, DNA, aggregates). This method does not require such detailed understanding; instead, it captures all the processes that actually influence the behavior of the chromatographic process through machine learning predictions of the phenomenological parameters of a mass balance model. Furthermore, this method does not require extensive experimentation because the model is easy to train even with limited data, and the trained model is applicable to columns of any geometry using the same stationary and mobile phases. Additionally, this method is flexible in utilizing historical experimental data and can be adapted to fractionated data or a combination of online and fractionated data. This method is also highly computationally efficient (compared, of course, to fully generalized rate models) while being able to account for competing binding and diffusion.

[0093] Narayanan et al. (2021) described a hybrid modeling approach where the behavior of chromatographic units is learned through a combination of neural networks and mechanical models, while fitting a suitable experimental breakthrough curve. The method described there differs from our approach in several ways. First, the mechanical model used is not a simple mass balance model and still retains much of the complexity of the physics in the column. In other words, the authors did not significantly reduce the complexity of the physical model and only reduced the experimental burden of parameterizing it through machine learning. At least in part for this reason, the authors struggled to stabilize their training algorithm. In their conclusions, they noted that the training time was cumbersome and gradient descent did not always converge. The different model architecture and associated improved solver proposed in this work address these issues. Furthermore, Narayanan et al.'s work explicitly neglected diffusion. In contrast, the model developed in this work accurately accounts for diffusion, especially when using the proposed recurrent machine learning model. Additionally, the use of recurrent machine learning in the implementation of this disclosure allows the method to be used with coarse spatial discretization, further reducing model complexity and improving the computational efficiency and stability of the method.

[0094] Example Exemplary methods for simulating chromatographic processes and the use of such simulations in chromatographic process optimization will now be described.

[0095] Example 1 – General Chromatography Model introduction The inventors set out to address problems associated with state-of-the-art chromatographic modeling methods that are based on first principles of controlling mass transfer (i.e., capture convection, diffusion through stagnant membranes, diffusion in pores, etc.), are numerically unstable due to stiffness-related issues in partial differential equations, require parameterization from detailed experiments, and necessitate modeling experts to adjust the model for each chromatographic process.

[0096] They developed a chromatographic modeling framework that uses a hybrid approach combining machine learning algorithms (neural networks exemplified here) and physical derivation equations to provide robust predictions. This method can be used directly by chromatography practitioners rather than modeling experts (as it does not require detailed knowledge of the physicochemical phenomena that may affect the chromatographic process), has minimal data requirements, is computationally efficient, easily integrates with models of other unit operations, and is applicable to resins, membranes, and monolithic columns without user modification.

[0097] This new approach is particularly useful in facilitating the transition from batch to continuous processing, for example, by enabling the design of continuous chromatographic formulations based on batch data and the optimization of continuous chromatographic conditions to demonstrate the value of continuous processing without the need for lengthy and costly experimental trials. It is also particularly useful in reducing expensive process development experiments at manufacturing scale, for example, by reducing the number of experiments required in process scale-up, and in decoupling dependence on upstream process development and enabling large-scale process development of advanced columns such as membrane and monolithic columns. Furthermore, this new approach is particularly useful in the context of risk mitigation / column health monitoring, where digital twins of columns can be run to enable early detection of column failures, aid in root cause analysis of deviations, and allow for longer intervals between column repackings (through health monitoring). In addition, this new approach is particularly useful for chromatographic process optimization, including economic optimization. In fact, since the same method can be used to model chromatographic processes under a wide range of operating conditions, costs associated with different conditions can be simulated to optimize the economics of bioproduction processes (e.g., cost per unit of recovered product).

[0098] Overview of the General Chromatography Model Framework The method described in this paper combines a machine learning model for predicting intensive (volume-independent) processes with a simple physical model for capturing process scales. The architecture of both parts of the model is independent of column size or type of stationary phase (binding phase), meaning the same architecture can be used for membranes, monolithic columns, and resins.

[0099] This method requires a minimal amount of experimental data; the only data needed is for training the machine learning model, limited to breakthrough data (i.e., data on the change in adsorbate concentration in the column effluent over time, including at least the desired product, although the model can also account for inert substances—i.e., any other compounds in the feed that might affect the interaction between the product and the column). Note that this method can even replace time-resolved breakthrough data or utilize fractionated breakthrough data as a supplement to time-resolved breakthrough data. This is particularly useful because, in many cases, detailed concentration information (especially for compounds other than the specific desired product of the process, such as any host protein or other contaminants) is only available for fractions of the collected effluent, as these are collected offline.

[0100] This method is capable of capturing complex interactions, is easy to use, computationally efficient (sub-second execution), and applicable to poorly understood processes (such as advanced therapies) where accurate first-principles models are simply unavailable.

[0101] The proposed method combines a physical-based element (i.e., mass balance) for overall flow with a novel neural network architecture for binding and diffusion, such as... Figure 3As illustrated, a mass balance module 20 implementing a physics-based global flow differential equation model (note that this is an ordinary differential equation (ODE) model, not a partial differential equation (PDE) model) and a machine learning module 22 implementing a machine learning model are used to provide parameter estimates used by the mass balance module in the physics-based model. Figure 6 A discretization scheme for describing a general chromatographic column is shown. Note that the same architecture is used regardless of the column geometry because the focus is on the differential volume element, and the model does not explicitly model the diffusion geometry. Figure 6 The complete chromatographic column is schematically illustrated on the left, and the corresponding "stage" (also called a differential volume element) represented in the model is schematically illustrated on the right. The process receives a flow rate f... k The feed. Popular feed through a volume V 入口 The inlet dead volume is the volume through which the mobile phase travels past the outside of the column (i.e., before interacting with the stationary phase inside the column). The flow then proceeds through a series of consecutive volumes labeled ΔV, from stage 1 to N. (Note that in this example, for simplicity, it is assumed that all volumes ΔV are the same, but in reality, the volumes can differ depending on the stage; in this case, ΔV can be indexed by the stage number n, i.e., ΔVn). n —In the equations provided below, ΔV is the volume of stage n, which can also be written as ΔV n The product interacts with the stationary phase. Finally, the stream flows through a volume V 出口 The outlet dead volume is the volume of the mobile phase traveling through the outside of the column (i.e., after interacting with the stationary phase inside the column). The mass balance of the discrete volume elements controlling the entire column (stages 1 to N) is given by equations (1) to (3):

[0102] Where f k ΔV is the feed flow rate, and ΔV is the volume at each stage. It is the concentration vector of unbound products in stage n (i.e., each element of the vector is the concentration of unbound products in the current stage, i.e., the nth volume element). It is the concentration vector of the binding product in stage n (that is, each element of the vector is the concentration of the binding product in the current stage, i.e., the nth volume element). It is a vector of unbound product concentrations in stages prior to stage n (i.e., each element of the vector is the concentration of unbound products flowing into the current stage, i.e., the nth volume element). It is the concentration vector of inert substances in stage n (that is, each element of the vector is the concentration of inert substances in the current stage, i.e., the nth volume element). It is the concentration vector of inert material in the stages prior to stage n (i.e., each element of the vector is the concentration of inert material flowing into the current stage, i.e., the nth volume element), and This represents the Hadamard product (element-by-element product). In these equations, and The overall effect of binding and diffusion on the overall concentration of each non-inert substance in a discrete volume is described at any given sampling time. Figure 9B shows the complete set of equations expanded at all stages.

[0103] Note that the term “product” here refers to any molecule that interacts with the stationary phase. Typically, this is the desired product to be purified, but within the same framework, other molecules that are not the desired product but can also interact with the stationary phase to some extent (e.g., impurities) may also be included. This contrasts with “inert substance,” which is any compound that does not directly interact with the stationary phase, but whose presence affects the interaction between the product and the stationary phase. In this model, the representation of inert substance (Equation (3)) is optional. For example, in cases where the concentration of inert substance is unknown (i.e., there is no concentration of inert substance available for training the model) and / or the inert substance is not considered to substantially affect the behavior of the product, the model may use only Equations (1) and (2).

[0104] In the inlet and outlet dead volumes, all concentrations remain constant—volumes are considered to accurately reflect the observed time delays, which are proportional to the feed flow rate and inversely proportional to the inlet and outlet dead volumes. The inlet and outlet dead volumes also help ensure the numerical stability of the solution, as no abrupt changes in concentration can be directly provided to column kinetics, since all changes in concentration set by the user occur at the inlet (before the inlet dead volume) and at the outlet (after the outlet dead volume). Abrupt changes can produce large gradients, making discretization less accurate. Including the inlet and outlet dead volumes accurately reflects the actual state of the system (since it is impossible to construct a physical chromatography system with zero dead volume), and therefore including them in the model is both accurate and helpful for numerical integration.

[0105] vector and The values ​​in the equations are phenomenological parameters that describe the overall effect of binding and diffusion on the overall concentration of each non-inert substance in a discrete volume at any given sampling time. These can capture many different physicochemical processes that are not explicitly modeled but contribute to the overall (i.e., the observed overall level) concentration through kinetics, which manifest at the overall level as binding (i.e., the equilibrium between the overall bound and unbound products) and diffusion (i.e., the movement of bound products). In other words, the above equations represent only three macroscopic phenomena in a discrete volume along a column: the flow of unbound products in and out of the volume (and the flow of optional inert substances in and out of the volume), the diffusion of bound products, and the binding of unbound products with the stationary phase. The latter two are represented by vectors. and The "overall" parameter is parameterized. These vectors are computed as the output of the machine learning model, which will be described below.

[0106] As will be explained further below, the assumed parameters The corresponding parameter The linearized version is calculated as ,in This is the total bond capacity of the column (also known as the static bond capacity of the column). Parameter Following the traditional second-order rate law form (the Langmuir adsorption isotherm, which is commonly used for modeling chromatography), the overall combination of equations (1) and (2) can be expressed as: ,in This describes a relationship that depends on the number of unbound binding sites ( ) and the number of unbound molecules ( This follows the Langmuir adsorption model. The equations above use... And as the output of a machine learning model, it means we can use it As a parameter removal from the pillar model, this helps improve the stability of machine learning model training. Essentially, this makes the machine learning model responsible for considering the nonlinearities in the Langmuir model (since its task is to predict parameters that capture nonlinear phenomena). This parameter is used for linear equations (1) and (2) (as will be explained further below). and The relationship between them is only used during the pre-training of the machine learning model, because all subsequent training and prediction only use them. .

[0107] The number of stages N is unlimited, and any number of stages can be used. In practice, there is a balance between accuracy, stability, and computational efficiency. A higher number of stages results in a higher resolution of the physical (mass flow) model and a lower burden on the machine learning model to accurately capture complex dynamics, but also a higher likelihood of numerical integration encountering instability due to the stiffness of gradients within small volumes. Therefore, a higher number of stages increases the computational burden of running the model, but decreases the computational burden (and training data requirements) of training the machine learning model. Conversely, a lower number of stages results in a lower resolution of the physical (mass flow) model, a higher burden on the machine learning model to accurately capture complex dynamics (because accurate capture of the overall system dynamics is more derived from the physical model to the machine learning model), and a lower likelihood of numerical integration instability. Similarly, a lower number of stages decreases the computational burden of running the model, but increases the computational burden (and training data requirements) of training the machine learning model. While a higher number of stages is expected to lead to more accurate predictions, the inventors have found that very accurate results can still be obtained with a very small number of stages. This fewer stages reduces the risk of numerical problems due to very small gradients as the ΔV value decreases, and improves the robustness of the predictions (avoiding overfitting of the machine learning model, as the same model is used to predict the binding and diffusion coefficients in each stage, as described below). The inventors tested discrete volumes from 5 to 20, and all tests yielded results with similar accuracy (although computational efficiency decreased with increasing volume number). For general use, the inventors determined that 10 volumes should be used whenever possible to ensure robustness, accuracy, and computational efficiency across a wide range of scenarios. However, they believe that any number of volumes can be used, preferably including multiple volumes (i.e., two or more volumes).

[0108] Note that the machine learning model is trained on a specific set of products and inert substances, as well as specific stationary and mobile phases. However, the model is independent of the column geometry (and takes concentration and feed rate as inputs), so it can be immediately used to scale up and evaluate the effects of changes in feed concentration and flow rate.

[0109] The functionality of machine learning will now be explained. In this example, such as... Figure 3As illustrated, the machine learning model combines a parameter prediction sub-model 22B (a neural network in these instances) and a recurrent state sub-model 22A (also referred to herein as a "recurrent module"). This combination is referred to herein as a "recurrent neural network," although it is not a recurrent neural network in the traditional sense, where nodes in a layer influence subsequent inputs to the same node. In fact, a recurrent module is added here that captures information from previous states and provides input to the neural network itself. The recurrent module is optional. The recurrent module enables the capture of the dynamics of the system by allowing the machine learning model to make predictions informed by the system's previous states. The architecture of the machine learning model used in this example is... Figure 7 As shown in the diagram. In each iteration of the integral of the physics-based model... k (That is, at each time point being simulated), the model will include all discrete volumes. n The concentration vector of unbound products ( That is, for each stage n and iteration k, including the vector of the corresponding concentration of the unbound product for each corresponding product, and the vector of the concentration of the bound product. That is, for each stage n and iteration k, including the vector of the corresponding concentration of the binding product of each corresponding product and the concentration vector of the inert substance. That is, for each stage n and iteration k, including the vector of the corresponding concentration of the inert substance for each corresponding inert substance and the flow rate f. k As input, in the implementation used in this example, data from all stages of the column is passed to the neural network in a single call (although this implementation prevents the network from using information about other stages when making predictions for any particular stage, to reduce the risk of overfitting). This advantageously enables parallel computation, for example, making it possible to implement on multi-core machines and / or GPUs. Alternatively, the model can be used to predict each discrete volume individually. n The parameters (which can still be run in parallel by multiple instances of the model) are determined. In either case, the machine learning model is trained to predict the parameters for each stage individually. In other words, the prediction for one discrete volume element (stage) does not depend on the prediction for another discrete volume element. Including the velocity variable allows the neural network to adapt to changes in the binding and diffusion effects observed in the column as the flow changes. The modeling framework does not explicitly use physics-based equations derived from fluid dynamics and binding dynamics, which is beneficial because it reduces the experimental burden of identifying the model. Instead, fluid dynamic binding and diffusion effects are learned from experimental data generated at different flow velocities. Due to the velocity variable f kThis variable is not used in the equations derived from first principles by the neural network, therefore it can be "transformed" by the user before being passed to the neural network. Transformations such as from volumetric flow rate to linear velocity or residence time have been demonstrated in other simulation methods to produce models with less scale dependence. This property is useful for applications that wish to identify models from experiments conducted on small columns and use these models to predict larger-scale (commercial manufacturing-related) columns. The method of the present invention has been shown to be applicable to scaled-up settings even without such a transformation, but the transformation is straightforward in the method of the present invention, making the benefits essentially limited to those expected from performing the transformation.

[0110] like Figure 7 The illustrated machine learning model also includes the cyclic state vector. As input, the loop state vector is used in each iteration. k and discrete volume n The state vector allows the vector to take into account information from one or more previous time steps captured in any "overall" state. As will be explained further below, the cyclic state storage is obtained by performing a nonlinear transformation on the column states (concentration and velocity vectors) from the previous iteration, where the cyclic state values ​​are updated in each iteration based on the cyclic state values ​​from the previous iteration and the column states in the current iteration. As will be explained further below, in principle... There is no restriction on the dimensionality of the elements (i.e., the number of cyclic states that the model tracks for each discrete volume element n at each iteration, i.e., the number of degrees of freedom in the cyclic state information). However, higher dimensionality leads to higher complexity and potential overfitting, and the inventors have found (see below) that one state is sufficient to accurately capture the dynamics of the system. Therefore, unless otherwise stated, a single cyclic state is used for each stage. Note that although the model can in principle consider any number of states from previous iterations, in practice, due to the physical characteristics of the system being modeled, the benefit of considering previous states is expected to lie primarily in considering the state that occurred in the most recent iteration. In reality, the system does not have a "memory" beyond the cyclic state immediately following the previous cyclic state, and the loops are designed to facilitate updating these states in each iteration. Note that recurrent neural network architectures such as Long Short-Term Memory (LSTM) networks can be used alternatively, but these recurrent structures are designed to facilitate longer "memories" and therefore cannot adequately reflect the dynamic behavior (physics) of the system. This distinction also has practical implications for training, as LSTMs consider many previous states, making them much less computationally efficient and less likely to converge to robust and accurate solutions compared to the solutions currently proposed. Figure 7 The illustrated state vector The state is cascaded with other input variables (concentration vector and flow rate), optionally after passing through a tanh function (hyperbolic tangent function) to ensure that the state value does not increase to dominate the other input variables. Note that the tanh function can be omitted or replaced by any other function that can take unbounded inputs and produce bounded outputs, such as tanh or logistic / sigmoid functions. The cascaded inputs are fed into both (a) the cyclic state submodel (722A) and (b) the parameter prediction submodel (722B). The role of the cyclic state submodel 722A is to provide updated state vectors. For use in the next iteration. The role of the parameter prediction sub-model 722B is to provide vectors. and Predictions, so that in the current iteration k Used for concentration , , Flow velocity f k and the current state vector Associated volume n (Right now and Flow rate is a parameter in the simulation, concentration... , , This is obtained by integrating the model provided by equations (1)-(3) (which itself uses data from a machine learning model). and The parameters are predicted, and the state vector is predicted by a trained recurrent state submodel. The recurrent state submodel takes as input a concatenated vector identical to the vector fed into the parameter prediction submodel 722B, along with the current state vector (optionally after tanh or other bounded transformations). As illustrated, the recurrent state submodel 722A comprises two branches, each including a learnable weight vector. The sigmoid function and a learnable weight vector Both the tanh function and the concatenated vector fed into the parameter prediction submodel 722B are used as inputs. Note that any function that can provide an output between 0 and 1 can be used instead of the sigmoid function, and any function that can provide a bounded output from an unbounded input can be used instead of the tanh function. (The text then mentions learnable weight vectors.) The first branch produces a factor α as output, which can be considered a "forgetting factor" and represents the probability that the state vector has not been updated in the current iteration. The lower the value of α, the greater the probability that the current state will be updated (i.e., the higher the value of (1-α), the greater the probability that the current state will be updated—note that α can be used alternatively with the opposite result). It has a learnable weight vector. The second branch determines the proposed update for the current state vector. If α=1, then the current state (in Figure 7 The example above, denoted as "x"), is simply used as is in the next iteration (i.e., no update, the top branch evaluates to 0). If α < 1, the current state (in...) Figure 7 The top branch (instance "x") is updated to (1-α)x (in x It is the current state (i.e., the current state multiplied by 1-α) and αx (in x It is composed of learnable weights The value of the sum of the updated states output by the tanh function. In other words, the new updated state vector is obtained as a weighted sum of the current state and the new proposed state, where the weighting factors (1-α) and α are used for the current state and the new proposed state, respectively. The parameter prediction submodel 722B is exemplified here as having parameters W. [1…L] A simple fully connected neural network, where these parameters are weights associated with each neuron in each layer L. , and W [1…L] Learn using the training process described below.

[0111] The recurrent structure in the proposed neural network is specifically designed for this application. It differs from recurrent neural networks from other domains, such as the most common Long Short-Term Memory (LSTM) structures. Essentially, this application of recurrent networks removes the "long memory" portion of the LSTM structure, as states observed in many past sampling instances are unlikely to influence the current dynamics of the system. Instead, the proposed structure can be viewed as adding "free" states that evolve with the nonlinear dynamics determined by the neural network. The training algorithm is left to determine how best to apply these new nonlinear dynamics. The use of recurrent states enables the capture of dynamic behavior caused by diffusion. This diffusion effect can occur in other parts of the path between the binding substrate, the mobile phase, or the bulk liquid phase within the column and the binding site. Many existing models explicitly or implicitly ignore diffusion effects that are difficult to model using first-principles models.

[0112] A key benefit of the proposed method is that the neural network uses the same training weights at each discrete volume in the spatial discretization of the pillars. In other words, The vectors in the column are not indexed by n. In effect, this decision implies that the dynamic response of the column should be the same at the inlet as at the outlet. This design decision is technically accurate for new columns, where the stationary phase should be homogeneous throughout the column volume. In older columns, this assumption may be less accurate because irreversible binding effects can disproportionately affect the inlet portion of the column. This can be addressed by providing the machine learning model with one or more additional inputs (additional states) indicating the column's lifespan. For example, the machine learning model could additionally take as input a variable indicating the number of cycles the column has undergone (i.e., the number of complete loading, washing, elution, and regeneration cycles) or a variable indicating the total column volume the column has undergone. Alternatively or otherwise, the machine learning model can be trained using training data that includes data from multiple complete cycles, allowing the model to learn how the column parameters change over time. However, training a single binding dynamic model for the entire column has significant advantages in greatly reducing the likelihood of overfitting. This approach is similar to techniques developed in image analysis using bound weights in convolutional neural networks. In both cases, by training the weights on a “sliding view” of the same system, local anomalies are downweighted, and a more representative set of weights is generated during training.

[0113] Model training The inventors have developed a training algorithm capable of reliably training a neural network to incorporate the kinetic behavior from commonly available column eluent (outlet) data, including experimental data collected on the column outlet stream using a fractionating collector (gradation). The algorithm is considered novel in at least three aspects. First, the method directly considers sample aggregation that occurs during product development through fractionation in common laboratory-scale chromatographic experiments. The ability to use fractionated sample data makes the proposed technique practically feasible compared to alternatives that require complete time-series concentration data. Second, the inventors have developed a series of heuristics for staged training of the proposed recurrent neural network to achieve numerically stable gradient descent during the training phase. Finally, the inventors have developed a method for linearizing and discretizing the spatial dimension (using the aforementioned differential volume element model) and the temporal dimension (using discrete time steps corresponding to the iterations of the machine learning model prediction and the column model ODE solution process). This discretization algorithm eliminates the need for an adaptive step-size partial differential equation solver. Therefore, the proposed algorithm is easy to implement in a computational graphics environment (such as PyTorch), allowing the loss function error to be backpropagated to the neural network via the physical equations and ultimately to the training weights. The complete training algorithm flowchart is shown in Figure 8.

[0114] At step 810, use and (Here, all n stages are represented as 10 and 1 respectively) and The model is initialized using the default value (100 in this example). Parameters This is a vector of the corresponding total binding capacity (static binding capacity) of the column for each corresponding product. This parameter is only explicitly used in the pre-training step (steps 810-830) illustrated in Figure 8. At step 812, the column is modeled by solving the column model provided by equations (1)-(3) using these default values ​​and the maximum feed concentration and maximum feed rate available in the training data. In the illustrated implementation, the model is solved iteratively over 60 discrete time intervals. The time length corresponding to any number of intervals k depends on the time discretization frequency (i.e., the time length corresponding to iteration k), which is a user-defined parameter (as is the total number of iterations). The inventors have found that 60 sample instances are long enough to observe any instabilities in the model for most reasonable time discretizations, since the time when the values ​​are most unstable in most column sample data occurs early in the run, as the concentration changes are greatest at this time, and therefore the gradient (stiffness) of the problem is highest. Therefore, 60 iterations have proven sufficient for this pre-training step. Note that in practice, when simulating a column (i.e., not during model training), the model can be allowed to run as many iterations as needed to capture the column behavior of interest to the user (e.g., the complete loading phase until a stable phase of the penetration curve is reached). When k=0, assume... , , The initial values ​​are typically 0 for bound and unbound products (because the column has not yet been loaded with products when simulating the loading phase), and also typically 0 or constant for any inert substances present in the buffer initially packed into the column. These concentrations (the concentration of any inert substances being modeled in the buffer initially packed into the column) are known for the specific chromatographic process being modeled. When modeling the washing or elution phase, these can be obtained from the simulation of the previous phase. , , The initial value. At step 814, check whether the simulation output contains any NA, i.e., whether the numerical integration encounters instability due to the stiffness of the gradient in the volume element during the selected time interval. If so, at step 816, and The current default value is reduced by a predefined factor, exemplified here as 25% (but any other value can be used). Steps 812, 814, and 816 are repeated iteratively until… and The current value makes the model converge for all time points (i.e., there are no longer any instabilities). At step 818, for each dataset in the training and validation data, using the number of discrete time intervals corresponding to the duration from the corresponding dataset, leveraging the feed rate trajectory from the corresponding dataset and the inlet concentration trajectory from the corresponding dataset, and using the values ​​obtained during the last iterations in steps 812, 814, and 816... and The value is used to simulate the column. If any training and validation datasets are tiered data, then at step 820, the corresponding simulation obtained in step 818 is converted into tiered results by copying the tiering scheme from the corresponding dataset (i.e., combining the effluent volumes corresponding to the corresponding tiers) and calculating the corresponding concentrations. Note that this is optional and is only performed if the data includes tiered data. At step 822, the training and validation losses (all losses shown are mean squared error (MSE), although root mean squared error (RMSE) has also been used and the results are the same) are calculated as the differences between the simulated data and observed data from the training and validation sets, respectively. At step 824, one or more stopping criteria are evaluated for the losses calculated in step 822. In this example, the stopping criteria include criteria regarding the validation loss (i.e., early stopping using the validation loss). In this example, the validation data is also used for learning rate scheduling, where the learning rate is adaptively reduced based on the improvement rate of the validation data. This is optional, and the model can also be trained using only the training data. When one or more stopping criteria are met, and Set to the value to be used in the current iteration. If the stopping criterion is not met, a gradient descent procedure is used at step 826 to obtain... , and The updated values ​​are then used in further iterations in steps 818, 820, 200, and 824.

[0115] As a result of the above process, we obtain , and The "warm start" value. Specifically, steps 810-816 are used to ensure identification. and The process of setting initial values ​​begins with initial guesses that will not lead to numerical instability in the integral column model (simply by decreasing the values ​​of these parameters until a sufficiently small gradient appears in the model to make it solvable in all iterations). This is performed on a single default setting (which can be informed by the training / validation data), and is therefore extremely computationally efficient. Steps 818-826 are then used to provide initial values ​​informed by the training and validation data by exploring a value space that is unlikely to lead to numerical instability. This is less computationally efficient than steps 810-816, as it requires a separate simulation of each set of operating parameters in the training and validation data, but is still highly computationally efficient compared to the step of also updating the weights of the machine learning model at each iteration. The resulting values ​​are used to provide a “warm start” for the training of the machine learning model, which ensures that the model training converges every time. Note that steps 810-826 (and steps 828-830 through which the weight values ​​of the machine learning model corresponding to these warm start values) can be omitted, and the machine learning model can utilize the default weights. , and W [1…L] (These can be, for example, all identical values, random values, or values ​​from a previously trained model, if available) to train. This is essentially equivalent to performing only steps 810 and 832-840. However, due to numerical instability, the likelihood of the model failing to converge increases significantly.

[0116] At step 828, random sampling is performed. , , f k and The value is based on the value obtained from steps 810-826. and Through calculation To calculate linearized value ( This generates pre-training data. At step 818, random sampling is performed within the corresponding range of each value defined based on the range of values ​​seen in the forward pass step of the initial fit. For example, a range calculated as ±20% (or any other percentage, such as 10%, 15%, 20%, 25%, or 30%) of the range seen in the forward pass step of the initial fit at step 818 can be used. As described above, using... replace and Reducing the number of parameters from the neural network decreases the number of possible solutions, which helps the solver converge, and through In neural networks, including and The relationship between them makes the solution more stable and computationally tractable. At step 830, the pre-training data obtained in step 828 is used to pre-train a neural network (in the exemplary implementation, a fully connected neural network and a recurrent module) using a fixed number of rounds (e.g., 10,000, but other numbers can be used) and a loss function that penalizes: (i) the data from step 828. With targeting The differences between network predictions, and (ii) the differences from steps 810-826 With targeting The difference between the network predictions. Essentially, step 830 is used to train the model to provide predictions that match the "warm-start" predictions obtained through steps 810-826. Then, in steps 832-840, the corresponding pre-trained weights are further trained using the training data and a backpropagation strategy. , and W [1…L] Specifically, at step 832, the values ​​from steps 810-826 are used. , For each dataset in the training and validation data, the column model is modeled using the number of discrete time intervals corresponding to the duration from the corresponding dataset, utilizing the feed rate trajectory and the inlet concentration trajectory from the corresponding dataset. If any training and validation datasets are stratified data, at step 834, the corresponding simulation obtained in step 832 is converted into stratified results by copying the stratification scheme from the corresponding dataset (i.e., combining the effluent volumes corresponding to the corresponding strata) and calculating the corresponding concentrations. Note that this is optional and is only performed if the data includes stratified data. At step 836, the training and validation losses (MSE, but similarly RMSE or other losses will also produce the same result) are calculated as the differences between the simulated data and observed data from the training and validation sets, respectively. At step 838, one or more stopping criteria are evaluated for the loss calculated in step 836 or the gradient applied to the weights in step 840. When one or more stopping criteria are met, the weights are... , and W [1…L] The values ​​are set to be used in the current iteration, i.e., the trained model is obtained. If the stopping criterion is not met, updated weight values ​​are obtained at step 840 using a gradient descent procedure based on the training loss. , and W [1 …L] As mentioned above, the validation loss is used both as part of the early stopping criterion and for learning rate scheduling, where the learning rate adaptively decreases based on the improvement rate of the validation data. This is optional, and the model can also be trained using only the training data.

[0117] The solution to the column model (at steps 818 and 832) is explained in the “Model Deployment” section below, and follows the same principles during model training and deployment. To solve the column model, at each discrete time point k, the column model is discretized based on the current state of the system (concentration and cyclic state), as described below. Specifically, the concentration and cyclic state are passed forward through a neural network (722B), and then the data from that network (…) are processed. , The output value is substituted into the ODE equation of the column model, which is solved at the discrete time step.

[0118] Model Deployment Figure 9 illustrates a method for deploying the above model, namely, using the trained hybrid model as described above to simulate the column. Figure 9A The general principles applied are illustrated. First, a machine learning model (here, the neural network mentioned above) and input are used. , , , , Get all of , and These are predictions. , The parameters are used as models in equations (1)-(3) to solve the column model at the current discrete time point k. Specifically, the ODE in (1)-(3) is used to surround the current state (by... , , , (Definition) Linearization. Note that during model training and subsequent applications, the cyclic state... They are initialized to 0 (i.e., they are 0 when k=0). Since these states are arbitrary, this is a safe assumption as long as training and application are consistent. As mentioned above, , , Initialize the bound and unbound products to 0, and initialize the inert material to 0 or the known concentration in the buffer solution filling the column. These values ​​can also be initialized to any known concentration (e.g., from a previous stage simulation or for cases where a certain amount of irreversible binding is expected), such that... (Not 0 when k=0).

[0119] The matrix in Figure 9B illustrates how to construct the linearized system dynamics and linearized states. Once linearized (by obtaining predictions from a machine learning model, which captures all nonlinearities, i.e., specific predictions given the current time step), , Equations (1)-(3) are linear, although formally (i.e., when not considered in the context of a single iteration with fixed predicted values ​​for each of these parameters) they are nonlinear, as these parameters change nonlinearly with time, by solving the system over discrete intervals using a discrete state-space model:

[0120] Where A and B are the matrices shown at the top of Figures 9B1 to 9B3, and in Figure 9B-4 Expanding in the middle, that is: in , .

[0121] Calculate A d and B d As a result of the matrix exponentiation operation in equation (4), it becomes very simple to calculate the updated state for one or more intervals using the following formula (until the linearization changes significantly, i.e. until the values ​​of A and B are significantly different):

[0122] Where x k+1 It is any updated state (i.e., , , (any one of them), and x is the corresponding current state (i.e., , , (Any of the following). By default, A can be recalculated on each iteration. d and B d The value of . However, since calculating equation (4) is computationally expensive compared to the rest of the solution process, computational efficiency can be significantly improved by calculating the values ​​of A and the matrix at each iteration, comparing them with those of the previous iteration, and reusing the values ​​of A and B from the previous iteration if the values ​​of A and B have not changed beyond a predetermined threshold. d and B d The value is used to calculate x in the current iteration. k+1 (That is, the same A can be used) d and B d To calculate the updated state for multiple subsequent intervals, each interval being compared with the state calculated in A. d and B dThe value is related to the values ​​of A and B within a predetermined range based on the value of A and B.

[0123] Interestingly, the inventors empirically observed that any errors introduced by the linearization scheme (especially in the spatial dimension—i.e., any errors introduced by staged discretization) can be readily explained by the learning dynamics of the recurrent neural network. In other words, the method is robust to the number of stages used. Simultaneously, the physics-based structure of the flow model prevents the model's data-driven components from generating invalid outputs (such as negative concentrations).

[0124] Example 2 – Demonstrating the Use of a Universal Chromatography Model The method described in Example 1 has been demonstrated on a variety of datasets and for a range of applications.

[0125] Formula optimization First, the inventors demonstrated the applicability of this method for detailed characterization of the design space of chromatographic processes (e.g., for process optimization and scale-up).

[0126] Figure 10A -D shows simulated results of the chromatographic process using the method described herein, with different flow rate values ​​throughout the chromatographic process (A: flow rate = 20 ml / min, B: flow rate = 13.9 ml / min, C: flow rate = 5.9 ml / min, D: flow rate = 1.8 ml / min). Each figure shows the mobile phase concentration of the product (in this case, monoclonal antibody on column A of protein). cu ) and the concentration of the bound phase (c b Within the range of ), the adsorption rate calculated from simulation data at the indicated flow rate ( ) and desorption rate ( The adsorption and desorption rates were calculated by maintaining the cycle at nominal (zero) values ​​and then sweeping the grid across Cu and Cb values ​​at different flow rates (i.e., exhaustive combinations). Figure 11 The figure shows representative model prediction performance for the same column and product, using training data (i.e., data used to identify model parameters) and validation data not seen by the training algorithm. The scatter points (solid circles) in the figure represent experimental measurements of product concentration (monoclonal antibody titer, in mg / ml) at the column outlet, while the solid lines represent the corresponding model predictions. Examples of three different feed flow rates used as training data and two feed flow rates used as validation cases are shown. Figure 10 illustrates how the binding model (data-driven component) works for hypothetical concentrations, where mobile phase and binding phase concentrations (Cu and Cb) are generated in a grid across ranges representing values ​​seen during the model's training phase. These concentrations are fed into a neural network (from... Figure 7The forward pass of 722B) is used, where the flow rate is also taken from the range in the training data. and The resulting output values ​​are shown in the heatmap. It is worth noting that these heatmaps allow for human-readable insights into the relationships captured by the neural network, making the model interpretable (unlike many black-box, purely data-driven models). For example, from the graphs we can clearly understand that, as expected, total adsorption is highest when the mobile phase concentration is relatively high and the bound phase concentration is relatively low. Figure 11 The predictions made using these relationships for the actual settings are shown (with corresponding experimental data showing that the predictions from the machine learning model and the corresponding column behavior simulations have high accuracy across both visible and invisible conditions).

[0127] The transition from batch processing to continuous chromatography Furthermore, the inventors have demonstrated the ability to transition from batch to continuous chromatography using this method. Specifically, the inventors applied the described modeling framework to predict multi-column chromatography systems from batch data. This allows process development teams to predict how multi-column chromatography equipment will improve upon conventional batch chromatography without using laboratory-scale multi-column setups.

[0128] So-called “continuous” chromatography, which uses multiple columns connected in tandem during the sample loading stage of preparative chromatography, is a relatively new technique in biomanufacturing. In other words, instead of traditional batch chromatography where the product is loaded into one column, washed, and then eluted, columns are placed in tandem in multi-column chromatography. The product is loaded onto the first column, and the permeate is captured onto the second column. Then, when the first column is saturated (or at a predetermined percentage of product penetration), the feed is switched to direct loading column 2 (which, if available, permeates to column 3). While the product is being loaded onto column 2, column 1 is washed, eluted, and regenerated. Once column 1 is ready again and column 2 is saturated (or reaches a predetermined percentage of product penetration), column 2 is washed, eluted, and regenerated, and the feed is switched to column 3, while the permeate from column 3 enters column 1.

[0129] The use of continuous chromatography systems offers readily understandable theoretical advantages. Perhaps the most compelling argument is the ability to utilize the full column binding capacity during the loading phase without product loss. However, despite these advantages, the adoption of continuous chromatography in commercial biomanufacturing remains limited. One of the challenges hindering its implementation is the relatively more complex task of designing formulations for multi-column systems compared to traditional single-column batch chromatography. Modeling tools are a potential solution to this adoption problem. Simple tools have been designed to assist in the use of continuous chromatography systems, such as Resolute from Sartorius StedimChromatography Systems. ® BioSC and Resolute® The BioSMB platform. These typically rely on simple column capacity calculations to help determine the duration of each step in a multi-column formulation. While these tools are helpful for simple, traditional use cases (e.g., protein A resin columns for mAb capture), they may not accurately predict the performance of advanced columns (e.g., resin columns, monolithic columns, etc.) and advanced therapeutics (e.g., viral chromatography applications). Furthermore, these tools often fail to accurately account for the effects of varying feed rates, feed titers, and impurity profiles. In most cases, this means that the resulting formulation is at best a starting point, requiring additional experiments to determine the final formulation. The flexibility and broad applicability of the universal column modeling proposed in this work make it an attractive alternative for multi-column formulation design. Moreover, the computational efficiency of the proposed method makes it suitable for numerical optimization to automate multi-column formulation design.

[0130] The proposed modeling framework has been used in a prototype application to aid in formulation design for multi-column chromatography systems. Screenshots of the application are shown below. Figure 12 As shown. This application works by connecting two instances of the model, such that the effluent concentration of the first simulated column becomes the feed for the second column. In this way, the mobile phase concentration of a multi-column system can be predicted for different formulation parameters. The model used is a two-layer deep network with 30 activation functions (i.e., 30 nodes) per layer. Two cycling states were used. The model was trained on batch breakthrough experiments in a resin protein A column (5 ml Cytiva MabSelect column). The target product was a monoclonal antibody. The model was trained with three breakthrough curves at different feed rates (1.5 ml / min to 10 ml / min) and feed concentrations ranging from 0.8 to 1 g / L. The model was validated with two additional breakthrough curves at new feed rates and concentrations. Fractions used for these experiments were collected in 1 ml volumes. Fraction titers were determined by size exclusion chromatography (SEC). The parameters varied by formulation design were: feed rate (ml / min), feed concentration (g / L), simulation duration (min), and switching time (i.e., the time from fresh feed to loading each column) (min). In the illustrated multi-column configuration, there are three columns (and in some cases, even more). Initially, column 1 is fed with fresh feed, and column 2 is fed with the eluent from column 1. Column 3 is in elution / regeneration. When the switching time is reached, column 1 enters regeneration, column 2 is fed with fresh feed, and column 3 (newly regenerated) is fed with the eluent from column 2. In the next cycle, column 3 is fed with fresh feed, column 1 is fed with the eluent from column 1, and column 2 enters regeneration. This process ensures that there is always a fresh column at the end of the chain to prevent product loss from the column with fresh feed. Figure 12In the diagram, the blue line represents the concentration of the target product flowing between the first and second columns in series (i.e., the product concentration in the effluent from the first column), while the pink line represents the product concentration leaving the second column. Users can manipulate the loading time, feed rate, and titer by changing the sliders to simulate different conditions that may occur in production and develop multi-column formulations robust to these variations. The simulation results (changes in product concentration in the column effluent over time) also allow for the calculation of the total capture (calculated as c = total product concentration at the end of column loading). b The sum of these values ​​multiplied by ΔV before regeneration occurs—this assumes the sampled product will be fully recovered during the elution phase), the binding capacity per cycle (calculated as total capture divided by (number of cycles * column volume)), the recovery percentage (calculated as total capture divided by the integral concentration in the feed during the sample stage), the maximum breakthrough concentration (the maximum product concentration observed at the outlet of the last column in series in the simulation), and the maximum breakthrough percentage (the ratio of the maximum breakthrough concentration to the feed concentration).

[0131] Comparison of different chromatographic techniques Another practical use case for the described method is comparing different chromatographic techniques, such as different stationary phases (e.g., membranes, monolithic columns, and resins). Because the framework is independent of the type of stationary phase (its effects are captured during the training of the machine learning model), different techniques can be directly compared within the same modeling framework (albeit using the corresponding machine learning model trained using training data obtained with the respective technique).

[0132] The inventors trained two machine learning models (both including those with different stationary phases) on data from columns used to purify protein A using different stationary phases (i.e., MAbSelect SuRe resin chromatography and Sartobind Rapid A membrane chromatography). Figure 7 The neural network architecture is described, where the prediction sub-model 722B is a fully connected neural network with two hidden layers, each containing 20 nodes, and the final layer contains two nodes, each with a tanh activation function, used for prediction. and This potential was demonstrated. Using four experimentally determined breakthrough curves obtained with the appropriate chromatographic techniques, each machine learning model was trained for 1000 epochs, as explained in Example 1. The models were trained for approximately 3 minutes on an Intel I9 14900K processor. They were then used to simulate a column with the same parameters: feed rate = 2.5 ml / min, feed concentration = 1, simulation duration = 200 minutes, and breakthrough threshold % = 5.

[0133] Figure 13 shows the results of this experiment using (AB) MAbSelect SuRe resin chromatography (calculated breakthrough time = 53.77 min, calculated dynamic binding capacity = 134.42 mg / ml) and (CD) Sartobind Rapid A membrane chromatography (calculated breakthrough time = 24.10 min, calculated dynamic binding capacity = 50.20 mg / ml). A and C show the simulation results, and B and D show the model validation data and the correlation R between the predicted (solid line) and observed (spotted) breakthrough curves. 2 And RMSE.

[0134] The economic impact of different formulations using the respective chromatographic platforms was then comprehensively estimated using the model used to generate the data in Figure 13. Specifically, two chromatographic platforms were simulated on a grid for flow rate and titer values ​​(the concentration of product in the feed). Note that the columns had the same volume, thus providing a direct comparison of the two platforms for the same operating parameters and mobile phase. The costs and benefits associated with each formulation were then estimated using an economic model that considered the costs associated with regeneration (using the known fixed cost per regeneration associated with each column and the assumption of a fixed cycle life of the column, here 100 regenerations—but any number corresponding to the known or expected life of a particular column could be used), the cost of buffer consumed, the cost of waste generated, and the benefits associated with the amount of product recovered. The costs and profits were combined into a single profit metric for running the process in $ / hour (considering the time to run through the loading-washing-elution-regeneration cycle, buffer consumption rate, buffer preparation requirements (including buffer storage costs), and the amount of product recovered in each cycle). Figure 14 illustrates the results of this experiment: the heatmap shows the profits associated with running the chromatographic process using a MAbSelect SuRe resin column (A) or a Sartobind Rapid A membrane column (B) at specified titer and flow rate values. These results enable the informed selection of the chromatographic platform and formulation, thereby maximizing the profits associated with the process. Note that similar simulations can also be used to optimize any other desired characteristics, such as the concentration of the product in the effluent, the concentration of any impurities, etc. Furthermore, the same method outlined can also be used to compare the economics of multi-column chromatography versus batch chromatography.

[0135] Scale-up during process development The novel method presented in this paper can also predict large-scale binding capacities from small-scale experiments, design formulations for large-scale continuous chromatography based on development-scale equipment, and investigate the effects of bed height on column diameter (or equivalent cross-sectional area). The latter can be explored by using the linear velocity of the feed flow as the feed rate input to a neural network. In this case, changing the bed height while keeping the cross-sectional area constant at the same flow rate does not affect the linear velocity seen by the neural network (if the discrete volumes remain the same ΔV, only more discrete volumes are needed to simulate the system). In contrast, increasing the cross-sectional area reduces the linear velocity at the same flow rate, thus affecting the neural network's predictions, which ultimately influences the simulation output.

[0136] Figure 15 An example of column amplification prediction using the method described in this paper is shown. This is achieved using columns containing protein A (specifically, Sartobind from Sartorius Stedim Biotech GmbH). ® The training data of the Rapid A membrane was used to train the model as described in Example 1 (including data with Rapid A membrane). Figure 7 The neural network architecture in the model, where the prediction submodel 722B is a fully connected neural network with two hidden layers, each containing 20 nodes, and the last layer containing two nodes, each with a tanh activation function, used for prediction. and The training data consisted of six breakthrough curves at two different feed concentrations (3 g / L and 0.6 g / L) and two different feed rates [3 ml / min and 10 ml / min] for the monoclonal antibody. Validation was performed for the same product and column at the same two feed concentrations using six additional feed rates. The model was then used to predict breakthrough curves and dynamic binding capacities for any process using the same chromatographic technique with a range of bed heights and column cross-sectional areas.

[0137] Real-time monitoring and adaptive real-time optimization of chromatographic formulations The method described in Example 1 can also be usefully deployed in the context of chromatographic process monitoring and control.

[0138] Simulations can be run using the same operating parameters as the chromatography process while it is in progress (i.e., the simulation can act as a digital twin), enabling comparisons of measurements from the column with predicted values ​​from a “healthy” column. These comparisons can be used for: early detection of deviations (and optional diagnostics) (i.e., fault detection), triggering reloading (e.g., when unacceptable deviations are detected), and monitoring the column in a way that provides data notification, allowing for broader column utilization between reloadings (i.e., enabling less conservative and therefore less costly operations).

[0139] Furthermore, simulations can be run simultaneously with one or more candidate sets of operating parameters for the chromatographic process to allow for the automatic adaptation of operating parameters in response to measurements or anticipated changes in the feedstock (which are typically influenced by upstream processes). Similarly, simulations can be run simultaneously with one or more candidate sets of operating parameters for the chromatographic process to allow for the optimization of column usage in multi-column chromatography (using economic forecasts or any other criteria or set of criteria to be optimized and applying them to the output of the simulation or indicators derived therefrom) (e.g., deciding when to switch columns, how to set flow rates, etc., at any point during the process in order to optimize the selected criteria).

[0140] Furthermore, simulation can be used to provide information to upstream processes, for example, enabling the upstream processes to be controlled in a manner that optimizes any criteria or set of criteria applied to or derived from the simulation output (since the impact of changes in chromatographic process feeds related to upstream process harvesting feeds on optimization criteria can be readily obtained by simulating chromatographic processes as described herein).

[0141] Example 3 – Robustness assessment of a general chromatographic model In this embodiment, the inventors set out to evaluate the robustness of the method described in Example 1 to various settings. Specifically, the inventors tested the impact of various parameters of the machine learning model training on the performance of the method. Figure 16 illustrates the results of these robustness evaluations. Training data was collected from the purification process on a protein A column, including breakthrough curve experiments performed at three different feed rates, repeated multiple times at each feed rate. Simulations were performed at 1-minute time discretization intervals.

[0142] Use one or two loop states (i.e., two states that are updated in each iteration, namely x). r This is a variant of the machine learning model trained with a 2×1 vector of k and discrete volume n for each iteration. Each variant contains a predictive submodel, which is a fully connected neural network with 2 hidden layers, each with 8 to 60 nodes, and the last layer (2 nodes) has a tanh activation function, using a feed concentration of 3 g / L and a feed rate of 4 ml / min. The capture amount, dynamic binding capacity, and validation loss associated with each of these simulations are shown in [the table / image / image]. Figure 16A -C on. These results show that having more than one cyclic state (where the cyclic state is the sum of parameters of the past states of the column remembered during the simulation, as described above) does not lead to significant differences between the metrics derived from the simulation. This suggests that one cyclic state is sufficient, although more may be possible, but the main cost is likely computational efficiency (and potential overfitting in some cases).

[0143] A variant of the machine learning model was trained using a single cyclic state. Each variant contained a predictive sub-model, which was a fully connected neural network with four hidden layers, each with 8 to 60 nodes, and the last layer (two nodes) had a tanh activation function, using a feed concentration of 3 g / L and a feed rate of 4 ml / min. To evaluate the reproducibility of the model fitting procedure, model fitting was repeated twice (i.e., with different random initializations of weights) at each of a range of layer sizes using the same data and network configuration. The simulation results for each of these repeated fittings were then compared. This reproducibility demonstrates the reliability of identifying consistent parameters. Figure 16D -F indicates the results in terms of simulated capture size, simulated dynamic combination capacity, and validation loss. The data shows that iterations are similar across all model types, indicating that all models provide robust predictions regardless of the exact configuration of the neural network.

[0144] Variants of the machine learning model were trained using the model, each containing a predictive sub-model, which was a fully connected neural network with 1, 2, or 4 hidden layers, each with 8 to 60 nodes, and the last layer (2 nodes) had a tanh activation function, using a feed concentration of 3 g / L and a feed rate of 4 ml / min. The amount of capture, dynamic binding capacity, and validation loss associated with each of these simulations are shown in [the table / image / image]. Figure 16G -I. Model complexity increases with the number of layers and nodes. Higher complexity increases the likelihood of overfitting. Judging from the validation error, it appears that 4 layers tend to lead to higher errors, indicating potential overfitting. However, models with 1 or 2 layers show very similar results, suggesting that the approach is robust to the choice of architecture, although overfitting is possible as in any other machine learning problem.

[0145] A variant of the machine learning model is trained using a single cyclic state. Each variant contains a predictive sub-model, which is a fully connected neural network with two hidden layers, each with 20 nodes, and the final layer (with two nodes) has a tanh activation function. The model is trained using training data with various granularities (number of data points) obtained by downsampling available online data (1000x downsampling, 500x downsampling, 100x downsampling). The model is then used to simulate a process with the same parameters. The simulated penetration curves are compared with the corresponding training data (3 sets, 3 repetitions per set, each set with different corresponding flow rates between sets). These results show that the model can be successfully trained in each of these cases. In this case, approximately 10 points describing the penetration curve are sufficient to find a meaningful model. This demonstrates that the proposed method is extremely robust to the amount of available training data (and particularly readily supports low-resolution training data, such as graded sample data).

[0146] A variant of the machine learning model is trained using a single cyclic state. Each variant contains a predictive submodel, which is a fully connected neural network with two hidden layers, each with 20 nodes, and a final layer (with two nodes) with a tanh activation function. Training data is used, consisting of one or three repetitions for each of five or three flow rate groups. The resulting simulated penetration curves are compared with the corresponding training data. The results show that the model attempts to adjust between repetitions, and for a given repetition, the predicted expectation matches that repetition. This demonstrates that the proposed method can be trained with a minimal amount of training data repetitions and is able to learn from the variability between repetitions when repetitions are available.

[0147] Example 4 – Validation of a Universal Chromatographic Model In this embodiment, the inventors set out to extensively validate the method using data from state-of-the-art detailed first-principles modeling tools. Specifically, the inventors conducted a detailed validation of the new method against CADET (mechanical) simulation data. CADET (Chromatography Analysis and Design Toolkit, von Lieres & Andersson 2010) is an open-source chromatography simulation platform available at cadet.github.io / master / index.html. CADET implements a detailed, general rate model for column liquid chromatography. The software is used to build a data generation pipeline for the numerical simulation model, which is then validated using the general chromatographic model described in Example 1. The data pipeline phase includes the following steps: (i) storing the user-defined design space as a set of parameters; (ii) creating a numerical model in CADET based on the set of parameters; (iii) integrating the column effluent results into fractions; and (iv) saving the fraction data to an Excel spreadsheet for use by the general chromatographic model. The data is then used to train and validate the general chromatographic model.

[0148] Experimental runs were conducted to demonstrate the ability of the general chromatographic model to extrapolate to unseen flow rates in the training data. By showing the error of the model solution compared to validation data, the inventors determined that the model learned the fundamental physical laws of the synthetic data and was able to predict mass transfer at unseen flow rates. Multiple numerical models were set up using the following settings: modulated Langmuir isotherms were used as the combined model, with axial dispersion from values ​​{1*10...} -7 1*10 -5 1*10 -4} m 2 s -1 Sampling was performed in low, medium, and high axial dispersion. Column volume was sampled from values ​​{1, 5, 15, 75, 200} ml, length-to-volume ratio was sampled from values ​​{2.5, 5, 7.5}, and column flow rate was sampled from values ​​{0.05, 0.25, 1.0, 2.5, 7.5} ml·min. -1 Mid-sampling, as well as loading time, column capacity, adsorption rate, and desorption rate constant (excluding modulation effects), were used. A series of experiments were established using the Cartesian product of all parameter sets. The flow rates in each experiment were then scaled according to the set {2.0, 3.0, 4.0, 5.0, 6.0} to generate five time series for each experiment. These time series were graded and collected in increments corresponding to {30, 60, 120} s to increase the variation in the number of data points collected in the set. For each experiment (five time series), a general chromatographic model was trained on four time series and validated on the last series.

[0149] Then, after training the mechanical (CADET) and general chromatography models used for training and validation sets, a PDF report and results are automatically generated. This includes a selection of images generated from the data in the lower half of the dataset.

[0150] The process is illustrated in Figure 17, which shows the mobile phase concentration of the target molecule (target) to be separated at the column inlet and outlet for a single synthesis experiment, as well as the mobile phase concentration of the buffer solution that counteracts the binding effect of the target molecule to the solid phase (thus resulting in the elution modifier of the target molecule). Figure 17A ), and how to use Figure 17A The data shown is used to integrate over time periods of the synthetic dataset to generate synthetic fractional measurements of the target mobile phase concentration, indicated by black squares. Figure 17B ). Figure 17C A template for generating the dataset is shown. Here, the “experiment” consists of 5 model evaluations; the solid line represents the generated high-resolution data (from the CADET software), from which points (represented by squares) are selected to generate the data for this experiment (every 60 seconds). Each individual simulation run that constitutes the synthetic experiment used to train and validate the general chromatographic model differs in initial flow rate scaling, as indicated.

[0151] When evaluating new numerical simulation methods, the inventors look for steep gradients or "stiffness" effects, mesh refinement effects, stability or oscillatory behavior, and vector norms and their convergence. Here, since the methods being evaluated are hybrid approaches that include machine learning models (neural networks), they also assess the impact of parameters related to neural networks.

[0152] Based on the experiments described in Example 3, the inventors have hypothesized that a larger network size (e.g., 10 or more nodes per layer across two layers) is beneficial for reducing losses. Therefore, all experiments were conducted using a model with 3 layers and 256 nodes per layer.

[0153] The results of these extensive experiments (a total of 180 experiments) are summarized in Figure 18A In, and specific examples are shown in Figure 18B -E in. Figure 18A The loss histograms on the validation and training datasets are shown (top left and top right, respectively), as well as the loss distributions on the validation and training datasets (bottom left and bottom right, respectively), as illustrated by the box plots. These results indicate that the validation loss for the vast majority of results is below 0.1 (10). -1 The median validation loss is 4.3 × 10⁻⁶. -3This demonstrates that the general chromatographic model can generalize the behavior of a much more complex and computationally inefficient general rate model with extremely high average accuracy. Typically, the inventors also observed that more data points (implied here as higher grading frequencies) contribute to higher model accuracy, indicating that the method can achieve extremely high accuracy with good training data. Stiffness is not an issue in these settings because no instability or oscillatory behavior was observed after training, meaning that these effects (if significant) are offset by the action of the machine learning model (i.e., the overall model is stable and there are no oscillatory behavior issues).

[0154] There are some outliers in the validation and training losses, most of which can be explained by the dataset that includes the washing phase (this is not what the specific general chromatography model being tested was designed to capture, as the machine learning model used was only trained on the loading phase data). This is in Figure 18B The middle has 10 -1 An example of a simulation to validate the loss is used as an illustration. For four training breakthrough curves (left) and one validation breakthrough curve (right) in a single experiment, this is shown as a solid line from CADET and a dashed line from the corresponding simulation from a general chromatography model. The parameters for each simulation are indicated below each figure, i.e., in this experiment, the training data were generated with the following parameters: column volume 75 ml, time 33 min, fractionation 120 s, axial dispersion 1*10 -4 m 2 s -1 The length-to-volume ratio was 2.5, and the flow rates were 7.5, 10.0, 12.5, or 15 ml / min. Validation data were generated using the same parameters, except that the flow rate was set to 5 ml / min. The results showed that the high validation loss (compared to other experiments), i.e., 0.1, was due to a mismatch in the automated data generation, rather than due to the performance of the general chromatographic model. In other words, this data suggests that if the model has been evaluated against the correct training and validation data (limited to the wash start up to approximately 30 minutes and the prior breakthrough curve), the validation and training losses could be close to the observed median of 4.4 × 10⁻⁶. -3 .

[0155] Figure 18C An example of an experiment with a validation loss of approximately 0.01 is shown. Similarly, for the four training breakthrough curves (left) and one validation breakthrough curve (right) in a single experiment, this is shown as a solid line from CADET, and the corresponding simulation from the general chromatography model is shown as a dashed line. The parameters for each simulation are indicated below each figure, i.e., in this experiment, the training data were generated with the following parameters: column volume 15 ml, time 33 min, fractionation 30 s, axial dispersion 1*10 -4 m 2 s-1 The length-to-volume ratio was 5, and the flow rate was 3, 4, 5, or 6 ml / min. Validation data were generated using the same parameters, except that the flow rate was set to 2 ml / min. The data shows good consistency.

[0156] Figure 18D Another example of an experiment with a validation loss of approximately 0.01 is shown. Similarly, for the four training breakthrough curves (left) and one validation breakthrough curve (right) in a single experiment, this is shown as a solid line from CADET, and the corresponding simulation from the general chromatography model is shown as a dashed line. The parameters for each simulation are indicated below each plot, i.e., in this experiment, the training data were generated with the following parameters: column volume 75 ml, time 33 min, fractionation 60 s, axial dispersion 1*10 -7 m 2 s -1 The length-to-volume ratio was 2.5, and the flow rates were 7.5, 10, 12.5, or 15 ml / min. Validation data were generated using the same parameters, except for a flow rate set to 5 ml / min. This is an example of a numerically challenging scenario due to stiffness and the limited number of relevant data points for the neural network. However, the data demonstrate that even under these challenging conditions, the general chromatographic model provides simulations with relatively high accuracy.

[0157] Figure 18E The validation loss is shown to be approximately 4.4 × 10. -3 (This is an example of an experiment with a median validation loss, meaning that 50% of all 180 experiments performed have a validation loss that is at least as low as this.) Similarly, for the four training breakthrough curves (left) and one validation breakthrough curve (right) in a single experiment, this would show the data from CADET as solid lines and the corresponding simulations from the general chromatography model as dashed lines. The parameters for each simulation are indicated below each figure, i.e., in this experiment, the training data were generated with the following parameters: column volume 15 ml, time 33 min, fractionation 90 s, axial dispersion 1*10 -5 m 2 s -1 The length-to-volume ratio was 5, and the flow rate was 3, 4, 5, or 6 ml / min. Validation data were generated using the same parameters, except that the flow rate was set to 2 ml / min. This demonstrates that the general chromatographic model can provide extremely accurate simulations (as mentioned above, this level of accuracy is more common in all experiments than the few outliers with lower accuracy, all of which can be explained by data generation problems or edge cases). The higher accuracy of the training data compared to the validation data (which was at an unseen flow rate) suggests that even higher validation accuracy can be obtained when evaluating data within the design space of the training data (rather than using parameters outside the parameter range of the training model).

[0158] References All references listed below and any documents mentioned in this specification are incorporated herein by reference in their entirety.

[0159]

[0160] Equivalents and scope Unless the context otherwise requires, the description and definition of the above features are not limited to any particular aspect or embodiment of the invention, and equally apply to all aspects and embodiments described. Any section headings used herein are for organizational purposes only and should not be construed as limiting the subject matter described.

[0161] As used herein, “and / or” is considered a specific disclosure of each of two specified features or components together or apart from the other. For example, “A and / or B” is considered a specific disclosure of each of (i) A, (ii) B, and (iii) A and B, as if each were stated separately herein. It must be noted that, unless the context clearly indicates otherwise, the singular forms “a / an” and “described” as used in this specification and the appended claims include a plural of the referred objects. Ranges may be expressed herein as from “about” a particular value and / or to “about” another particular value. When such a range is expressed, another embodiment includes from one particular value and / or to another particular value. Similarly, when a value is expressed as an approximation using the antecedent “about” or “approximately”, it should be understood that the particular value forms another embodiment. The terms “about” or “approximately” in relation to numerical values ​​are optional and mean, for example, + / - 10%. Throughout the specification, including the appended claims, unless the context otherwise requires, the words “comprising” and “including”, as well as variations such as “containing” and “covering”, shall be understood to implicitly include the indicated integers or steps or groups of steps, but do not exclude any other integers or steps or groups of steps. Other aspects and embodiments of the invention are provided for in the foregoing unless the context otherwise requires, wherein the term “comprising” is replaced by the terms “consisting of” or “substantially consisting of”.

[0162] Features disclosed in the foregoing specification or the following claims or drawings, expressed in their specific form or according to the means for performing the disclosed functions or the methods or processes for obtaining the disclosed results (as the case may be), may be used individually or in any combination of these features to implement the invention in various forms. While the invention has been described in conjunction with the exemplary embodiments described above, many equivalent modifications and variations will be apparent to those skilled in the art when this disclosure is given. Therefore, the exemplary embodiments set forth above are to be considered illustrative rather than restrictive. Various changes may be made to the described embodiments without departing from the spirit and scope of the invention as defined by the appended claims.

[0163] To avoid any doubt, any theoretical explanations provided herein are intended to enhance the reader's understanding. The inventor does not wish to be bound by any of these theoretical explanations.

Claims

1. A computer-implemented method for simulating a chromatographic process, wherein a feed stream comprising one or more products passes through a chromatographic unit comprising a stationary phase, the one or more products interacting with the stationary phase, the method comprising: The overall flow mass balance model is solved by numerical integration over one or more discrete volume elements along the chromatographic unit. The overall flow mass balance model is an ordinary differential equation model, which represents the concentration changes of bound and unbound fractions of one or more products in a discrete volume element. The ordinary differential equation model includes binding terms and diffusion terms, wherein the binding term captures the binding of the product to the stationary phase, and the diffusion term captures the diffusion of the bound product, wherein the binding term and the diffusion term are each parameterized by a single corresponding parameter predicted by a machine learning model trained to take as input the concentrations of the bound fractions and the unbound fractions of the one or more products in a discrete volume element, and to produce predictions of the parameters of the binding term and the diffusion term as output.

2. The method of claim 1, wherein the overall flow mass balance model comprises a linear term representing the flow of unbound compounds (products and optionally inert substances) into and out of the discrete volume element, and the binding term and the diffusion term, wherein the binding term captures the nonlinearity of the adsorption process of unbound products on the static phase by the machine learning model predicting the corresponding parameters of the term at each iteration of the numerical integration; and / or The overall flow mass balance model mentioned therein includes the following equations (1) and (2) and optional equation (3): Where f k It is the feed flow rate, and ΔV is the discrete volume element. n volume, It is the concentration vector of the unbound products in the discrete volume element n. The discrete volume element n The concentration vector of the binding product described in the text, The discrete volume element n The concentration vector of unbound products described in the previous discrete volume element, where the discrete volume elements are labeled sequentially from the input to the output of the chromatographic unit. The discrete volume element n The concentration vector of one or more inert substances. The discrete volume element n The concentration vector of the inert substance described in the previous discrete volume element, and It is an element-wise product.

3. The method of claim 1 or claim 2, wherein the overall flow mass balance model is solved on N discrete volume elements, wherein N is at least 2, wherein N is between 5 and 20, wherein N is between 5 and 15, wherein N is selected from 8, 9, 10, 11, 12, or wherein N is 10; and / or wherein the discrete volume elements comprise a plurality of discrete volume elements along the chromatographic unit in which binding and diffusion occur, the plurality of discrete volume elements preceding a discrete volume element in which no binding or diffusion occurs (inlet dead volume) and following a discrete volume element in which no binding or diffusion occurs (outlet dead volume).

4. The method of any of the preceding claims, wherein the overall flow mass balance model further represents the concentration change of one or more inert substances in the discrete volume element, and the machine learning model input further includes the concentration of the one or more inert substances in the discrete volume element, and / or wherein the machine learning model input further includes the feed flow rate.

5. The method of any of the preceding claims, wherein the machine learning model is a recurrent machine learning model, wherein the recurrent machine learning model is a machine learning model capable of taking into account one or more predictions made in one or more previous iterations of the numerical integral when making a prediction at the current iteration of the numerical integral.

6. The method of claim 5, wherein the machine learning model further includes the current iteration. k and discrete volume element n A cyclic state vector of one or more state values As input, and to produce an updated loop state vector This is output for use in subsequent iterations.

7. The method of claim 6, wherein the machine learning model comprises a parameter prediction sub-model and a recurrent state sub-model, wherein the recurrent state sub-model is configured to predict the updated recurrent state vector based on the input of the machine learning model. For use in subsequent iterations, and the parameter prediction sub-model is configured to predict the parameters of the combination term and the diffusion term based on the input of the machine learning model.

8. The method of any preceding claim, wherein the machine learning model comprises a cyclic state submodel and a parameter prediction submodel parameterized by corresponding weights learned simultaneously, and / or wherein the trained machine learning model is associated with the same learned weights for each discrete volume element and each iteration of the numerical integral, and / or wherein the machine learning model is a nonlinear regression model, and / or wherein the machine learning model comprises a neural network, optionally wherein the neural network is a fully connected neural network, a neural network comprising at least two hidden layers, a neural network comprising one to four hidden layers, a neural network comprising two or three hidden layers, and / or a neural network comprising eight to sixty nodes in each hidden layer.

9. The method of any preceding claim further comprises training the machine learning model using training data comprising feed concentration data and effluent concentration data from multiple chromatographic processes, and / or wherein the machine learning model has been trained using training data comprising feed concentration data and effluent concentration data from multiple chromatographic processes, wherein the feed concentration data is data indicating inlet product concentration and the effluent concentration data is data indicating outlet product concentration, optionally wherein the training data comprises feed concentration data and effluent concentration data respectively associated with corresponding discrete time points during the chromatographic process and / or feed concentration data and effluent concentration data associated with a time range during the chromatographic process, such as data collected using a fraction collector.

10. The method of claim 9, wherein training the machine learning model comprises iteratively updating the weights of the machine learning model in the following manner: For each of one or more training datasets, each comprising feed concentration data, effluent concentration data, and feed flow rate data corresponding to multiple time points during the chromatographic process, the overall flow mass balance model is solved using the values ​​of the parameters of the combining term and the diffusion term predicted by the machine learning model at the previous iteration of the training over discrete time intervals corresponding to multiple time points from the training datasets, wherein the feed rate trajectory corresponds to the feed flow rate data and the feed concentration data from the training datasets, thereby obtaining simulated data corresponding to each of the one or more training datasets; The loss function is used to evaluate and quantify the difference between the simulated data and one or more corresponding training datasets; as well as Optionally, a gradient descent procedure is used to update the weights of the machine learning model based on the weights of the machine learning model at the current iteration and the value of the loss function, until one or more predetermined stopping criteria are met.

11. The method of claim 10, wherein training the machine learning model comprises: In the first iteration of the iterative training, the weights of the machine learning model are set to initial weights corresponding to predetermined values ​​of the parameters of the combination term and the diffusion term. Optionally, setting the weights of the machine learning model to the initial weights includes: obtaining predetermined values ​​for the parameters of the combination term and the diffusion term, setting the weights of the machine learning model to default values, and pre-training the machine learning model, wherein the pre-training includes iteratively updating the weights of the machine learning model in the following manner: Using the machine learning model, and using the input of the machine learning model sampled from the training data, the values ​​of the parameters of the combination term and the diffusion term are predicted. A loss function is used to evaluate the difference between the predicted values ​​of the parameters of the combination term and the diffusion term and the predetermined values ​​of the parameters of the combination term and the diffusion term; and The weights of the machine learning model are updated based on the weights of the machine learning model in the current pre-training iteration and the value of the loss function.

12. The method of claim 11, wherein training the machine learning model comprises determining the predetermined values ​​of the parameters of the combination term and the diffusion term by performing one or both of the following: (a) Set the values ​​of the parameters of the diffusion term and the parameters of the binding term, or the corresponding parameters associated with the corresponding nonlinear binding term, to their respective default values. The overall flow mass balance model is solved by numerical integration using the default values ​​of the parameters of the diffusion term and the binding term, along with predetermined feed concentration and feed rate data, wherein optionally, the predetermined feed concentration and feed rate data are selected as the maximum values ​​of the feed rate and feed concentration observed in the training data. Determine whether the numerical integration failed to compute any solution to the model, and When the numerical integration fails to compute any solution to the model, the default values ​​of the parameters of the combination term and the diffusion term are updated by reducing the default values ​​by a predetermined factor; The above steps are repeated until the numerical integration can calculate all the solutions of the model in an iterative process, and the values ​​of the parameters of the combination term and the diffusion term are selected as those values ​​used in the iteration. (b) Set the values ​​of the parameters of the diffusion term and the parameters of the binding term, or the corresponding parameters associated with the corresponding nonlinear binding term, to their respective default values, optionally wherein the default values ​​are obtained using the method of step (a). For each of one or more training datasets, each including feed concentration data, effluent concentration data, and feed flow rate data corresponding to multiple time points during the chromatographic process, the overall flow mass balance model is solved using the default values ​​of the parameters of the combination term and the diffusion term, thereby obtaining simulated data corresponding to each of the one or more training datasets. The loss function is used to evaluate and quantify the difference between the simulated data and one or more corresponding training datasets; as well as Optionally, a gradient descent procedure can be used to update the default values ​​of the parameters of the combination term and the diffusion term based on the value of the loss function. The above steps are repeated until one or more predetermined stopping criteria are met.

13. The method of any preceding claim, wherein solving the overall flow mass balance model comprises: (a) Iteratively integrating the model over multiple discrete time intervals of a predetermined duration, wherein at each iteration, the machine learning model and a current state vector are used to obtain predictions of the parameters of the binding and diffusion terms for each discrete volume element, the current state vector including the concentration of the bound product in each discrete volume element at the most recent iteration, the concentration of the unbound product in each discrete volume element at the most recent iteration, and optionally the concentration of inert material in each discrete volume element at the most recent iteration, and optionally the feed rate; identifying the discrete state-space model using the overall flow mass balance model parameterized by the predictions; and determining an updated state vector corresponding to the time interval of the current iteration using the value of the current state vector and the coefficients of the discrete state-space model; and / or (b) Integrating the model for each of the one or more discrete volume elements at multiple discrete time points to obtain simulated data including the concentration of the product in the effluent of the chromatographic unit at the multiple discrete time points, wherein the method further includes using the simulated data to determine one or more of the following: effluent product concentration, product adsorption rate, product desorption rate, total product capture, dynamic binding capacity of the chromatographic process with respect to the product, product binding capacity per cycle, product recovery percentage, maximum breakthrough concentration with respect to the product, maximum breakthrough percentage with respect to the product, and cost associated with the simulated chromatographic process.

14. A method for monitoring or controlling a chromatographic process, the method comprising: (a) Simulating the chromatographic process using the method as described in any one of claims 1 to 13 and feed concentration data and feed flow rate data corresponding to the measured or planned feed concentration and feed flow rate of the chromatographic process, thereby obtaining a simulated effluent concentration corresponding to the effluent concentration of the chromatographic process; and The simulated effluent concentration or one or more indicators derived therefrom are compared with the observed effluent concentration or indicators derived therefrom, and based on the results of the comparison, it is determined whether the chromatographic unit should be refilled, whether the feed should be switched to a different column during multi-column chromatography, or whether there is a malfunction or aging condition in the chromatographic unit. And / or (b) Using the method as described in any of the preceding claims, the chromatographic process is simulated using multiple candidate sets of process parameters, each including at least a feed product concentration and a feed flow rate, to obtain simulated effluent concentrations for each candidate set of process parameters, and The simulated effluent concentration or one or more indicators derived therefrom are compared to select a set of process parameters from the set of candidate process parameters for operating the chromatographic process, optionally wherein the candidate set of process parameters includes the expected feed product concentration or feed flow rate.

15. A system comprising: At least one processor; and At least one non-transitory computer-readable medium, the at least one non-transitory computer-readable medium containing instructions that, when executed by the at least one processor, cause the at least one processor to perform the method as described in any of the preceding claims; Optionally, the system further includes one or more of the following items operably connected to the processor: Chromatographic unit; User interface; and One or more sensors.

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