Multi-objective optimization for molecular design

Abstract

Multiple molecular designs can be computationally generated. One or more characteristic computation models can be applied to determine multiple properties of each molecular design. Each characteristic computation model can be trained to approximate the probability distribution of possible values ​​for the corresponding property. A cumulative distribution function index corresponding to the predicted multivariate rank can be determined for each molecular design based on the output of the characteristic computation model. The multivariate rank of a molecular design can quantify the probability that none of its properties can be improved without degrading at least one other property. Based on the cumulative distribution function index of each molecular design, one or more molecular designs can be selected as candidates for wet lab evaluation. Molecular designs selected for wet lab evaluation may exhibit progressively better properties than those from previous design iterations.

Description

[Technical Field]

[0001] Cross-reference of related applications This application claims priority to U.S. Provisional Application No. 63 / 502,658, filed on 17 May 2023, entitled “Multipurpose Active Learning for Molecular Design,” and U.S. Provisional Application No. 63 / 515,447, filed on 25 July 2023, entitled “Multipurpose Active Learning for Molecular Design,” the disclosures of these U.S. Provisional Applications being incorporated herein by reference in their entirety.

[0002] Technical field The subject matter described herein generally relates to molecular design, and more specifically, to multi-purpose active learning techniques for molecular design. [Background technology]

[0003] Introduction A molecule is a group of two or more atoms held together by chemical bonds. Molecules form the smallest recognizable units that can divide a pure substance while still retaining its composition and chemical properties. Various properties of a molecule, including its ability to function as a therapeutic agent, can depend on the molecule's conformation (or three-dimensional structure). An example of a molecule is a small molecule, which is a low-weight compound with a molecular weight of approximately 100 to 1000 daltons. Small molecule therapeutics, which modulate biochemical processes to diagnose, treat, and prevent various diseases, form the basis of modern pharmacology due to several compelling advantages. For example, small molecule drugs can penetrate cell membranes to reach intracellular targets. Furthermore, small molecule drugs can be adapted to a wide variety of therapeutic applications. For example, small molecule drugs can be formulated as pills and capsules, intravenous or subcutaneous injections, inhalants, or suppositories. The development of small molecule drugs can be further extended to modulating various pharmacokinetic properties, including release, absorption, dispersion, metabolism, potency, efficacy, phenotypic effects, and excretion.

[0004] In contrast, large molecules (also known as biopharmaceuticals, biologics, or biological drugs) can have molecular weights ranging from approximately 3,000 to 150,000 daltons. Large molecule drugs are often derivatives of native human proteins that regulate many essential cellular functions such as enzymatic reactions, molecular transport, regulation and execution of several biological pathways, cell proliferation, growth, nutrient uptake, morphology, motility, and intercellular communication. A single large molecule commonly has more than 1,300 amino acid residues linked by peptide bonds to form one or more polypeptides. Due to their size and complexity, large molecule drugs are recombinantly produced by engineered cells, rather than being chemically synthesized like most small molecule drugs. Furthermore, large molecule therapeutics are usually delivered by injection or infusion due to the ineffectiveness of oral administration. The development of large molecule drugs can involve designing sequences of one or more amino acid residues that can bind to a target (e.g., protein, nucleic acid, etc.) with sufficient specificity and that do not possess undesirable properties such as immunogenicity, self-association, or instability. [Overview of the project]

[0005] A system, method, and product are provided, including a computer program product, for molecular design with multi-objective optimization, in which molecular designs are selected as candidates for wet lab evaluation (e.g., synthesis, in vitro measurement, in vivo characterization, etc.) based on multiple objectives. In one embodiment, a system for molecular design with multi-objective optimization is provided. The system may include at least one data processor and at least one memory. The at least one memory may store instructions that cause actions when executed by the at least one data processor. The operation may include generating multiple molecular designs, applying one or more property calculation models to determine multiple properties exhibited by the multiple molecular designs, the one or more property calculation models being trained and applied to approximate the probability distribution of each of the multiple properties, determining a cumulative distribution function (CDF) index for each of the multiple molecular designs based at least on the output of the one or more property calculation models, the cumulative distribution function (CDF) index of the molecular designs corresponding to the multivariate rank of the molecular designs, the multivariate rank of the molecular designs quantifying and determining the probability that none of the multiple properties present in the molecular design can be improved without degrading at least one of the other properties, and selecting one or more molecular designs from the multiple molecular designs as candidates for wet lab evaluation based at least on the cumulative distribution function (CDF) index of each molecular design.

[0006] In another embodiment, a method for molecular design involving multi-objective optimization is provided. This method may include generating a plurality of molecular designs, applying one or more characteristic computation models to determine a plurality of properties exhibited by the plurality of molecular designs, the one or more characteristic computation models being trained and applied to approximate the probability distribution of each of the plurality of properties, determining a cumulative distribution function (CDF) index for each of the plurality of molecular designs based at least on the output of the one or more characteristic computation models, the cumulative distribution function (CDF) index of the molecular designs corresponding to the multivariate rank of the molecular designs, the multivariate rank of the molecular designs quantifying and determining the probability that none of the plurality of properties present in the molecular design can be improved without degrading at least one of the other properties, and selecting one or more molecular designs from the plurality of molecular designs as candidates for wet lab evaluation based at least on the cumulative distribution function (CDF) index of each molecular design.

[0007] In another embodiment, a non-temporal computer program product for molecular design with multi-objective optimization is provided. The non-temporal computer program product may store instructions that trigger an action when executed by at least one data processor. The action may include generating a plurality of molecular designs, applying one or more characteristic calculation models to determine a plurality of properties exhibited by the plurality of molecular designs, the one or more characteristic calculation models being trained and applied to approximate the probability distribution of each of the plurality of properties, and determining a cumulative distribution function (CDF) index for each of the plurality of molecular designs based at least on the output of the one or more characteristic calculation models, the cumulative distribution function (CDF) index of the molecular designs corresponding to the multivariate rank of the molecular designs, the multivariate rank of the molecular designs quantifying and determining the probability that none of the plurality of properties present in the molecular design can be improved without degrading at least one of the other properties, and selecting one or more molecular designs from the plurality of molecular designs as candidates for wet lab evaluation based at least on the cumulative distribution function (CDF) index of each molecular design.

[0008] In some variations of the method, system, and non-temporary computer-readable medium, one or more of the following features may be included in any feasible combination:

[0009] In some variations, one or more characteristic computation models may be trained to approximate a first probability distribution of a first set of possible values ​​for a first characteristic among a set of characteristics. One or more characteristic computation models may be further trained to approximate a second probability distribution of a second set of possible values ​​for a second characteristic among a set of characteristics.

[0010] In some variations, the output of one or more characteristic calculation models may include multiple predicted samples from a first probability distribution and a second probability distribution. Each predicted sample may include a first value of the first characteristic and a second value of the second characteristic present in the molecular design.

[0011] In some variations, the cumulative distribution function (CDF) index for each molecular design may be determined by at least determining the marginal distribution of each of several properties based at least on the output of one or more property calculation models; determining one or more copulas that describe the cross-correlations between several properties based at least on the output of one or more property calculation models; and determining the cumulative distribution function (CDF) index for each molecular design based at least on the marginal distribution of each property and one or more copulas.

[0012] In some variations, the cumulative distribution function (CDF) index for each molecular design may be further determined by determining at least a third marginal distribution of a third of several properties, and by determining a second copula that combines the third marginal distribution with at least one of the first and second marginal distributions.

[0013] In some variant forms, the first and second copulas may be bivariate copulas that form a vine.

[0014] In some variant forms, Vine may be determined to exhibit a hierarchical structure corresponding to a partial order in which the first property takes precedence over the second and / or third properties.

[0015] In some variations, the cumulative distribution function (CDF) index for each molecular design may be determined by performing pairwise factorization of multivariate joint distributions corresponding to multiple properties to determine at least one pairwise grouping of multiple properties, wherein each pairwise grouping of multiple properties corresponds to a bivariate joint distribution, and by determining the bivariate copula that combines each pairwise grouping of multiple properties.

[0016] In some variant forms, the cumulative distribution function (CDF) index for each molecular design can be determined by determining the type of bivariate copula that combines each pairwise grouping of multiple properties, based at least on the tail behavior of the bivariate joint distribution.

[0017] In some variant forms, the type of bivariate copula can be one of the following: a Clayton copula, a Gambler copula, or a Gauss copula.

[0018] In some variations, the cumulative distribution function (CDF) index for each molecular design can be determined by at least determining the mean and covariance of several properties based at least on a set of measurements; at least determining a multivariate Gaussian distribution of several possible values ​​of several properties based at least on the mean and covariance of several properties; and at least determining the cumulative distribution function (CDF) index for each molecular design based at least on the multivariate Gaussian distribution.

[0019] In some variations, the cumulative distribution function (CDF) metric for each molecular design is determined at least by determining an empirical cumulative distribution function based at least on a measurement set, the empirical cumulative distribution function including a step function that increases by 1 / n for each of the n data points in the measurement set, the empirical cumulative distribution function outputting a value corresponding to the proportion of measurement values in the measurement set that are below a specified value for any specified value of a plurality of characteristics, and determining the cumulative distribution function (CDF) metric for each molecular design based at least on the empirical cumulative distribution function.

[0020] In some variations, the cumulative distribution function (CDF) metric for each molecular design can be determined by at least performing kernel density estimation (KDE) to estimate a multivariate joint distribution corresponding to a plurality of characteristics, and determining the cumulative distribution function (CDF) metric for each molecular design based at least on the estimated value of the multivariate joint distribution.

[0021] In some variations, the cumulative distribution function (CDF) metric for each molecular design can be a predicted cumulative distribution function (CDF) metric determined such that its value accounts for the uncertainty in the output of one or more characteristic calculation models.

[0022] In some variations, one or more molecular designs can be selected as candidates for wet-lab evaluation based at least on one or more molecular designs having a better cumulative distribution function (CDF) metric than one or more molecular designs generated during previous iterations of multi-objective Bayesian optimization.

[0023] In some variations, a first molecular design can be selected as a candidate for wet-lab evaluation based at least on a first cumulative distribution function (CDF) metric of the first molecular design that meets one or more thresholds. A second molecular design can be excluded from candidates for wet-lab evaluation based at least on a second cumulative distribution function (CDF) metric of the second molecular design that does not meet one or more thresholds.

[0024] In some variants, the first molecular design may be selected as a candidate for wet lab evaluation instead of the second molecular design, at least on the basis that the first cumulative distribution function (CDF) index of the first molecular design is better than the second cumulative distribution function (CDF) index of the second molecular design.

[0025] In some variations, a threshold quantity for molecular designs with the best cumulative distribution function (CDF) index can be selected as a candidate for wet lab evaluation, based at least on the cumulative distribution function (CDF) index of each molecular design.

[0026] In some variants, a set of measurements associated with multiple previous molecular designs may be received. For each previous molecular design, the measurement set may include one or more measurements of multiple properties exhibited by each previous molecular design. Based on at least the measurement set, one or more property calculation models may be trained to approximate the probability distribution of each of the multiple properties.

[0027] In some variants, one or more additional measurements of several properties may be received for one or more molecular designs selected as candidates for wet lab evaluation. One or more characterization models may be retrained based on at least one or more additional measurements. One or more retrained characterization models may be applied to determine several properties exhibited by one or more subsequent molecular designs.

[0028] In some variations, retraining one or more characteristic calculation models may involve updating the probability distribution of each of the multiple characteristics approximated by one or more characteristic calculation models, based on at least one or more additional measurements.

[0029] In some variants, multiple previous molecular designs may be generated during preceding iterations of multi-objective Bayesian optimization (MOBO). Multiple molecular designs may be generated during the current design iteration of multi-objective Bayesian optimization (MOBO). One or more subsequent molecular designs may be generated during subsequent iterations of multi-objective Bayesian optimization (MOBO).

[0030] In some variations, one or more characteristic calculation models may include at least one ensemble of characteristic calculation models, where multiple characteristic calculation models are trained to determine a single characteristic among multiple characteristics.

[0031] Embodiments of this subject matter include, but are not limited to, methods of operation as described herein, and articles comprising a tangibly embodied machine-readable medium capable of operating one or more machines (e.g., a computer) to produce operations that implement one or more of the features described herein. Similarly, computer systems are also described, which may include one or more processors and one or more memories coupled to one or more processors. A memory, which may include a non-temporary computer-readable or machine-readable storage medium, may contain, code, or store one or more programs causing one or more processors to perform one or more of the operations described herein. Computer implementations consistent with one or more embodiments of this subject matter may be implemented by one or more data processors residing in a single computing system or multiple computing systems. Such multiple computing systems may be connected and exchange data and / or commands or other instructions, etc., over one or more connections, including, for example, connections over a network (e.g., the Internet, a wireless wide area network, a local area network, a wide area network, a wired network, etc.), connections via direct connections between one or more of the multiple computing systems.

[0032] Details of one or more variations of the subject matter described herein are described in the accompanying drawings and the following description. Other features and advantages of the subject matter described herein will become apparent from the description and drawings, as well as from the claims. Certain features of the subject matter now disclosed are described for illustrative purposes in relation to the design of larger molecules such as protein molecules, but it should be readily understood that such features are not intended to be limiting. The claims following this disclosure define the scope of the subject matter protected. [Brief explanation of the drawing]

[0033] The accompanying drawings incorporated herein and constituting part of this specification illustrate specific aspects of the subject matter disclosed herein and, together with the description, help to illustrate some of the principles relating to the disclosed embodiments. The drawings depict the following:

[0034] [Figure 1] A system diagram illustrating an example of a molecular design system based on several exemplary embodiments.

[0035] [Figure 2A] A flowchart illustrating an example of a process for molecular design involving multi-objective optimization, based on several exemplary embodiments.

[0036] [Figure 2B] A flowchart illustrating another example of a process for molecular design involving multi-objective optimization, based on several exemplary embodiments.

[0037] [Figure 2C] A flowchart illustrating another example of a process for molecular design involving multi-objective optimization, based on several exemplary embodiments.

[0038] [Figure 3A] A flowchart illustrating an example of the process for determining the properties of a molecular design, based on several exemplary embodiments.

[0039] [Figure 3B] A flowchart illustrating another example of the process for determining the properties of a molecular design, using several exemplary embodiments.

[0040] [Figure 4A] A graph illustrating a comparison of different utility metrics, including hypervolume, multivariate rank, and cumulative distribution function (CDF) indices, using several exemplary embodiments.

[0041] [Figure 4B] A graph illustrating another comparison of different utility metrics, including hypervolume, multivariate rank, and cumulative distribution function (CDF) indices, using several exemplary embodiments.

[0042] [Figure 4C] A graph showing a comparison of contour lines of the cumulative distribution function (CDF) and probability distribution function (PDF) from kernel density estimation (KDE) in several exemplary embodiments.

[0043] [Figure 5A] A schematic diagram illustrating an example of a multivariate joint distribution estimated using marginal distributions and copulas that join these marginal distributions, according to several exemplary embodiments.

[0044] [Figure 5B] A schematic diagram illustrating an example of vine copula decomposition by several exemplary embodiments.

[0045] [Figure 5C] A schematic diagram illustrating the use of copulas in the context of optimizing multiple objectives in tasks with sparse data, using several exemplary embodiments.

[0046] [Figure 6] A graph illustrating a comparison of rescaling different utility metrics, including the cumulative distribution function (CDF) index and hypervolume, using several exemplary embodiments.

[0047] [Figure 7] A graph showing the changes in the values ​​of hypervolume (HV) and cumulative distribution function (CDF) indices of molecular designs obtained over simulation iterations of Bayesian optimization for the Branin-Currin test function and the DTLZ problem set, in several exemplary embodiments.

[0048] [Figure 8] A graph illustrating a comparison of the time costs of different acquisition functions, including improvement-based acquisition functions and multivariate ranking-based acquisition functions, across several exemplary embodiments.

[0049] [Figure 9A] A figure showing two examples of molecules exhibiting desirable properties, according to several exemplary embodiments.

[0050] [Figure 9B] A figure illustrating examples of molecules exhibiting undesirable properties in several exemplary embodiments.

[0051] [Figure 10] A block diagram illustrating an example of a computing system in several exemplary embodiments.

[0052] In practical terms, similar reference numbers indicate similar structures, features, or elements. [Modes for carrying out the invention]

[0053] Molecules can be designed to exhibit multiple desirable properties, including drug-like properties such as affinity, specificity, biological activity, and suitability for development, in the case of therapeutic agents. In some cases, whether a molecule exhibits a particular desirable property may depend on whether the molecule can assume a corresponding conformation (or three-dimensional structure). For example, the binding affinity between a drug molecule and a target molecule (e.g., protein, nucleic acid, etc.) may depend on the ability of the drug molecule to assume a conformation (or three-dimensional structure) complementary to the conformation of the target molecule. Therefore, in some cases, designing a molecule may involve determining its composition and conformation (or three-dimensional structure). For example, in the case of small molecules (e.g., low-weight compounds with a molecular weight of about 100-1000 daltons), the design process may involve scoring and ranking different molecules selected from at least a portion of the molecular space (or chemical space) occupied by all possible chemical compounds (e.g., any possible combination of atoms of two or more chemical elements). For larger molecules such as protein molecules, whose primary structure is a linear sequence of amino acid residues linked from one or more polypeptide chains, the design process may include determining the identity of the amino acid residues in each polypeptide chain and the conformation (or three-dimensional structure) that is expected by the folding of the polypeptide chains.

[0054] Despite the time and cost efficiency achieved by adopting in silico design tools, computational molecular design remains a challenging task when approached with conventional brute-force methods that generate molecular designs through indiscriminate searching of a vast combination space of possible molecular compositions and conformations. This is because the nearly infinite number of possible molecular compositions and conformations is overwhelming, even for state-of-the-art computational resources. For example, for small molecules, the molecular space (or chemical space) is 10⁻¹⁰ 60It is estimated to contain 1000 possible chemical compounds, scaling exponentially with molecular size (e.g., the number of constituent atoms), meaning that state-of-the-art computing resources can only support the exploration of a small fraction of the molecular space (e.g., a small region of molecular space selected based on prior expertise). The size of the combination space is larger for larger molecules and biologics. For example, for a protein molecule containing N amino acid residues, if each of the N amino acid residues is one of 20 standard amino acid residues, then approximately 20 N There are 20 possible protein sequences. N Each of the n possible protein sequences can further take on an exponential number of conformations (or three-dimensional structures). Each of the N amino acid residues in a possible protein sequence can take on M N Even when limited to assuming one of several discrete geometric states (e.g., rotational isomers), the aforementioned 20 N All of the possible protein sequences are still M N It can take on a number of possible conformations (or three-dimensional structures).

[0055] In some exemplary embodiments of this disclosure, molecular design engines can improve upon current practices of indiscriminate exploration of a vast combination space of possible molecular compositions and conformations (or three-dimensional structures). Rather, the molecular design engines of this disclosure can, in principle, generate one or more molecular designs by sampling a data distribution of molecules exhibiting one or more desirable properties. For example, in some cases, a molecular design engine can generate one or more molecular designs by sampling a data distribution of protein molecules or non-protein molecules such as small molecules, ions, nucleic acids, polysaccharides, glycolipids, etc. In the case of drug design, the data distribution may be occupied by molecules exhibiting drug-like properties such as affinity, specificity, biological activity, development suitability, etc. In some cases, a molecular design engine may include a molecular design computation model trained to approximate a data distribution such that one or more molecular designs can be generated by sampling one or more molecular designs from regions within the data distribution that are more likely to be occupied by one or more molecules exhibiting one or more desirable properties. For example, in some cases, a molecular design computation model may be trained to approximate a data distribution based on a training dataset of known molecules exhibiting one or more desirable properties.

[0056] In some exemplary embodiments, training a molecular design computation model to approximate a data distribution may involve adjusting one or more parameters of the molecular design computation model (e.g., weights, biases, etc.) to increase (or maximize) the similarity between the molecular designs output by the molecular design computation model and known molecules in the training dataset. In some cases, doing so may also involve determining a function (e.g., score function, energy function, etc.) that distinguishes its output (e.g., score, energy value, etc.) from high-density regions of the data distribution that are more likely to be occupied by molecules exhibiting one or more desirable properties to low-density regions of the data distribution that are less likely to be occupied by molecules exhibiting one or more desirable properties. Thus, once trained, the molecular design computation model can be applied to generate one or more molecular designs. For example, one or more molecular designs may be generated by one or more iterations of gradient-based Markov chain Monte Carlo (MCMC) sampling (e.g., Markov chain Monte Carlo (MCMC) sampling with Langevin dynamics, etc.). In some cases, each iteration of gradient-based Markov chain Monte Carlo (MCMC) sampling may involve extracting a sample (or molecule) from the data distribution, for example, by applying a molecular design computation model to modify the initial molecular design of a known molecule or a noise molecule. Sampling may also be performed based on a function (e.g., a score function, an energy function, etc.), and each successive sampling iteration involves extracting a sample (or molecule) from an increasingly dense region of the data distribution.

[0057] While molecular design computation models can accelerate the generation of molecular designs, the limited availability and exorbitant costs of laboratory resources still impose significant obstacles to the speed at which molecular designs generated by these models can undergo wet-lab evaluation. For example, in a typical drug development pipeline, molecular designs must be validated in vitro and undergo multiple optimizations before they can proceed to preclinical development and clinical trials where the performance of the molecule is tested in vivo. Even if molecular design computation models can generate a large number of molecular designs (e.g., millions of molecular designs) quickly and at relatively low cost, practical limitations on wet-lab resources make wet-lab evaluation of all molecular designs impossible. Instead, only a subset of molecular designs generated by molecular design computation models may be selected for wet-lab evaluation, including, for example, in vitro measurements and in vivo characterization.

[0058] In some exemplary embodiments, molecular designs may be computationally generated and evaluated in a web lab across multiple consecutive design iterations, with each design iteration generating one or more molecular designs that have better molecular properties than those from previous design iterations. However, indiscriminate selection of molecular designs for wet lab evaluation may lead to better designs being overlooked, while those with suboptimal molecular properties, such as suboptimal pharmacological and physicochemical properties, may advance to subsequent stages of the drug development pipeline, increasing the risk of failure along the way. Therefore, instead of indiscriminate selection of molecular designs, those selected for wet lab evaluation during the current design iteration should exhibit better molecular properties than those from previous design iterations. As will be described in more detail below, in some exemplary embodiments, the selection engine may perform multi-objective optimization, such as multi-objective Bayesian optimization (MOBO), across a mixed set of variable molecular properties when identifying which molecular designs generated by the molecular design computation model should be selected for further wet lab evaluation (e.g., in vitro measurements, in vivo characterization, etc.). In this context, each objective may correspond to molecular properties (e.g., drug-like properties such as affinity, specificity, biological activity, and suitability for development) that have been optimized across multiple computational molecular designs and wet lab evaluations. Therefore, in some cases, the selection engine can perform multi-objective optimization by exploring the objective space occupied by various molecular designs, each having a different combination of objectives (or molecular properties). Doing so in principle increases the likelihood that a better molecular design, such as one exhibiting better molecular properties than those from previous design iterations, will be selected for wet lab evaluation (e.g., in vitro measurements, in vivo characterization, etc.).

[0059] In some exemplary embodiments, the selection engine may perform multi-objective Bayesian optimization (MOBO) to explore the aforementioned objective space in principle. For example, the selection engine may apply one or more characteristic computation models trained to approximate a first probability distribution of possible values ​​for a first characteristic and a second probability distribution of possible values ​​for a second characteristic. That is, one or more characteristic computation models may be applied to determine one or more predicted samples from the first and second probability distributions for each molecular design generated by the molecular design engine. Each predicted sample in this case may include a first value for the first characteristic and a second value for the second characteristic present in the molecular design. In this regard, one or more characteristic computation models may serve as in silico surrogates for in vitro and / or in vivo evaluations that are too resource-intensive to apply to all molecular designs generated by the molecular design computation model, as described. In some cases, multi-objective Bayesian optimization (MOBO) may involve trade-offs between exploring and utilizing the objective space. For example, in some cases, multi-objective Bayesian optimization (MOBO) may involve sampling molecular designs from the objective space to balance the search for highly uncertain molecular designs (e.g., molecular designs with highly uncertain molecular properties) with the search for those that are more likely to increase or maximize the objective (e.g., molecular designs that are more likely to exhibit better molecular properties).

[0060] In some exemplary embodiments, one or more characteristic calculation models may be implemented as one or more stochastic surrogate models to account for the uncertainty associated with predicting the molecular properties of each molecular design. Since one or more characteristic calculation models are trained against wet lab measurements of individual molecular properties, this uncertainty may be at least in part due to noise that may be present in those wet lab measurements. Therefore, in some cases, each characteristic calculation model may be implemented as a stochastic surrogate model trained to approximate the probability distribution of possible values ​​of the corresponding molecular property exhibited by its molecular design. Furthermore, in some cases, one or more characteristic calculation models may output one or more predicted samples of each molecular design generated by the molecular design engine, at least based on the probability distribution. For example, if a molecular design is optimized for two objectives (or molecular properties), each predicted sample may include a first value of the first property exhibited by the first molecular design, and a second value of the second property exhibited by the first molecular design having the first value of the first property.

[0061] In some exemplary embodiments, the selection engine can perform multi-objective Bayesian optimization (MOBO) and explore the objective space in principle to identify one or more molecular designs that satisfy specific criteria for several molecular properties (e.g., drug-like properties) based on predicted samples output by one or more property computation models. It should be understood that these criteria do not necessarily mean that a molecular design has the best values ​​for all molecular properties of interest (e.g., maximum expression level and maximum binding affinity), as there may be cases where at least one such molecular design does not exist. Instead, at least some of the molecular properties of interest may be competitive in that improving one molecular property may hinder one or more other molecular properties. Thus, the selection engine can perform multi-objective Bayesian optimization (MOBO) to identify molecular designs in which the properties cannot be further improved without degrading at least one other property. In some cases, such molecular designs may be called Pareto optimal solutions or non-dominant solutions. A set of Pareto optimal solutions that may include one or more such molecular designs may form a Pareto frontier (or Pareto front). Therefore, in some cases, the selection engine may perform multi-objective Bayesian optimization (MOBO) during each design iteration to determine a set of Pareto optimal solutions as candidates for wet lab evaluation.

[0062] In some exemplary embodiments, each Pareto optimal solution may be identified by a selection engine that applies an acquisition function. In some cases, the acquisition function may output a utility metric for each molecular design generated by a molecular design computation model, indicating the predicted utility of the molecular design. For example, in the context of drug design, the utility metric of a molecular design may correspond to the probability that the molecular design is one of the Pareto optimal solutions occupying the Pareto frontier. In some cases, the utility metric of a molecular design may correspond to the distance (or proximity) between the molecular design and the Pareto frontier, meaning that the molecular design can be considered a Pareto optimal solution on the Pareto frontier if its utility metric satisfies one or more thresholds. As mentioned, in some cases, molecular designs that qualify as Pareto optimal solutions because their utility metric satisfies one or more thresholds may be identified as candidates for wet lab evaluation (e.g., in vitro measurements, in vivo characterization, etc.). Furthermore, in some cases, at least some of the molecular designs included in the set of Pareto optimal solutions identified for the current design iteration can serve as baseline molecular designs for one or more subsequent design iterations, and may play a role as a basis for identifying the next set of Pareto optimal solutions.

[0063] In some exemplary embodiments, instead of the conventional acquisition function used in multi-objective Bayesian optimization (MOBO), the selection engine may apply a multivariate ranking-based acquisition function. Doing so reduces the time cost of identifying Pareto optimal solutions across multiple frequently competing objectives (or molecular properties of interest), as conventional acquisition functions do not adequately scale to accommodate the larger number of objectives (or molecular properties of interest) typically found in the context of drug design. For example, conventional acquisition functions are sensitive to non-informative transformations of individual objectives, such as rescaling one objective to another, or even monotonic transformations of a single objective. Such transformations are often performed to standardize across different units of measurement common to different objectives (or molecular properties of interest) in drug design.

[0064] Improvement-based acquisition functions are an example of conventional acquisition functions with low time complexity. When a selection engine applies an improvement-based acquisition function, for example, the resulting utility metric may correspond to the difference between the first hypervolume of a first polytope bounded by a combination of molecular properties associated with a molecular design, and the second hypervolume of a second polytope bounded by a combination of molecular properties associated with a baseline molecular design. However, the time complexity of calculating hypervolumes (HVs) that need to determine the volume of irregularly shaped polytopes scales hyperpolynomially depending on the number of objectives (or molecular properties of interest). Thus, despite the efficiency of some state-of-the-art techniques for calculating hypervolumes, such as box decomposition, applying improvement-based acquisition functions to identify Pareto optimals remains slow, even if the number of objectives (or molecular properties of interest) is relatively small.

[0065] Another example of a conventional acquisition function is an entropy-based acquisition function that focuses on increasing (or maximizing) the information gain from subsequent observations (e.g., the next set of Pareto optimals). However, while improvement-based acquisition functions require computing the volume of a volume of irregular shape, entropy-based acquisition functions require computing a higher-dimensional definite integral. For example, in some cases, the utility metric for an entropy-based acquisition function may be determined by computing a higher-dimensional definite integral of an M-dimensional multivariate Gaussian distribution, where M is the number of objectives (or molecular properties of interest). Even with more efficient techniques such as box decomposition, the higher-dimensional definite integral of an M-dimensional multivariate Gaussian distribution is more costly to evaluate than hypervolume (HV).

[0066] In some exemplary embodiments, the time cost of identifying Pareto optimal solutions across multiple objectives (or molecular properties of interest), particularly a large number of objectives in the case of drug design, can be reduced by a selection engine that applies a multivariate ranking-based acquisition function. For example, in some cases, the multivariate ranking-based acquisition function may output a utility metric corresponding to the predicted multivariate rank of each molecular design generated by the molecular design computation model. In some cases, the predicted multivariate rank of a molecular design may be a ranking of the molecular design based on several properties present in the molecular design. In the context of antibody design, for example, the multivariate rank of a molecular design may be a ranking of the molecular design based on its expression level, affinity, and development suitability properties. The multivariate ranking-based function can output a predicted multivariate rank of each molecular design to account for uncertainties that may exist in the output of a stochastic surrogate model. In some cases, the multivariate rank of a molecular design may correspond to the probability that the molecular design is one of the Pareto optimal solutions occupying the Pareto frontier. Therefore, in some cases, the predicted multivariate rank of a molecular design can indicate its distance (or proximity) to the true Pareto frontier (or Pareto front). Furthermore, in some cases, the multivariate rank of a molecular design can quantify the quality of the molecular design as a Pareto optimal solution, meaning that molecular designs closer to the Pareto frontier may be associated with different multivariate ranks than molecular designs further from the Pareto frontier.

[0067] However, unlike ranking multiple molecular designs based on a single objective (or molecular property of interest), determining the multivariate rank of individual molecular designs that is equivalent to a higher-dimensional ranking based on multiple objectives (or molecular properties of interest) remains a non-trivial task. This is because, when the number M of objectives (or molecular properties of interest) is greater than 1 (e.g., M ≥ 2), there is no natural order (or ranking) in Euclidean space. Therefore, in some exemplary embodiments, a selection engine may determine a cumulative distribution function (CDF) index that coincides with the multivariate rank of molecular designs as a utility metric for each molecular design generated by a molecular design computation model. Furthermore, in some cases, the Pareto optimal solution for each design iteration can be identified based on the cumulative distribution function (CDF) index of each molecular design generated by a molecular design computation model. For example, in some cases, molecular designs that are Pareto optimal solutions on the Pareto frontier may be associated with the same (or linked) multivariate rank, which means that the corresponding cumulative distribution function (CDF) index is also the same (or linked). The cumulative design function (CDF) metric for molecular designs can be estimated in a variety of different ways, including the use of copulas, empirical cumulative distribution functions (CDFs), kernel density estimation (KDEs), and multivariate Gaussian cumulative distribution functions (CDFs). As will be discussed in more detail below, when estimated using copulas, the cumulative distribution function (CDF) metric for each molecular design can be a particularly robust utility metric with higher scalability than hypervolume (HV).

[0068] In some exemplary embodiments, a cumulative distribution function (CDF) index of molecular designs can quantify the quality of a molecular design as a Pareto optimal solution by indicating at least the probability that the molecular design has a larger function value than other molecular designs. When there is a single objective (or molecular property of interest), the cumulative distribution function (CDF) index of a molecular design can represent the probability that the value of the molecular property exhibited by the molecular design satisfies one or more thresholds. When there are two or more objectives (or molecular properties of interest), the cumulative distribution function (CDF) index of a molecular design becomes the multivariate joint distribution corresponding to the highest multivariate rank of the molecular design. As mentioned above, calculating the multivariate joint distribution is a computationally difficult task, sometimes involving estimating the multivariate density function before calculating its integral; therefore, ranking molecular designs in high dimensions is at least a non-trivial task. Thus, in some cases, a selection engine can determine a cumulative distribution function (CDF) index for a molecular design by decomposing at least the corresponding multivariate joint distribution into two or more constituent marginal distributions and a combined function called a copula. For example, as will be explained in more detail below, the selection engine can decompose a multivariate joint distribution into one or more bivariate joint distributions, each containing marginal distributions of two or more paired groups of objectives (or molecular properties of interest). Furthermore, the multivariate joint distribution can be decomposed into one or more bivariate copulas, each combining a single paired grouping of objectives (or molecular properties of interest). These bivariate copulas can form a kind of dependency model called a vine copula. In some cases, further computational efficiency can be achieved by truncating one or more copulas. By doing so, higher-order dependencies between some objectives (or molecular properties of interest) that are trivial enough to be ignored when determining the cumulative distribution function (CDF) index of each molecular design can be eliminated. However, it should be understood that some copulas may be preserved during truncation to maintain dependencies between some objectives (or molecular properties of interest) that include a partial order in which some objectives (or molecular properties of interest) take precedence over others.

[0069] In some exemplary embodiments, the selection engine can determine the cumulative distribution function (CDF) index of a molecular design by at least estimating a copula (e.g., a bivariate copula) that combines the marginal distributions of each constituent objective (or molecular property of interest). For example, if a molecular design is optimized for a first property and a second property, the cumulative distribution function (CDF) index of the molecular design may be determined by estimating a copula that combines the first marginal distribution of possible values ​​for the first property and the second marginal distribution of possible values ​​for the second property. In this regard, the copula can describe a dependency structure (e.g., a copula matrix) that specifies the cross-correlation between the possible values ​​of the first property and the possible values ​​of the second property. It should be understood that the marginal distributions of the possible values ​​of the first property are probability distributions of those values ​​independent of the possible values ​​of the second property. On the other hand, the marginal distributions of the possible values ​​of the second property are probability distributions of those values ​​independent of the possible values ​​of the first property. If the molecular design is further optimized for a third property, the selection engine can determine the cumulative distribution function (CDF) index by determining at least a set of bivariate copulas, each describing the cross-correlations between pairwise groupings of the first, second, and third properties. The computational complexity of using copulas to estimate the cumulative distribution function (CDF) index of the molecular design can be lower than the computational complexity of determining the underlying multivariate joint distribution, since at least each marginal distribution and its corresponding copula can be estimated separately.

[0070] In some exemplary embodiments, the selection engine may determine a set of bivariate copulas by performing pairwise factorization, where objectives (or molecular properties of interest) are grouped in pairs. In some cases, vine copulas may form a cascade of bivariate copula blocks. The resulting vine structure may include a nested tree hierarchy called vines, which allows for the execution of dependencies between different objectives (or molecular properties of interest). For example, if a molecular design is optimized for a first and second property, the partial order of the first and second properties may require that the first property of the molecular design meets a first criterion before the molecular design is evaluated to determine whether the second property of the molecular design meets a second criterion. In the context of antibody design, this partial order may reflect experimental and / or biological dependencies that the molecular design must reach a certain level of expression before a sufficient amount of the molecular design can be synthesized and assayed for other properties, such as binding affinity to a target antigen. Therefore, in some cases, pairwise factorization may be performed to group desired (or molecular properties of interest) such that the resulting hierarchy of vine structures includes two or more conditional copulas that encode a partial order in which, for example, a first property takes precedence over a second property.

[0071] In some exemplary embodiments, the selection engine may apply an active learning technique in which one or more molecular designs selected for wet lab evaluation during the current design iteration become baseline molecular designs during subsequent design iterations. For example, a first molecular design selected for wet lab evaluation during the current design iteration may become one of the baseline molecular designs during subsequent designs. Thus, in some cases, the selection engine may select a second molecular design generated by a molecular design computation model during subsequent design iterations based at least on the utility metric of the second molecular design, the utility metric of the second molecular design being an improvement over the utility metric of the baseline molecular design and, optionally, the utility metrics of other molecular designs generated for that design iteration. The value of the trait used to determine the utility metric of the first molecular design may be determined based on the output of one or more trait computation models. Alternatively and / or additionally, the value of each trait present in the first molecular may be determined based on one or more in vitro measurements or in vivo characterizations related to the first molecular design. In the latter case, in order to reduce (or minimize) the impact of this noise on the utility metric calculated therefrom, the values ​​of each characteristic present in the first molecular design may be determined based on the output of one or more characteristic calculation models, after one or more characteristic calculation models have been updated and then retrained, for example, on one or more in vitro measurements or in vivo characterizations associated with the first molecular design.

[0072] Figure 1 shows a system diagram illustrating an example of a molecular design system 100 according to several exemplary embodiments. Referring to Figure 1, the molecular design system 110 may include a molecular design engine 110, a selection engine 120, one or more wet laboratory instruments 130, and a client device 140. As shown in Figure 1, the molecular design engine 110, the selection engine 120, one or more laboratory instruments 130, and the client device 140 may be communicatively coupled via a network 150. One or more laboratory instruments 130 may include any wet lab equipment and dry laboratory equipment capable of performing in vitro measurements and / or in vivo characterization. Examples of one or more laboratory instruments 130 may include a sequencer, mass spectrometer, centrifuge, etc. The client device 140 may be a processor-based device including, for example, a workstation, desktop computer, laptop computer, smartphone, tablet computer, wearable device, etc. Network 150 may be a wired network and / or wireless network, including, for example, a local area network (LAN), a virtual local area network (VLAN), a wide area network (WAN), a public land mobile network (PLMN), or the internet.

[0073] Referring again to Figure 1, the molecular design engine 110 may apply the molecular design computation model 115 to generate multiple molecular designs, including, for example, a first molecular design 160a, a second molecular design 160b, and so on. For example, the first molecular design 160a and the second molecular design 160b may, in some cases, correspond to protein molecules or non-protein molecules such as small molecules, ions, nucleic acids, polysaccharides, glycolipids, etc. Furthermore, in some cases, the molecular design computation model 115 may be a machine learning model trained to approximate a data distribution of molecules exhibiting one or more desirable properties (e.g., drug-like properties such as affinity, specificity, biological activity, development suitability, etc.). In some cases, the molecular design computation model 115 may be trained by adjusting one or more parameters of the molecular design computation model 115 to increase (or maximize) the similarity between the molecular designs output by the molecular design computation model 115 and known molecules in a training dataset (e.g., known molecules exhibiting one or more desirable properties). Doing so may involve the parameters corresponding to the parameters of the molecular design calculation model 115, and its output (e.g., score, energy value, etc.) determining a function (e.g., score function, energy function, etc.) that distinguishes different density regions of the data distribution. In some cases, high-density regions of the data distribution may be more likely to be occupied by one or more molecules exhibiting desirable properties than low-density regions of the data distribution. Therefore, once trained, the molecular design calculation model 115 may sample from the data distribution to generate one or more molecular designs, including, for example, a first molecular design 160a, a second molecular design 160, etc. For example, each molecular design, such as the first molecular design 160a and the second molecular design 160b, may be generated by one or more iterations of gradient-based Markov chain Monte Carlo (MCMC) sampling (e.g., Langevin Markov chain Monte Carlo (MCMC) sampling).Sampling may be induced by the output of a function (e.g., score, energy value, etc.) such that each iteration of gradient-based Markov chain Monte Carlo (MCM) sampling involves drawing a sample (or molecule) from an increasingly dense region of the data distribution.

[0074] In some exemplary embodiments, the molecular design engine 110 can generate a large number of molecular designs, but not all molecular designs generated by the molecular design engine 110 are eligible for wet lab evaluation, such as in vitro measurements and in vivo characterization. In some cases, practical limitations, including limited availability of laboratory resources and exorbitant costs, may prevent at least some molecular designs generated by the molecular design engine 110 from undergoing wet lab evaluation. However, molecular designs selected for wet lab evaluation should, in some cases, exhibit satisfactory characteristics, including a combination of properties (e.g., drug-like properties) that are superior to those from previous design iterations that have already undergone wet lab evaluation. Therefore, in some cases, the selection engine 120 can perform one or more iterations of active learning to identify one or more molecular designs that meet specific criteria for one or more properties (e.g., drug-like properties) for synthesis and testing by one or more laboratory instruments 130. In some cases, one or more criteria associated with a property (e.g., drug-like property) may include values ​​of the property, such as satisfying one or more thresholds, falling within an interval of one or more values, or being a member of a set. For example, in the case of antibody design, the selection engine 120 may perform one or more iterations of active learning to identify one or more molecular designs that exhibit sufficient expression levels and appropriate binding affinity to the target antigen. Furthermore, depending on the circumstances, the selection engine 120 may perform one or more iterations of active learning to identify one or more molecular designs that, in addition to having sufficient expression levels and appropriate binding affinity, also exhibit specific development suitability such as specificity and thermal stability.

[0075] In some exemplary embodiments, the selection engine 120 can identify molecular designs for wet lab evaluation by determining at least a utility metric indicating the predicted utility of the molecular designs. In some cases, the utility metric of a molecular design may correspond to the probability that the molecular design is a Pareto optimal solution that exhibits a combination of properties (e.g., drug-like properties) superior to one or more baseline molecular designs. In some cases, a molecular design being a Pareto optimal solution may mean that none of the properties of the molecular design can be further improved without degrading at least one other property of the molecular design. For example, if the selection engine 120 optimizes a first property and a second property, a Pareto optimal molecular design may exhibit a first value for the first property that cannot be further improved without degrading a second value of the second property present in the molecular design. In some cases, the design engine 110 can determine the utility metric of a molecular design by applying at least an acquisition function. However, to avoid the excessive computational complexity of conventional acquisition functions (e.g., improvement-based acquisition functions, entropy-based acquisition functions, etc.) or the naive application of multivariate ranking-based acquisition functions, the selection engine 120 can determine a cumulative distribution function (CDF) index corresponding to the multivariate rank of the molecular design as a utility metric for the molecular design. As will be described in more detail below, in some cases, the selection engine 120 can apply a cumulative distribution function (CDF) acquisition function to determine a cumulative distribution function (CDF) index corresponding to the predicted multivariate rank of the molecular design for each molecular design generated by the molecular design engine 110. In some cases, the selection engine 120 can determine a cumulative distribution function (CDF) acquisition function to determine the predicted multivariate rank of the molecular design, at least based on the output of one or more characteristic calculation models 125. In some cases, the cumulative distribution function (CDF) acquisition function can determine the predicted multivariate rank of each molecular design to account for any uncertainties that may exist in the output of one or more characteristic calculation models 125.

[0076] In some exemplary embodiments, the selection engine 120 can estimate the cumulative distribution function (CDF) index of a molecular design in a variety of different ways. For example, in some cases, the selection engine 120 can estimate the cumulative distribution function (CDF) index of a molecular design using copulas (e.g., bivariate copulas). Thus, in some cases, the cumulative distribution function (CDF) index of a molecular design may be determined by estimating at least one or more copulas (e.g., bivariate copulas) that describe the marginal distributions of each objective (or molecular property of interest) being optimized, and the cross-correlations between different objectives. Alternatively, the selection engine 120 may determine the cumulative distribution function (CDF) index of each molecular design using other estimation means such as multivariate Gaussian cumulative distribution function (CDF), empirical cumulative distribution function (CDF), and kernel density estimation (KDE).

[0077] Figure 2A depicts a flowchart illustrating an example of a process 200 for molecular design with multi-objective optimization, according to several exemplary embodiments. Referring to Figures 1 to 2A, process 200 may be carried out by the molecular design engine 110 and the selection engine 120 to identify a subset of molecular designs generated by the molecular design engine 110 as candidates in, for example, in vitro measurements, in vivo characterization, etc.

[0078] In 202, multiple molecular designs are generated. In some exemplary embodiments, multiple molecular designs may be generated that include protein molecules or non-protein molecules, such as small molecules, ions, nucleic acids, polysaccharides, glycolipids, etc. In some cases, each molecular design may be generated computationally by sampling a data distribution of molecules that exhibit one or more desirable properties (e.g., drug-like properties such as affinity, specificity, biological activity, and suitability for development). For example, in some cases, each molecular design may be generated by applying a molecular design computation model 115, which may be trained to approximate a data distribution, including determining a function (e.g., energy function, score function, etc.) whose output (e.g., energy value, score, etc.) distinguishes different density regions of the data distribution. Thus, in some cases, each molecular design may be generated by multiple iterations of gradient-based Markov chain Monte Carlo (MCMC) sampling (e.g., Langevin Markov chain Monte Carlo (MCMC) sampling, etc.). Sampling may be performed based on the output (e.g., score, energy value, etc.) of a function (e.g., score function, energy function, etc.), and as a result, each successive iteration of the sampling iteration involves drawing a sample (or molecule) from an increasingly dense region of the data distribution, which is more likely to be occupied by one or more molecules exhibiting desirable properties than the low-density region of the data distribution.

[0079] In 204, one or more property calculation models may be applied to determine multiple properties exhibited by multiple molecular designs. In some exemplary embodiments, the properties of each computationally generated molecular design may be determined by applying one or more property calculation models trained to approximate the probability distribution of possible values ​​for each property. For example, in some cases, one or more property calculation models may be trained by at least updating the prior probability distribution of possible values ​​for each property (e.g., drug-like properties) based on observations such as wet-lab measurements of properties exhibited by previous molecular designs. This training of one or more property calculation models can yield a posterior probability distribution of possible values ​​for each property. Thus, in some cases, the application of one or more property calculation models to determine the properties of a molecular design may involve drawing multiple predictive samples from the posterior probability distribution of possible values ​​for each property. In some cases, the outputs of one or more property calculation models may each include predictive samples containing combinations of values ​​for different properties of the molecular design. For example, if two objectives (or molecular properties of interest) are optimized, each predictive sample output from one or more property calculation models may include a first value for a first property present in the molecular design and a second value for a second property present in the molecular design. It should be understood that one or more characteristic calculation models can output multiple predicted samples for a single molecular design to reflect the uncertainty associated with the predictions of the properties of each molecular design. In other words, instead of one or more characteristic calculation models outputting a single possible value for each property, they may output multiple different values ​​corresponding to the probability distribution of possible values ​​for each property. Doing so may be consistent with the observation that there may be some variation in the observed properties of each molecular design.

[0080] In 206, a cumulative distribution function (CDF) index corresponding to the multivariate rank is determined for each of the multiple molecular designs, based on at least the output of one or more characteristic calculation models. In some exemplary embodiments, for each molecular design, a utility metric corresponding to the probability that the molecular design is a Pareto optimal (or non-dominant) solution may be determined. In the context of drug design, a molecular design may be a Pareto optimal if none of the properties of the molecular design (e.g., drug-like properties) can be improved without reducing at least one other property of the molecular design. For example, if a molecular design is optimized for a first and a second property, the molecular design may be a Pareto optimal if the first value of the first property cannot be improved without reducing the second value of the second property.

[0081] In some exemplary embodiments, an acquisition function may be applied to determine the utility metric for each molecular design. Conventional acquisition functions, such as improvement-based acquisition functions (e.g., predicted hypervolume improvement (EHVI), noisy predicted hypervolume improvement (NEHVI)) and entropy-based acquisition functions (e.g., maximum entropy search (MESMO), joint entropy search (JES)), exhibit poor time costs. Therefore, in some cases, a multivariate ranking-based acquisition function may be applied. In some cases, the multivariate ranking-based acquisition function may be a cumulative distribution function (CDF) acquisition function, where the utility metric determined for each molecular design is a cumulative distribution function (CDF) index corresponding to the multivariate rank of the molecular design. As will be described in more detail below, the cumulative distribution function (CDF) index of a molecular design may coincide with the multivariate rank and the hypervolume (HV) bounded by the molecular design. In other words, if a molecular design is a Pareto optimal, the cumulative distribution function (CDF) index of the molecular design, as well as the corresponding hypervolume (HV) and multivariate rank, may be more favorable than those of the molecular design in which it is dominant. In some cases, the computational complexity of determining the cumulative distribution function (CDF) index can be further reduced by separately estimating one or more copulas (e.g., bivariate copulas) that describe the marginal distributions of the objective (or molecular property of interest) being optimized, and the cross-correlations between them.

[0082] In 208, one or more molecular designs from a group of molecular designs may be selected as candidates for wet lab evaluation, based at least on the cumulative distribution function (CDF) index of each molecular design. In some exemplary embodiments, one or more molecular designs may be identified as candidates for synthesis and testing if the utility metric (e.g., the cumulative distribution function (CDF) index) of the molecular designs meets one or more thresholds. Alternatively and / or additionally, N molecular designs with the best utility metrics may be selected as candidates for synthesis and testing. In the latter case, one or more molecular designs may be selected as candidates for synthesis and testing if these molecular designs are part of the N molecular designs with the highest utility metrics. In some cases, one or more additional conditions may be imposed in addition to the utility metrics associated with each molecular design. For example, in the case of antibody designs, one or more molecular designs may be selected as candidates for synthesis and testing based further on the presence (or absence) of a specific amino acid residue or sequence of amino acid residues (e.g., liability motif).

[0083] Figure 2B depicts a flowchart illustrating another example of process 225 for molecular design with multi-objective optimization, according to several exemplary embodiments. Referring to Figures 1 and 2B, process 225 may be carried out by a selection engine 120 to select one or more molecular designs having an increasingly better combination of properties for wet lab evaluation (e.g., synthesis and testing with one or more laboratory instruments 130) over one or more consecutive iterations of multi-objective Bayesian optimization (MOBO).

[0084] In step 232, a set of measurements associated with multiple preceding molecular designs is received. In some exemplary embodiments, a molecular design may be optimized over multiple successive iterations of multi-objective Bayesian optimization (MOBO). In some cases, the properties of a computationally generated molecular design (e.g., drug-like properties) may be too costly to evaluate, especially if a large number of molecular designs may be generated at once. Therefore, in some cases, one or more property computation models (e.g., property computation model 225) may be trained to act as in silico surrogates for determining the properties of a molecular design. In some cases, one or more property computation models may be trained to approximate the probability distribution of possible values ​​for each property. For example, in some cases, one or more property computation models may be trained using wet-lab measurements of properties of one or more molecular designs selected for synthesis and testing during preceding iterations of multi-objective Bayesian optimization (MOBO). As described in more detail below, the properties of a molecular design may be determined by sampling combinations of values ​​(e.g., one or more predicted samples) from these probability distributions. Furthermore, these probability distributions can be further updated by retraining the characterization model with actual wet lab measurements obtained for molecular design.

[0085] In 234, based on at least a set of measurements, one or more characteristic computation models are trained to approximate the probability distribution of each of a set of characteristics. In some exemplary embodiments, one or more characteristic computation models may be trained to approximate the probability distribution of each characteristic. For example, in some cases, a single characteristic computation model may be trained to approximate the probability distribution of a single or a set of characteristics. Alternatively and / or additionally, an ensemble of characteristic computation models, including a set of independent characteristic computation models, may also be trained to approximate the probability distribution of a single characteristic. Training each characteristic computation model may include updating the prior probability distribution of possible values ​​of a characteristic based on at least the measured values ​​of the characteristic presented by one or more molecular designs (e.g., from a preceding iteration of a multi-objective Bayesian optimization (MOBO)). In doing so, a posterior probability distribution of possible values ​​of the characteristic can be generated. As will be described in more detail below, once trained, one or more characteristic computation models may be applied to determine the characteristics of one or more molecular designs generated during the current iteration of a multi-objective Bayesian optimization (MOBO).

[0086] In 236, one or more characteristic calculation models are applied to determine multiple characteristics exhibited by multiple current molecular designs. In some exemplary embodiments, one or more characteristic calculation models may be applied to determine the characteristics of each molecular design generated during the current iteration of multi-objective Bayesian optimization (MOBO) by sampling from a probability distribution of possible values ​​of the characteristics. For example, in some cases, multiple predictive samples from a probability distribution may be generated for each molecular design from the current iteration of multi-objective Bayesian optimization (MOBO). Each predictive sample may include, for example, values ​​for each characteristic, including a first value for a first characteristic and a second value for a second characteristic present in the molecular design. As will be described in more detail below, a cumulative distribution function (CDF) acquisition function may be applied to determine a cumulative distribution function (CDF) index corresponding to the predicted multivariate rank of the molecular design, based at least on the predictive samples generated by one or more characteristic calculation models for each molecular design.

[0087] In 238, a cumulative distribution function (CDF) index corresponding to the multivariate rank may be determined for each current molecular design based on at least the output of one or more characteristic computation models. In some exemplary embodiments, a cumulative distribution function (CDF) acquisition function may be applied to determine the cumulative distribution function (CDF) index corresponding to the predicted multivariate rank of the molecular design for each molecular design generated during the current iteration of multi-objective Bayesian optimization (MOBO). In some cases, the predicted multivariate rank of a molecular design can rank the molecular design against other molecular designs generated during the current iteration of multi-objective Bayesian optimization based on a combination of characteristics (e.g., drug-like characteristics). Furthermore, the predicted multivariate rank of a molecular design may account for uncertainties that may exist in the output of characteristic computation models, which may be stochastic surrogate models as described. In some cases, the predicted multivariate rank of a molecular design may correspond to the probability that the molecular design is one of the Pareto optimal solutions occupying the Pareto frontier. In other words, a first molecular design with a better multivariate rank than a second molecular design is more likely to be closer to the Pareto frontier or even a Pareto optimal solution than the second molecular design. Therefore, in some cases, which molecular design generated during the current iteration of multi-objective Bayesian optimization (MOBO) is selected for wet lab evaluation (e.g., synthesis and testing) may depend on the respective multivariate rankings of each molecular design.

[0088] As will be described in more detail below, in some exemplary embodiments, the cumulative distribution function (CDF) index of a molecular design may be estimated using one or more copulas. For example, in some cases, one or more copulas describing the marginal distribution of each property and the cross-correlations between properties may be determined based on the predicted samples output by the property calculation model for each molecular design. Furthermore, in some cases, the cumulative distribution function (CDR) index of each molecular design may be determined based on the marginal distribution of each property and the corresponding copula. Alternatively, other cumulative distribution function (CDF) estimation means may be used instead of the copulas described above. The multivariate Gaussian cumulative distribution function (CDF) is used as the cumulative distribution function (CDF) index. TIFF2026518661000002.tif5170( This is an example in which the mean (μ) and covariance (Σ) of the training data (e.g., the set of measurements received in operation 232) are determined before a closed-form analytical solution is used to obtain a multivariate Gaussian distribution for calculating TIFF2026518661000003.tif5170). In the case of the empirical cumulative distribution function (CDF), the estimation means may be a step function that jumps by 1 / n at each of the n data points. As shown in equation (1) below, the value of the empirical cumulative distribution function (CDF) may be a portion of the observations of the measurement variable (e.g., in the set of measurements received in operation 232) that are less than or equal to a specified value. TIFF2026518661000004.tif8170

[0089] Another example of a cumulative distribution function (CDF) estimation method that can be used is kernel density estimation (KDE), which is a mixture of density estimation methods. Since TIFF2026518661000005.tif7170, the joint cumulative distribution function (CDF) is a mixture of cumulative density functions. It could also be TIFF2026518661000006.tif7170. The Gaussian kernel is It may also be expressed as TIFF2026518661000007.tif8170, and similarly, The filename is TIFF2026518661000008.tif8170, where σ represents the kernel bandwidth.

[0090] In 240, one or more current molecular designs from a plurality of current molecular designs may be selected as candidates for wet lab evaluation based at least on the cumulative distribution function (CDF) index of each current molecular design. In some exemplary embodiments, the cumulative distribution function (CDF) acquisition function can balance the exploration of uncertain molecular designs with the utilization of those most likely to maximize the objective when selecting one or more molecular designs generated during the current iteration of multi-objective Bayesian optimization (MOBO) for wet lab evaluation. In some cases, one or more molecular designs generated during the current iteration of multi-objective Bayesian optimization (MOBO) may be selected for wet lab evaluation based at least on the cumulative distribution function (CDF) index of each molecular design. For example, in some cases, the cumulative distribution function (CDF) index of a molecular design may be a value between [0,1]. The molecular designs generated during the current iteration of multi-objective Bayesian optimization (MOBO) may be ranked based on their respective cumulative distribution function (CDF) indices, and a threshold quantity (e.g., N) of those with the best cumulative distribution function (CDF) indices (or best predicted multivariate rankings) may be selected for wet lab evaluation. Alternatively and / or additionally, the molecular designs selected for wet lab evaluation may need to exhibit cumulative distribution function (CDF) indices (or predicted multivariate rankings) that satisfy one or more thresholds. As described above, the wet lab measurements of those molecular designs selected for wet lab evaluation during this current iteration of multi-objective Bayesian optimization (MOBO) may be used to further update one or more characteristic calculation models in subsequent iterations of multi-objective Bayesian optimization (MOBO).

[0091] Figure 2C depicts a flowchart illustrating another example of process 250 for molecular design with multi-objective optimization, according to several exemplary embodiments. Referring to Figures 1 and 2A–2C, process 250 may be performed, for example, by the selection engine 120 to determine the usefulness metrics of each molecular design generated by the molecular design engine 110. In some cases, process 250 may perform at least a portion of operation 206 of process 200 shown in Figure 2A or operation 238 of process 225 shown in Figure 2B.

[0092] In step 252, molecular designs are received. In some exemplary embodiments, one or more molecular designs may be received that are computationally generated by sampling a data distribution of molecules exhibiting one or more desirable properties (e.g., drug-like properties). In some cases, each molecular design may correspond to a protein molecule, or alternatively, a non-protein molecule such as a small molecule, ion, nucleic acid, polysaccharide, glycolipid, etc.

[0093] In 254, one or more property calculation models are applied to determine multiple properties of the molecular design. In some exemplary embodiments, the molecular design may be optimized for multiple purposes (or molecular properties of interest), such as a first property and a second property. In some cases, certain practical constraints, such as limited availability of laboratory resources and exorbitant costs, may prevent all computationally generated molecular designs from undergoing wet lab evaluation. Therefore, in some cases, one or more iterations of multi-objective Bayesian optimization (MOBO) are performed. In some cases, multi-objective Bayesian optimization (MOBO) may be a sequential design strategy in which molecular designs with an increasingly better combination of the first and second properties are selected for wet lab evaluation. For example, in some cases, the current molecular design selected for wet lab evaluation during the current iteration of multi-objective Bayesian optimization (MOBO) may exhibit a better combination of the first and second properties than one or more baseline molecular designs, which may include at least one preceding molecular design selected for wet lab evaluation during a preceding iteration of multi-objective Bayesian optimization (MOBO).

[0094] In some cases, the objective functions for the first and second properties may be unknown black-box functions that are too costly to evaluate. Therefore, in some cases, one or more property computation models may be trained to act as in silico surrogates for the objective functions. That is, one or more property computation models may be one or more machine learning models trained to determine the first and second properties of each molecular design computationally generated during each iteration of multi-objective Bayesian optimization (MOBO). For example, in some cases, a first property computation model may be applied that is trained to approximate a first probability distribution of possible values ​​for the first property, and a second property computation model may be applied that is trained to approximate a second probability distribution of possible values ​​for the second property. In some cases, the first property computation model may be applied to determine one or more values ​​of the first property present in the molecular design computationally generated during the current iteration of multi-objective Bayesian optimization (MOBO), based at least on the first probability distribution. On the other hand, the second property computation model may be applied to determine one or more values ​​of the second property present in the same molecular design, based at least on a second probability distribution. The outputs of the first and second characteristic calculation models can form one or more predicted samples, each containing a first value for the first characteristic and a second value for the second characteristic exhibited by a molecular design having the first value for the first characteristic.

[0095] It should be understood that in some cases, a single characteristic calculation model may be trained and applied to determine multiple properties of each molecular design. Alternatively, in some cases, two or more characteristic calculation models, such as an ensemble of characteristic calculation models, may be applied to determine the value of a single property of each molecular design. By including multiple characteristic calculation models (or an ensemble of characteristic calculation models) for a single property, at least some of the uncertainty that may exist in the output of individual characteristic calculation models can be compensated for. For example, in some cases, the output of the first characteristic calculation model may be more uncertain (or less reliable in terms of accuracy) for a particular molecular design, while the output of the second characteristic calculation model may be less uncertain (or more reliable in terms of accuracy) for the same molecular design. Thus, when applying multiple characteristic calculation models (or an ensemble of characteristic calculation models) to determine the properties of a molecular design, lower uncertainty in the output of some characteristic calculation models can compensate for higher uncertainty in the output of others.

[0096] In some exemplary embodiments, noise that may be present in the observed properties of one or more baseline molecular designs can be compensated for in various ways. For example, if the cumulative distribution function (CDF) index corresponds to the predicted multivariate ranking of molecular designs to the multivariate ranking of one or more baseline molecular designs, the values ​​of properties present in one or more baseline molecular designs may be observed in a wet lab. However, these observations may contain at least some noise due to measurement errors. Therefore, in some cases, the impact of this noise can be reduced (or minimized) by retraining one or more property calculation models on the measured values ​​and then determining the utility metric for each baseline molecular design based on the output of one or more property calculation models. For example, the retrained property calculation models may be applied to determine the values ​​of properties present in molecular designs and the values ​​of properties present in one or more baseline molecular designs. The utility metrics for molecular designs and each baseline molecular design may be determined based on the output of the retrained property calculation models instead of the observed values.

[0097] In 256, one or more copulas that describe the cross-correlations between multiple properties based on at least the marginal distributions of each property and the outputs of one or more property computation models. In some exemplary embodiments, a cumulative distribution function (CDF) acquisition function may be applied to each computationally generated molecular design to determine a utility metric indicating the probability that the molecular design is a Pareto optimal (or non-dominant) solution. As stated, in some cases, a molecular design that qualifies as a Pareto optimal may be one in which individual properties (e.g., drug-like properties) cannot be further improved without degrading at least one such property. In some cases, a cumulative distribution function (CDF) acquisition function may be applied instead of a conventional acquisition function (e.g., an improvement-based acquisition function, an entropy-based acquisition function, etc.). The application of a cumulative distribution function (CDF) acquisition function can generate a cumulative distribution function (CDF) index for each computationally generated molecular design. As mentioned, in some cases, the Cumulative Distribution Function (CDF) metric for molecular designs can correspond to its multivariate rank, or to the ranking of molecular designs based on multiple objectives (or molecular properties of interest) relative to one or more other molecular designs (e.g., from the same design iteration) and / or a baseline molecular design (e.g., from a preceding design iteration). Furthermore, the Cumulative Distribution Function (CDF) metric for molecular designs can also correspond to hypervolume (HV), a utility metric bounded by the properties of the molecular design, which is associated with conventional improvement-based acquisition functions.

[0098] In some exemplary embodiments, copulas, such as bivariate copulas, may be used to estimate the cumulative distribution function (CDF) index of a molecular design. For example, in some cases, a computationally generated cumulative distribution function (CDF) index of a molecular design may be determined by decomposing a multivariate joint distribution of multiple objectives (or molecular properties of interest) into at least the marginal distributions of each individual objective (or molecular property of interest) and one or more copulas (e.g., bivariate copulas). The marginal distribution of an objective (or molecular property of interest) in the multivariate joint distribution can specify the distribution of values ​​for that objective and is independent of the values ​​of other objectives in the multivariate joint distribution. A copula, on the other hand, is a coupling function that describes a dependency structure (e.g., a copula matrix) that specifies the cross-correlations between the marginal distributions of two or more objectives (or molecular properties of interest). It should be understood that each of the aforementioned marginal distributions and copulas may be determined separately from one another. Therefore, by using copulas to estimate the cumulative distribution function (CDF) index of molecular design, the computational complexity of determining the underlying multivariate joint distribution, which would require estimating the multivariate joint density function and calculating its integral, can be avoided.

[0099] In some exemplary embodiments, the computational complexity of estimating the cumulative distribution function (CDF) index for each molecular design can be further reduced by truncating certain copulas, such as those representing higher-order dependencies between several objectives (or molecular properties of interest), if those dependencies are trivial enough to be ignored when ranking two or more molecular designs. In some cases, truncating certain copulas can avoid removing certain dependencies, such as specific experimental dependencies, biological dependencies, or those corresponding to the priority of a particular type of molecular design. For example, a copula that combines a first peripheral distribution of expression levels with a second peripheral distribution of binding affinity may be preserved during truncation due to an experimental dependency where the expression level of the molecular design (e.g., in cell culture) may need to meet some threshold (e.g., mass per volume) in order to produce a molecular design in sufficient quantity for its binding affinity to the target antigen in a subsequent assay. In other words, in some cases, truncating copulas, particularly the selection of preserved copulas, can enable the execution of dependencies between specific objectives (or molecular properties of interest). Nevertheless, removing at least some copulas as part of the truncation process can further improve the computational efficiency of using copulas as a means of estimating the cumulative distribution function (CDF) index of computationally generated molecular designs.

[0100] In some exemplary embodiments, a multivariate joint distribution of two or more objective lenses (or molecular properties of interest) can be decomposed into one or more bivariate joint distributions, each containing a pair grouping of interest. For example, for M objectives (or molecular properties of interest), and M > 2, the corresponding M-dimensional joint distribution can be factorized into a set of bivariate copulas. In some cases, pairwise factorization of the M-dimensional joint distribution is performed to produce a structure called a vine, in which case this is TIFF2026518661000009.tif7170 This could be a hierarchical model containing a sequence of M-1 nested trees linked by 170 bivariate copulas. The mth tree T m is the edge set E mA set V of nodes interconnected by m can include (e.g., T m =(V m , E m )). The nodes in the tree T m can represent at least one optimized objective (or molecular property of interest) or a combination thereof. On the other hand, an edge e connecting two nodes of the tree can represent a bivariate copula c that combines the marginal distributions of the objectives associated with each node. Thus, the vine can include a set of trees T m =(V m , E m ) for m ∈ [M - 1], and a set of pair-copula trees m for e ∈ E TIFF2026518661000010.tif4170 and m ∈ [M - 1]. The factorization may not be unique, which means that the same M-dimensional joint distribution can be decomposed into different sets of bivariate copulas.

[0101] In some exemplary embodiments, the hierarchical nature of vines can enable the execution of dependencies between different objectives (or molecular properties of interest). For example, in some cases, the hierarchical structure of vines may encode a partial order in which some objectives (or molecular properties of interest) take precedence over others. This partial order may correspond to a particular experimental dependency in which one property of a molecular design must meet one or more criteria before other properties can be measured. For example, in antibody design, if the expression level of the molecular design (e.g., in cell culture) does not meet a certain threshold (e.g., mass per volume), the molecular design cannot be produced in sufficient quantity for subsequent assays of other properties, such as binding affinity to a target antigen. To capture this experimental dependency, the corresponding hierarchical structure of vines may encode a partial order in which expression takes precedence over affinity (e.g., expression → affinity). This may mean that a bivariate copula coupling the marginal distributions of expression and affinity can exclude expression levels that do not meet a certain threshold. In practice, it should be noted that experimental dependencies can introduce asymmetry between objectives (or molecular properties of interest). In the above example, since affinity measurements cannot be used for these designs, there may be less data available for molecular designs with insufficient expression levels.

[0102] In some cases, a partial order in which certain objectives (or molecular properties of interest) take precedence over others may reflect preferences for certain types of molecular designs. For example, in some cases, one or more properties may be prioritized to prevent a molecular design from progressing if it does not perform well in certain properties, regardless of how well the design performs in other properties. In the context of antibody design, if a molecular design does not bind to the target antigen, the molecular design has failed its primary function, and there is little interest in examining its developability properties, such as specificity and thermal stability to the target antigen. This may be true even though these developability properties are often still measurable, unlike molecular designs with inadequate expression levels. Furthermore, in some cases, a partial order capturing this preference, in addition to the aforementioned experimental dependence, may be encoded in the corresponding vine hierarchical structure, where expression takes precedence over affinity, and affinity takes precedence over developability properties such as specificity and thermal stability (e.g., expression → affinity → {specificity, thermal stability}).

[0103] In 258, the cumulative distribution function (CDF) index corresponding to the multivariate rank of the molecular design is determined based on at least the marginal distribution of each property and one or more copulas. In some exemplary embodiments, copulas (e.g., bivariate copulas) may be used to estimate the computationally generated cumulative distribution function (CDF) index for each molecular design. For example, in some cases, the cumulative distribution function (CDF) index of a molecular design may be determined based on at least estimating the marginal distribution of each objective (or molecular property of interest) and one or more copulas (e.g., bivariate copulas) describing the cross-correlations between different objectives. As described above, by doing so, at least the marginal distributions and the corresponding copulas can be determined separately, thereby reducing the computational complexity of estimating the underlying multivariate joint distribution. Furthermore, the cumulative distribution function (CDF) of a molecular design can be associated with a scale that is more interpretable than conventional utility metrics such as hypervolume (HV) indices, which carry no information about the internal ordering of molecular designs of different scales. For example, in some cases, the cumulative distribution function (CDF) index of a molecular design can be a value between 0 and 1. In some cases, the closer the CDF index is to 1, the more likely the molecular design is to be a Pareto optimal solution close to the Pareto frontier. In other words, in some cases, the CDF index of a molecular design may be sufficient to determine its candidacy for wet lab evaluation without necessarily needing to compare it with the CDF index of other molecular designs.

[0104] As stated, in some cases, the cumulative distribution function (CDF) index of each molecular design may correspond to its multivariate rank, which indicates the distance to the Pareto frontier occupied by the Pareto optimal solution for a form of molecular design whose properties cannot be further improved without degrading at least one such property. Therefore, in some cases, by determining the cumulative distribution function (CDF) index of each molecular design generated by the molecular design engine 110, the selection engine 120 can identify those that are more likely to be Pareto optimal solutions. In some cases, molecular designs that are Pareto optimal solutions on the Pareto frontier may be associated with the same (or linked) multivariate rank, which means that the corresponding cumulative distribution function (CDF) index is also the same (or linked).

[0105] In some exemplary embodiments, one or more molecular designs that meet specific criteria for one or more properties (e.g., drug-like properties) may be identified for wet lab evaluation (e.g., synthesis, testing, etc.). In some cases, the properties of a molecular design may be optimized by active learning over multiple successive design iterations. For example, in some cases, one or more molecular designs selected during the current iteration of multi-objective Bayesian optimization (MOBO) may exhibit a better combination of properties (e.g., drug-like properties) than one or more baseline molecular designs. In some cases, one or more baseline molecular designs may be one or more preceding molecular designs selected for wet lab evaluation during preceding iterations of multi-objective Bayesian optimization. Thus, in some cases, the properties of one or more baseline molecular designs may have been observed in the wet lab through, for example, in vitro measurements, in vivo characterization, etc. In some cases, the cumulative distribution function (CDF) index of molecular designs from the current iteration of multi-objective Bayesian optimization (MOBO) may correspond to the expectation that the molecular design exhibits a better combination of properties than baseline molecular designs from preceding iterations of multi-objective Bayesian optimization (MOBO).

[0106] As described above, observed properties of one or more baseline molecular designs may be contaminated by noise arising from, for example, measurement errors present in laboratory equipment. Therefore, in some cases, the effects of this noise can be reduced (or minimized) by at least retraining one or more property calculation models during subsequent iterations of multi-objective Bayesian optimization (MOBO) to refit one or more property calculation models with additional observations obtained for molecular designs generated during one or more preceding iterations of the MOBO. For example, in some cases, one or more property calculation models may be retrained based on observed properties of one or more baseline molecular designs. In some cases, one or more property calculation models may be stochastic surrogate models that account for uncertainties in wet lab measurements by at least approximating the probability distribution (e.g., probability density function (PDF)) of the possible values ​​of each property (e.g., drug-like property). For example, in some cases, retraining a property calculation model may involve updating the prior probability distribution of the possible values ​​of the properties so that the retrained property calculation model determines the properties of the molecular design based on the resulting posterior probability distribution. In some cases, a retrained property model may be applied to determine the properties of the baseline molecular design and the molecular design generated during the current iteration of multi-objective Bayesian optimization (MOBO).

[0107] To illustrate further, Figure 3A depicts a flowchart illustrating an example of a process 300 for determining one or more properties of a molecular design, according to several exemplary embodiments. Referring to Figures 1, 2A-2B, and 3A, the process 300 may also be performed by the selection engine 120, which may, for example, perform at least a portion of operation 206 of process 200 shown in Figure 2A or at least a portion of operation 238 of process 225 shown in Figure 2B.

[0108] In 302, one or more observations of the properties of the first molecular design from previous design iterations may be received. In some exemplary embodiments, one or more molecular designs generated during the current iteration of multi-objective Bayesian optimization (MOBO) may be selected for wet lab evaluation (e.g., in vitro measurement, in vivo characterization, etc.). In some cases, the selected molecular design may exhibit a better combination of properties (e.g., drug-like properties) than one or more baseline molecules. For example, in some cases, the molecular design may be selected at least on the basis of a comparison between its utility metric and that of each baseline molecular design. As stated, in some cases, the aforementioned utility metric may be a cumulative distribution function (CDF) index corresponding to the predicted multivariate rank of each molecular design. For example, in some cases, a molecular design that is a Pareto optimal may have a better coupled multivariate rank than molecular designs with a worse combination of properties (e.g., drug-like properties).

[0109] In some cases, at least some of the baseline molecular designs may be molecular designs selected for wet lab evaluation during one or more preceding design iterations. Therefore, the property values ​​(e.g., drug-like properties) of one or more baseline molecular designs may have been observed in the wet lab. For example, the available observations for the properties of each baseline molecular design may include one or more in vitro measurements and / or in vivo characterizations. However, as will be discussed in more detail below, the observations of the properties of these baseline molecular designs, which may be used during the current iteration of multi-objective Bayesian optimization (MOBO) to identify one or more molecular designs with a better combination of properties, may be contaminated with noise (e.g., arising from measurement errors associated with laboratory equipment, etc.).

[0110] In operation 304, one or more characteristic calculation models are retrained based on at least one or more observed values ​​of the characteristics of the first molecular design. In some exemplary embodiments, one or more characteristic calculation models may be stochastic surrogate models that account for the uncertainty in wet lab measurements by at least approximating the probability distribution (or probability density function (PDF)) of the possible values ​​of each characteristic (e.g., drug-like characteristics). As described above, in some cases, observed values ​​of the characteristics of one or more baseline molecular designs may be contaminated by noise arising from measurement errors present in, for example, laboratory equipment. This noise may distort the utility metric that is directly calculated based on the observed values ​​of the characteristics of each baseline molecular design. Therefore, in some cases, the observed values ​​of the characteristics of the baseline molecular designs may not be used directly. Instead, in some cases, the effects of noise that may be present in the observed values ​​of the characteristics of the baseline molecular designs received in operation 302 can be reduced (or minimized) by at least retraining one or more characteristic calculation models based on these observations. In this way, the retrained characteristic calculation models can update the prior probability distribution of the possible values ​​of these characteristics based on the observations so that they determine the characteristics of one or more molecular designs based on the obtained posterior probability distribution. For example, as described above, a characteristic calculation model can output one or more predictive samples for molecular design. In some cases, a single predictive sample may include a first value of the first characteristic, determined based on the posterior probability distribution of possible values ​​for the first characteristic, and a second value of the second characteristic, determined based on the posterior probability distribution of possible values ​​for the second characteristic.

[0111] In 306, one or more retrained characteristic calculation models are applied to determine a first value for the characteristics of a first molecular design from the current design iteration and a second value for the characteristics of a second molecular design. In some exemplary embodiments, the retrained characteristic calculation models may be applied to determine the characteristics of a baseline molecular design (e.g., from one or more preceding iterations of a multi-objective Bayesian optimization (MOBO)) and the characteristics of a molecular design generated during the current iteration of the multi-objective Bayesian optimization (MOBO). The retrained characteristic calculation models may, in some cases, be associated with a posterior probability distribution updated to reflect observations of the characteristics of the baseline molecular design, including any noise that may be present therein. In the case of expression levels, for example, the retrained characteristic calculation models may be applied to determine a first expression level of the first molecular design from preceding design iterations and a second expression level of the second molecular design from the current design iteration. The expression level of the first molecular design is observed by wet lab experiments, but the utility metric of the first molecular design (e.g., a cumulative distribution function (CDF) index) is not determined directly on the observed expression level of the baseline molecular design. Alternatively, as will be explained in more detail below, the utility metrics for the first molecular design from a previous design iteration and the utility metrics for the second molecular design from the current design iteration can be determined based on the respective expression levels of each molecular design determined by a retrained property calculation model.

[0112] In 308, the cumulative distribution function (CDF) index corresponding to the predicted multivariate ranks of the first and second molecular designs is determined based at least on the first value of the properties of the first molecular design and the second value of the properties of the second molecular design. In some exemplary embodiments, a first cumulative distribution function (CDF) index corresponding to the first predicted multivariate rank of the first molecular design from previous iterations of multi-objective Bayesian optimization (MOBO) may be determined. Furthermore, in some cases, a second cumulative distribution function (CDF) index corresponding to the second predicted multivariate rank of the second molecular design from the current iteration of multi-objective Bayesian optimization (MOBO) may also be determined. In some cases, the first cumulative distribution function (CDF) index of the first molecular design may be determined based on the values ​​of the properties of the first molecular design determined by a retrained property calculation model, or not based on observed values ​​of these properties. As mentioned above, this may be done to reduce (or minimize) the influence that noise present in the observations may have on the utility metric calculated directly from them. Returning to the example of expression levels, the first cumulative distribution function (CDF) index of a first molecular design from a preceding iteration of multi-objective Bayesian optimization may be determined based on a first expression level determined by a retrained characteristic computation model, while the second cumulative distribution function (CDF) index of a second molecular design from the current iteration of multi-objective Bayesian optimization (MOBO) may be determined based on a second expression level determined by a retrained characteristic computation model. In some cases, the first and second cumulative distribution function (CDF) indices can capture the distance (or proximity) between the corresponding molecular design and the true Pareto frontier. In this case, a molecular design with a better cumulative distribution function (CDF) index that can correspond to a better predicted multivariate rank is likely to be closer to the true Pareto frontier and therefore likely to be a Pareto optimal solution.In some cases, if the second cumulative distribution function (CDF) index of the second molecular design is better than that of the first molecular design, and possibly better than the third cumulative distribution function (CDF) index of the third molecular design generated during the current iteration of multi-objective Bayesian optimization (MOBO), the second molecular design may be selected for wet lab evaluation.

[0113] In some exemplary embodiments, instead of retraining the characteristic design calculation models, or in addition to doing so, the uncertainty of the output of each characteristic calculation model can also be reduced (or minimized) by leveraging at least multiple characteristic calculation models for each characteristic (e.g., an ensemble of characteristic calculation models). For example, as will be described in more detail below, the selection engine 120 may apply a first characteristic calculation model and a second characteristic calculation model to evaluate a single characteristic of a molecular design, such as each individual drug-like property, such as affinity, specificity, biological activity, and suitability for development. Thus, the value of that characteristic used to calculate the utility metric of the molecular design may be determined based on a first value of the characteristic determined by the first characteristic calculation model and a second value of the same characteristic determined by the second characteristic calculation model.

[0114] To illustrate further, Figure 3B depicts a flowchart illustrating another example of a process 350 for determining one or more properties of a molecular design, according to several exemplary embodiments. Referring to Figures 1, 2A–2C, and 3A–3B, the process 350 may also be performed by the selection engine 120, which may perform, for example, operation 204 of process 200 shown in Figure 2A, operation 236 of process 225 shown in Figure 2B, operation 254 of process 250 shown in Figure 2C, or optionally at least a portion of operation 306 of process 300 shown in Figure 3A.

[0115] In 352, a first property calculation model is applied to determine a first value of a property exhibited by the molecular design, and a second property calculation model is applied to determine a second value of a property exhibited by the molecular design. In some exemplary embodiments, multiple property calculation models (or an ensemble of property calculation models) may be applied to determine the values ​​of individual properties present in the molecular design. For example, an ensemble of property calculation models including a first property calculation model and a second property calculation model may be applied. In this example, each property calculation model in the ensemble may be trained to determine the same property (e.g., drug-like property). Thus, the first property calculation model can output a first value of the property present in the molecular design, while the second property calculation model can output a second value of the same property present in the molecular design. In some cases, the first and second values ​​of the property may each be determined based on a probability distribution that enumerates the probability of occurrence of each possible value of the corresponding property. For example, the output of a first property calculation model may include a first value determined based on a first probability distribution over a range of possible values ​​for the property (e.g., drug-like property), while the output of a second property calculation model may include a second value determined based on a second probability distribution over a range of possible values ​​for the same property. In some cases, the outputs of both the first and second property calculation models may be zero-inflated, meaning that the output includes one value (e.g., a binary value) indicating whether the value of the property meets a certain threshold, and another value indicating the actual value of the property present in the molecular design.

[0116] In 354, a third value of the characteristics exhibited by the molecular design for calculating a cumulative distribution function (CDF) index corresponding to the predicted multivariate rank of the molecular design is determined based at least on the first and second values. In some exemplary embodiments, the outputs of multiple characteristic calculation models may be utilized to reduce (or minimize) the uncertainty that may exist in the outputs of each individual characteristic calculation model. For example, in some cases, differences between a first and second characteristic calculation model, such as architecture and training, may cause one characteristic calculation model to be more reliable (or less reliable) than the other when applied to the same molecular design. In some cases, for example, the first characteristic calculation model may produce a more reliable output for a first molecular design than the second characteristic calculation model, while the second characteristic calculation model may produce a more reliable output for a second molecular design than the first characteristic calculation model. Therefore, in some cases, the outputs of multiple characteristic calculation models may be utilized when determining the utility metric of the molecular design to compensate for this uncertainty. In other words, in some cases, multiple values ​​of the same characteristic determined by an ensemble of characteristic calculation models may be used to determine the utility metric (e.g., a cumulative distribution function (CDF) index) of each molecular design generated by the molecular design engine 110. For example, in some cases, the utility metric of each molecular design may be determined based on the mean, median, maximum, minimum, mode, and / or range of the outputs generated by the ensemble of characteristic calculation models. Thus, if a first characteristic calculation model is applied to determine a first value of a characteristic present in a molecular design, and a second characteristic calculation model is applied to determine a second value of the same characteristic, a third value of the characteristic may be determined based on at least the first and second values. In some cases, the third value of the characteristic may correspond to the mean, median, maximum, minimum, mode, and / or range of the first and second values. Furthermore, in some cases, the cumulative distribution function (CDF) index of a molecular design corresponding to the predicted multivariate rank may be determined based on the third value instead of any individual value of the first and second values.

[0117] In some exemplary embodiments, multi-objective Bayesian optimization (BO) may be performed to trade off exploration (evaluating highly uncertain molecular designs) and utilization (evaluating molecular designs that are thought to increase or maximize an objective) by leveraging one or more property calculation models and multivariate rank-based acquisition functions. In the context of drug design, each objective (or molecular property of interest) TIFF2026518661000011.tif5170 is a design space Evaluating molecular designs sampled from TIFF2026518661000012.tif4170 (e.g., in a wet lab) can be considered a black-box function that is too costly. Therefore, the goal of Bayesian optimization (BO) is to evaluate each individual objective (or molecular property of interest). Molecular design to increase (or maximize) TIFF2026518661000013.tif5170 The objective is to efficiently identify TIFF2026518661000014.tif4170.

[0118] In some cases, Bayesian optimization (BO) is useful for each objective. Performing an in silico evaluation of TIFF2026518661000015.tif5170 may involve leveraging one or more characteristic computation models that act as stochastic surrogate models. Furthermore, in some cases, Bayesian optimization (BO) may be used for each molecular design based on the output of one or more characteristic computation models. To evaluate TIFF2026518661000016.tif3170, it may be necessary to apply a multivariate rank-based acquisition function, such as a cumulative distribution function (CDF) acquisition function. As mentioned, in some cases, the cumulative distribution function (CDF) acquisition function may be used for each molecular design Regarding TIFF2026518661000017.tif3170, molecular design This can be applied to determine the cumulative distribution function (CDF) index corresponding to the predicted multivariate ranks of TIFF2026518661000018.tif3170. For example, in some cases, molecular design The cumulative distribution function (CDF) index for TIFF2026518661000019.tif3170 is for multiple purposes. Molecular design as a Pareto optimal solution optimized over TIFF2026518661000020.tif5170 The quality of TIFF2026518661000021.tif3170 can be quantified. In some cases, molecular design The cumulative distribution function (CDF) index of TIFF2026518661000022.tif3170 is more reliable for molecular design with greater uncertainty (e.g., objective). To evaluate the molecular design (which may increase or maximize TIFF2026518661000023.tif5170) To explore TIFF2026518661000024.tif4170 and to achieve more reliable molecular design (e.g., objective It is possible to inform the trade-off between utilizing molecular designs that are more likely to increase or maximize TIFF2026518661000025.tif5170.

[0119] In some cases, characteristic calculation models TIFF2026518661000026.tif5170 is, Based on existing information such as observations in TIFF2026518661000027.tif5170, the objective The prior probability distribution of the values ​​in TIFF2026518661000028.tif5170 can be approximated. For example, TIFF2026518661000029.tif5170 is molecular design If the expression level is TIFF2026518661000030.tif3170, then the characteristic calculation model TIFF2026518661000031.tif5170 can be trained based on wet lab measurements of expression levels exhibited by known molecular designs, which may include molecular designs from preceding design iterations. Assuming the presence of observational noise (e.g., measurement errors associated with laboratory equipment, etc.), the characteristic calculation model TIFF2026518661000032.tif5170 is a given design iteration. It can be trained on noisy datasets available up to TIFF2026518661000033.tif3170. In other words, each iteration TIFF2026518661000034.tif4170 is each y (n) The purpose This dataset contains noisy observation results from TIFF2026518661000035.tif5170. This can be associated with TIFF2026518661000036.tif6170. Characteristic calculation model TIFF2026518661000037.tif5170 is a preceding design iteration. Based on the dataset from TIFF2026518661000038.tif5170, the objective is... To further update the prior probability distribution of the values ​​of TIFF2026518661000039.tif5170, for example, current design iteration D t The characteristic calculation model can be retrained (or refitted). TIFF2026518661000040.tif5170 is for surrogate purposes. Posterior probability distribution to quantify the validity of TIFF2026518661000041.tif5170 It can be trained (and retrained) to infer TIFF2026518661000042.tif6170. For example of expression levels, the posterior distribution TIFF2026518661000043.tif6170 quantifies the probability distribution of possible expression levels exhibited by the next batch of molecular design.

[0120] Retrieval function An example of TIFF2026518661000044.tif5170 is shown as equation (2) below. In conventional acquisition functions such as improvement-based acquisition functions, the integral of equation (2) is the backward sample It can be approximated by Monte Carlo (MC) with TIFF2026518661000045.tif5170, but this is computationally burdensome. In some cases, the acquisition function Molecular design that maximizes TIFF2026518661000046.tif5170 is performed on a characterization model augmented by observations on dataset D. t Before refitting, It can be selected for wet lab evaluation of TIFF2026518661000047.tif5170. TIFF2026518661000048.tif6170

[0121] If there is a single objective (or molecular property of interest), the best molecular design can be identified based on a ranking of the property values. If there are multiple objectives (or molecular designs of interest), at least all objectives Because there may not be a single superior molecular design in TIFF2026518661000049.tif5170, the best molecular design may not have the best value for all purposes (or properties). TIFF2026518661000050.tif4170 purposes Assume we have TIFF2026518661000051.tif5170. The goal of multi-objective Bayesian optimization (BO) in this paradigm is: TIFF2026518661000052.tif4170 This could involve identifying a set of Pareto optimal solutions such that improving one of the objectives leads to a deterioration of another objective. Molecular design TIFF2026518661000053.tif3170 is another molecular design Can you control TIFF2026518661000054.tif4170, or all Regarding TIFF2026518661000055.tif5170 TIFF2026518661000056.tif6170, and some Regarding TIFF2026518661000057.tif3170 If the filename is TIFF2026518661000058.tif6170, This is TIFF2026518661000059.tif6170. It represents a set of non-dominant solutions. TIFF2026518661000060.tif4170 is a Pareto frontier as shown in equation (3) below. This can be defined for TIFF2026518661000061.tif5170. A set of non-dominant solutions. While TIFF2026518661000062.tif4170 can be infinite, it should be understood that multi-objective Bayesian optimization (BO) can attempt to identify a finite subset of it within a threshold number of design iterations. TIFF2026518661000063.tif5170

[0122] In some exemplary embodiments, approximate Pareto sets The quality of TIFF2026518661000064.tif4170 is the optimal Pareto set within the target space. The distance (or proximity) from TIFF2026518661000065.tif4170, or It can be evaluated by calculating TIFF2026518661000066.tif5170. Distance metric TIFF2026518661000067.tif4170 can quantify the difference between sets of targets. TIFF2026518661000068.tif4170 is a target space This represents the power set of TIFF2026518661000069.tif5170. Traditional acquisition functions, including improvement-based acquisition functions such as hypervolume improvement (HVI), may be sensitive to any type of improvement (e.g., approximate set TIFF2026518661000070.tif4170 is another approximate set Whenever you are governing TIFF2026518661000071.tif4170, these acquisition functions are also sensitive to scaling and transformation of the target. In fact, scaling is the objective The amount of TIFF2026518661000072.tif5170 TIFF2026518661000073.tif4170 can be hyperpolynomial, which makes conventional improvement-based acquisition functions impractical.

[0123] In some cases, When TIFF2026518661000074.tif5170 is available, and only at that time, a certain molecular design TIFF2026518661000075.tif3170 is another molecular design It must be at least as good as TIFF2026518661000076.tif4170 (for example) (for example, To demonstrate (TIFF2026518661000077.tif4170), we explore the (weak) Pareto dominance relation in the search space. Priority relationships on TIFF2026518661000078.tif4170 It can be used as TIFF2026518661000079.tif4170. This relationship is, When the filename is TIFF2026518661000080.tif5170, and only at that time, a certain set TIFF2026518661000081.tif4170 is a different set When weakly controlling TIFF2026518661000082.tif4170 (for example, (TIFF2026518661000083.tif4170), can be standardized to a set of molecular designs. Priority relationships Given TIFF2026518661000084.tif4170, the goal of multi-objective Bayesian optimization (BO) may include approximating a set of Pareto optima and identifying a set of molecular designs not strictly governed by any other set of approximate Pareto optima.

[0124] A generalized weak Pareto advantage is Defining a partial order on TIFF2026518661000085.tif4170 may cause difficulties regarding exploration and utility evaluation. There may be sets that cannot be compared within TIFF2026518661000086.tif4170. These difficulties are, It may worsen at higher values ​​in TIFF2026518661000087.tif4170. Therefore, one way to avoid this problem is, This could be done by defining a total order on TIFF2026518661000088.tif4170, which guarantees that any two sets of objective vectors are comparable to each other. For this purpose, in the simplest case, each set of approximate Pareto optima is given a function The unamonic index is TIFF2026518661000089.tif4170. To assign real numbers such as TIFF2026518661000090.tif4170, quality metrics such as the utility metrics mentioned above may be introduced. In some cases, this quality metric (or utility metric) should exhibit Pareto conformance, meaning it must not contradict the order induced by the Pareto hierarchy. Therefore, Whenever TIFF2026518661000091.tif4170 is, The index values ​​for TIFF2026518661000092.tif4170 are It cannot be worse than the index value in TIFF2026518661000093.tif4170. A stricter version of Pareto compliance is shown in equation (4) below: The index value of TIFF2026518661000094.tif4170 It may be necessary to be strictly better (e.g., higher) than the index value of TIFF2026518661000095.tif4170. TIFF2026518661000096.tif5170

[0125] In some exemplary embodiments, each molecular design Quality indicators for TIFF2026518661000097.tif3170 To determine TIFF2026518661000098.tif4170, the cumulative distribution function (CDF) acquisition function is used. TIFF2026518661000099.tif5170 may be applicable. In some cases, real-valued random variables The cumulative distribution function (CDF) of TIFF2026518661000100.tif4170 may be the function shown in equation (5) below. According to equation (5), a real-valued random variable The cumulative distribution function (CDF) of TIFF2026518661000101.tif4170 is: This can be used to determine the probability that the real value of TIFF2026518661000102.tif4170 is less than or equal to y. TIFF2026518661000103.tif7170

[0126] When there are 170 objectives, the simultaneous or multivariate cumulative distribution function (CDF) can be given by the following equation (6): TIFF2026518661000105.tif7170

[0127] All multivariate cumulative distribution functions (CDFs) are not monotonically decreasing with respect to each objective (or constituent variable), and are right-continuous with respect to each objective (or constituent variable). Please understand that TIFF2026518661000106.tif5170 may be a possible case. The property of not being monotonically decreasing is: Whenever TIFF2026518661000107.tif5170 This means that TIFF2026518661000108.tif5170. In some cases, these characteristics can be utilized when defining various exemplary embodiments of the cumulative distribution function (CDF) index described herein.

[0128] In some exemplary embodiments, the cumulative distribution function (CDF) index is calculated according to equation (7) below. TIFF2026518661000109.tif5170 can be defined as the maximum multivariate rank. TIFF2026518661000110.tif8170, TIFF2026518661000111.tif4170 is This represents the approximate set within TIFF2026518661000112.tif4170. In some cases, the cumulative distribution function (CDF) index defined according to equation (7) follows the concept of Pareto dominance. In particular, any approximate set TIFF2026518661000113.tif4170 and Regarding TIFF2026518661000114.tif4170, The equation TIFF2026518661000115.tif5170 is true.

[0129] In some cases, the multivariate joint distribution F Y Calculating the integral is a difficult task. For example, naive methods may involve estimating the multivariate density function before calculating its integral, the latter being a particularly computationally intensive task. Therefore, in some exemplary embodiments, the copula (e.g., a bivariate copula) is used to calculate the cumulative distribution function (CDF) index I. F It can be used to estimate a continuous random vector. For example, in some cases, a continuous random vector TIFF2026518661000116.tif5170 is, The joint distribution is only valid if there is a unique copula C which is the joint distribution of TIFF2026518661000117.tif5170. TIFF2026518661000118.tif4170 and marginal distribution It may have TIFF2026518661000119.tif5170. Therefore, the copula is a multivariate distribution function that joins (or combines) uniform marginal distributions according to equation (8) below. It could be TIFF2026518661000120.tif5170. Therefore, the multivariate cumulative joint distribution (CDF) is copula It may be accessible by calculating TIFF2026518661000121.tif4170. Furthermore, copula To estimate TIFF2026518661000122.tif4170, it should be understood that individual objectives (or molecular properties of interest) can be transformed into uniform marginal distributions by marginal stochastic integral transforms (PIT). In some cases, the distribution The purpose of TIFF2026518661000123.tif5170 The Probability Integral Transform (PIT) of TIFF2026518661000124.tif4170 is for uniformly distributed random variables. TIFF2026518661000125.tif5170 (for example, It may also be TIFF2026518661000126.tif4170([0,1])). TIFF2026518661000127.tif5170

[0130] Using copulas as a means of estimating cumulative distribution function (CDF) metrics offers several advantages. For example, copula-based estimation exhibits scalability and flexibility in higher-dimensional objective spaces and can be scale-invariant with respect to different objectives. Furthermore, copula-based estimation can be invariant under monotonic transformations of the objective. For example, if Y1 and Y2 are copulas... Assuming a continuous random variable has TIFF2026518661000128.tif5170, If TIFF2026518661000129.tif5170 is a strictly increasing function, The filename is TIFF2026518661000130.tif5170, and here, TIFF2026518661000131.tif5170 is a variable TIFF2026518661000132.tif5170 and This is the copula function corresponding to TIFF2026518661000133.tif5170. These properties of copula-based estimation indicate that the resulting cumulative distribution function (CDF) metric may be more robust than utility metrics derived from conventional improvement-based acquisition functions.

[0131] Figure 4A depicts a schematic diagram comparing different utility metrics, including hypervolume, multivariate rank, and cumulative distribution function (CDF) indices, for different molecular designs (candidates) optimized for two objectives, Objective 1 and Objective 2. The hypervolume (HV) (or polytope) bounded by each candidate is shown in Graph 410, while the cumulative distribution function (CDF) indices and multivariate ranks of the candidates are shown in Graphs 420 and 430, respectively. As shown in Figure 4A, the cumulative distribution function (CDF) indices of the molecular designs coincide with those of the multivariate rank. Furthermore, the hypervolume (or polytope) bounded by the candidates also coincides with the multivariate rank and cumulative distribution function (CDF) indices of the molecular designs. This correspondence between the hypervolume (HV), multivariate rank, and cumulative distribution function (CDF) indices of the candidate molecules is further illustrated in Figure 4B. Graph 440 in Figure 4B, which plots hypervolume (HV) against the corresponding multivariate rank and cumulative distribution function (CDF) indices, shows strong correlations between the utility metrics. These three metrics exhibit a Pearson correlation coefficient of 0.9 and a Spearman correlation coefficient of 0.99. The relationship between multivariate ranking via the cumulative distribution function (CDF) and the corresponding probability density function (PDF) is shown in Figure 4C. Graph 460 in Figure 4C shows the probability density function (PDF) fitted to 200 result samples (gray dots) by kernel density estimation (KDE), where the result samples are drawn from an elliptic Gaussian distribution. Graph 450 shows the contour lines of the corresponding cumulative distribution function (CDF). TIFF2026518661000134.tif3170 These contour lines represent the Pareto frontier. The contour lines converge to approximate TIFF2026518661000135.tif4170. The bottom contour closely traces the convex shape of the true Pareto frontier 455.

[0132] As described above, in some cases, copulas can be used to estimate the cumulative distribution function (CDF) index of each computationally generated molecular design. In some cases, the cumulative distribution function (CDF) index of a molecular design can correspond to the multivariate rank of the molecular design. Thus, in some cases, the cumulative distribution function (CDF) index of a molecular design can be estimated by decomposing the underlying multivariate joint distribution into at least two or more marginal distributions of the objective (or molecular property of interest) being optimized and one or more copulas (e.g., bivariate copulas). This is schematically shown in Figure 5A, where two variables TIFF2026518661000136.tif4170 and Joint distribution across TIFF2026518661000137.tif4170 TIFF2026518661000138.tif5170 is the first variable The first marginal distribution and the second variable of TIFF2026518661000139.tif4170 Copulas describing the second marginal distribution of TIFF2026518661000140.tif4170, as well as the cross-correlations between them. It is broken down into TIFF2026518661000141.tif5170.

[0133] In some cases, each copula may be modeled according to a parametric family depending on the shape of the dependency structure. Examples of dependency structures of different shapes include the Clayton copula, the Gambler copula, and the Gauss copula. In some cases, pairwise factorization may be performed to decompose a multivariate joint distribution into a bivariate copula coupling that combines pair groupings of marginal distributions of the object being optimized (or molecular property of interest). In doing so, each edge represents a bivariate copula associated with a parametric or nonparametric estimation means. TIFF2026518661000142.tif7170 can be used to generate a structure called a vine (e.g., a graphical model) containing 71 trees. Considering the formula mentioned above, the cumulative distribution function (CDF) TIFF2026518661000143.tif5170) is the result obtained so far. TIFF2026518661000144.tif5170 measurements The acquisition function, which conforms to TIFF2026518661000145.tif5170, can be obtained as shown in equation (9) below. TIFF2026518661000146.tif6170

[0134] As mentioned, in some cases, pairwise factorization can be performed to decompose a multivariate joint distribution into marginal distributions joined by one or more bivariate copulas (or pair copulas). To illustrate further, consider any bivariate random vector The concurrent density of TIFF2026518661000147.tif5170 can be expressed as shown in equation (10) below, where, TIFF2026518661000148.tif5170 is the peripheral density, TIFF2026518661000149.tif5170 is a marginal distribution. Please understand that TIFF2026518661000150.tif3170 is a copula density. TIFF2026518661000151.tif5170

[0135] Therefore, any bivariate density can be uniquely described by the product of its peripheral density and copula density, the latter being a dependency structure that specifies the cross-correlations between peripheral densities. When there are three or more objectives (or molecular properties of interest), a bivariate copula (or pair copula) structure can be used. A bivariate copula formed by the decomposition of a simultaneous multivariate distribution with three or more variables can form a vine, which is a hierarchical structure with a cascade of bivariate copula blocks. In some cases, any TIFF2026518661000152.tif4170 dimensional copula density, TIFF2026518661000153.tif7170 can be decomposed into a product of 170 bivariate (conditional) copula densities. Even if the same simultaneous multivariate distribution can be factorized in different ways, the resulting bivariate copula is called a vine. TIFF2026518661000154.tif4 can form a sequence consisting of 170 nested trees. The trees are, It is represented as TIFF2026518661000155.tif5170, TIFF2026518661000156.tif5170 and TIFF2026518661000157.tif5170 is a tree TIFF2026518661000158.tif3170( Represents a set of nodes and edges in TIFF2026518661000159.tif4170. In this case, a tree Set of TIFF2026518661000160.tif3170 Each edge in TIFF2026518661000161.tif5170 TIFF2026518661000162.tif3170 can be associated with a bivariate copula. (4 variables) TIFF2026518661000163.tif4170, TIFF2026518661000164.tif4170, TIFF2026518661000165.tif4170, and TIFF2026518661000166.tif4170 and four marginal distributions TIFF2026518661000167.tif5170, TIFF2026518661000168.tif5170, TIFF2026518661000169.tif5170, and An example of a vine with six bivariate copulas obtained from pairwise factorization of a simultaneous multivariate distribution having TIFF2026518661000170.tif5170 is shown in Figure 5B. In practice, a single vine can contain two components. The first is a tree TIFF2026518661000171.tif5170( The second is a vine structure containing a set of TIFF2026518661000172.tif5170). TIFF2026518661000173.tif5170 and This is TIFF2026518661000174.tif5170.

[0136] In low-data regimes where actual wet-lab molecular design is largely unavailable, empirical Pareto frontiers can be particularly noisy. Therefore, in some cases, domain knowledge about one or more of the optimized objectives (or molecular properties of interest), such as the relative priorities of at least several objectives, can be leveraged when using vine copulas to construct model-based Pareto frontiers. For example, in some cases, known correlations between objectives (or molecular properties of interest) may be incorporated to specify the vine hierarchical structure. Furthermore, the selection of the copula model (e.g., the type of dependency, including tail behavior) can be indicated by a pairwise joint distribution that can be approximated based on domain knowledge. Thus, it should be understood that the advantages of integrating copula-based estimation means into the multivariate rank-based utility metrics and acquisition functions described herein include scalability from convenient pair-copula construction of vine, robustness to marginal scales and transformations due to intrinsic copula properties, and domain-aware copula structures from explicit encoding of dependencies in the vine copula matrix, including the selection of dependency types (e.g., low or high tail dependency).

[0137] To illustrate further, Figure 5C illustrates the use of copulas in the context of optimizing multiple objectives in drug discovery, where data tend to be sparse. Panel (a) shows a stochastic integrated transform (PIT) that yields a uniform margin before the vine copula is fitted to panel (b). Fitting the vine copula in panel (b) may include, for example, the selection of the copula shape from the parametric or nonparametric family. Finally, panel (c) shows the evaluation of the cumulative distribution function (CDF) from the copula. It should be understood that, through separate estimations of marginal distributions and copulas (e.g., dependency structures), different marginal distributions may have the same Pareto front in the stochastic integrated transform (PIT) space from which the cumulative distribution function (CDF) index is evaluated. Thus, by copula-based estimation means, the resulting cumulative distribution function (CDF) index can be robust without any overhead for scaling or standardization (e.g., across different units of measurement) as required for conventional acquisition functions and utility metrics. In other words, the cumulative distribution function (CDF) index estimated using the copula remains the same regardless of the marginal distribution. This robustness to any scaling of interest is further illustrated in the graph in Figure 6. As shown in Figure 6, the values ​​of conventional hypervolume (HV) indices are sensitive to scaling (e.g., TIFF2026518661000175.tif5170 is via TIFF2026518661000176.tif5170 (This is converted to TIFF2026518661000177.tif6170), but the values ​​of the cumulative distribution function (CDF) index are scale-invariant.

[0138] Panel (b) demonstrates that domain knowledge, including interactions between different objectives (or molecular properties of interest), can be encoded in a hierarchical structure of copula-based estimation means for a Caco2+ dataset associated with a Caco-2 cell line derived from human colorectal adenocarcinoma cells. In the Caco2+ example shown in Panel (b), the permeability of a molecular design is often highly positively correlated with its lipophilicity (measured by calculated logP (ClogP)) and negatively correlated with its topological polar surface area (tPSA). These correlations are particularly pronounced in the tails of the data distribution. Thus, in some cases, such dependencies can be encoded in the selection of vine copula structures and copula families for each pair. For example, in the Caco2+ example, a rotated Clayton copula may be selected to maintain the tail dependency between topological polar surface area (tPSA) and the permeability of the molecular design.

[0139] Table 1 below describes an example of an algorithm for multi-objective Bayesian optimization (MOBO) with a multivariate rank-based acquisition function that uses a copula to estimate cumulative distribution function (CDF) metrics corresponding to the multivariate ranks of each molecular design.

[0140] TIFF2026518661000178.tif172170

[0141] As mentioned above, In scenarios such as drug design with TIFF2026518661000179.tif4170 objectives (or molecular properties of interest), molecular design The multivariate ranks in TIFF2026518661000180.tif3170 may correspond to cumulative distribution function (CDF) metrics estimated using one or more copulas (e.g., bivariate copulas). For example, in some cases, at least TIFF2026518661000181.tif4170 characteristic calculation models TIFF2026518661000182.tif5170( TIFF2026518661000183.tif4170) may be applied, each being a probabilistic surrogate model that approximates a probability distribution enumerating the probability of occurrence of each possible value for the corresponding objective (or molecular property of interest). In some cases, due to the competing nature of at least some objectives (or molecular properties of interest), a single molecular design that has the best value for all objectives (or molecular properties of interest) may be applied. TIFF2026518661000184.tif3170 may not exist. Therefore, the goal of multi-objective Bayesian optimization (MOBO) is molecular design in which improving one objective (or molecular property of interest) leads to deterioration of at least one other objective (or molecular property of interest). This could involve identifying a set of Pareto optimal solutions, which is TIFF2026518661000185.tif3170. For example, Pareto optimal solutions for optimization across expression levels and binding affinity are molecular designs where improvement in expression level leads to a decrease in binding affinity. This could be a set of TIFF2026518661000186.tif4170. In some cases, molecular design that is a Pareto optimal solution. TIFF2026518661000187.tif3170 can be identified in this case based on its utility metric, which is a cumulative distribution function (CDF) index corresponding to the multivariate rank of the molecular design. Two molecular designs TIFF2026518661000188.tif4170 and The cumulative distribution function (CDF) of TIFF2026518661000189.tif4170 is based on the quality of each as a Pareto optimal solution for molecular design. TIFF2026518661000190.tif4170 and TIFF2026518661000191.tif4170 can be ordered. Second molecular design First molecular design with better cumulative distribution function (CDF) index than TIFF2026518661000192.tif4170 TIFF2026518661000193.tif4170 is the first molecular design TIFF2026518661000194.tif4170 is the second molecular design It may be possible to show that this is likely a Pareto optimal solution exhibiting a better combination of properties (e.g., drug-like properties) than TIFF2026518661000195.tif4170. In this case, the first molecular design TIFF2026518661000196.tif4170 is closer to the Pareto frontier occupied by Pareto optimal (or non-dominant) solutions, while the second molecular design It can be said that TIFF2026518661000197.tif4170 is dominant.

[0142] In some cases, a single-molecule design property model is used for each design iteration. Sequential optimization, including querying TIFF2026518661000198.tif5170, may be impractical for many applications due to feedback waiting times. For example, in protein engineering, it may be necessary to select a batch of molecular designs in a given iteration and wait several months to receive measurements. From a large pool of 170 candidates, TIFF2026518661000199.tif5 Selecting a batch of 170 molecular designs simultaneously may, in some cases, require evaluation of combinations of acquisition functions, which may be multivariate rank-based acquisition functions rather than conventional acquisition functions such as improvement-based or entropy-based acquisition functions. In the context of optimizing molecular designs based on the gradient of the acquisition function, during each design iteration... Sequential greedy selection of 170 molecular designs is performed using various acquisition functions, including the multivariate rank-based acquisition function described herein. TIFF2026518661000202.tif4 can achieve equivalent performance compared to simultaneously selecting 170 candidates.

[0143] Many molecular design applications require execution at several hierarchical levels among multiple objectives (or molecular properties of interest). For example, in some cases, some properties may take precedence over others. TIFF2026518661000203.tif4170 partially ordered objective (or molecular property of interest) is an ordered set of properties: It can be represented as TIFF2026518661000204.tif7170. TIFF2026518661000205.tif4170 is a hierarchy level The characteristics of TIFF2026518661000206.tif5170 are shown. TIFF2026518661000207.tif5170 is at the same level TIFF2026518661000208.tif4170 TIFF2026518661000209.tif5170 is its index among the sibling properties. As mentioned, in some cases, partial ordering can arise from experimental dependencies where one property of a molecular design must satisfy one or more criteria (e.g., passing a certain threshold) before other properties can be measured. Alternatively and / or additionally, partial ordering can reflect priorities for certain types of molecular designs. For example, in some cases, one or more properties may be prioritized such that a molecular design that does not perform well in these properties may be rejected regardless of how well it performs in the other properties. In some cases, corresponding When performing pairwise factorization of a 170-dimensional joint distribution, TIFF2026518661000211.tif4 can encode a partial order of 170 objective (or molecular properties of interest). Pairwise factorization of TIFF2026518661000212.tif4170-dimensional joint distribution is, TIFF2026518661000213.tif7 is concatenated by 170 bivariate copulas. A vine can be generated, which is a hierarchical structure consisting of a sequence of 170 nested trees. In some cases, the hierarchical structure of a vine may have a first objective that takes precedence over a second objective, occupying a higher level of the hierarchy than the second objective. TIFF2026518661000215.tif4170 may correspond to a partial order of objectives (or molecular properties of interest).

[0144] Exemplary Tasks for Multiobjective Bayesian Optimization (MOBO)

[0145] The performance of the selection engine 120 using various different acquisition functions and utility metrics was evaluated experimentally on four tasks, including the production of Branin-Currin, DTLZ, and penicillin, which were simulated tasks, as well as real-world drug design set up in the form of Caco2+. In these exemplary use cases, the selection engine 120 performed multi-objective Bayesian optimization (MOBO) using the hypervolume (HV) and cumulative distribution function (CDF) metrics described herein. Different acquisition functions include conventional acquisition functions such as the Noised Predictive Hypervolume Improvement (NEHVI) acquisition function, the Noised Pareto Efficient Global Optimization (Noised ParEGO) acquisition function, and two versions of the multivariate rank-based acquisition function described herein. The Bayesian optimization (BO) simulation was performed on the number of design iterations. While changing TIFF2026518661000216.tif4170, for all experiments The batch processing was performed with the batch size of TIFF2026518661000217.tif4170. Other parameters for the experiment were the initial data size. TIFF2026518661000218.tif5170, size of the design candidate pool The file TIFF2026518661000219.tif4170 included the number of predicted post-hoc samples L output by each characteristic calculation model. The pool size was for the selected batch. The file is fixed at TIFF2026518661000220.tif7170, and the number of predicted backsamples is It will be fixed to TIFF2026518661000221.tif4170.

[0146] For the DTLZ benchmark task, the selected engine 120 is: TIFF2026518661000222.tif4170 and three different number objectives Using TIFF2026518661000223.tif5170 TIFF2026518661000224.tif4 170 design iterations were performed. The problem with penicillin manufacturing is, TIFF2026518661000225.tif4170 and TIFF2026518661000226.tif4170 TIFF2026518661000227.tif4 includes 170 design iterations. Branin-Currin benchmark task ( TIFF2026518661000228.tif4170) has two purposes, as shown below. TIFF2026518661000229.tif4170 and Two functions in TIFF2026518661000230.tif4170 TIFF2026518661000231.tif5170 and This configuration of Branin and Currin functions features a concave Pareto front (in the maximized setting) and includes maximizing TIFF2026518661000232.tif5170. The selection engine 120 is, Perform multi-objective Bayesian optimization (MOBO) over 170 design iterations in TIFF2026518661000233.tif4. TIFF2026518661000234.tif26170

[0147] Returning to the Caco2+ example, this task is optimized TIFF2026518661000235.tif4170 objectives (or molecular properties of interest) TIFF2026518661000236.tif4 was run for 170 design iterations. The Caco2+ example uses the Caco2+ dataset, generated by modifying the Caco-2 dataset, which contains 906 drug molecules annotated with experimentally measured permeability through human colon epithelial cancer cell lines. Each of these molecules is represented as a concatenation of fingerprint and fragment feature vectors. Modifications involve augmenting the dataset with additional properties such as drug-likeness score (quantitative estimate of drug-likeness (QED)) and topological polar surface area (TPSA). As will be discussed in more detail below, subsets of these properties, such as permeability and topological polar surface area (TPSA), can be competitive, meaning that improving one property leads to a deterioration of the other. Such trade-offs become more dramatic as additional objectives (or molecular properties of interest) are introduced, as is often the case during late-stage drug optimization.

[0148] As mentioned above, in the Caco2+ task, the goal of multi-objective Bayesian optimization is to identify molecular designs that exhibit maximum cell permeability, which is a measure of how easily a molecule can pass through the cell membrane. Permeability is a crucial property in drug discovery (DD) programs, often because the targeted disease protein is located inside the cell, i.e., present within the cell. In this experiment, molecular design TIFF2026518661000237.tif4170 was applied to a monolayer of Caco2 cells, and after incubation, both the input and output sides of the monolayer were... Concentration of TIFF2026518661000238.tif4170 TIFF2026518661000239.tif3170 was measured, and the value TIFF2026518661000240.tif4170 and The file TIFF2026518661000241.tif4170 is obtained. TIFF2026518661000242.tif7170 is a molecular design Final transmission label for TIFF2026518661000243.tif4170 It will be treated as TIFF2026518661000244.tif6170.

[0149] Cell membranes contain a complex mixture of lipids and other biomolecules. For molecules to enter the membrane and (passively) diffuse, they must interact favorably with these biomolecules and / or avoid disrupting their packing structure. Therefore, molecular design is crucial. Increasing the lipophilicity (logP) of TIFF2026518661000245.tif4170 increases permeability. One strategy to increase TIFF2026518661000246.tif6170 is to increase lipophilicity (logP). However, increasing lipophilicity (logP) can also increase the disorderly binding of molecules to non-disease-related proteins, potentially leading to undesirable side effects. Therefore, in some cases, multi-objective Bayesian optimization (MOBO) tasks may be more suitable for molecular design. The calculated logP(clogP) for TIFF2026518661000247.tif4170, TIFF2026518661000248.tif6170) at least reduces (or minimizes) its transparency Increasing (or maximizing) TIFF2026518661000249.tif6170 may include optimizing two competing objectives. Furthermore, other objectives for multi-objective Bayesian optimization in drug discovery (DD) settings may include increasing the affinity and specificity of binding to the target molecule. In contrast to the aforementioned non-specific lipophilic interactions, polar contacts (e.g., hydrogen bonding) between the drug molecule and the target protein molecule can result in higher affinity and more specific binding. Molecular design Topological polar surface area (TPSA) of TIFF2026518661000250.tif4170, TIFF2026518661000251.tif5170) is one indicator of the ability to form such interactions, and therefore another objective optimized for the Caco2+ task. However, as in the case of reducing logP, molecular design Topological polar surface area (TPSA) of TIFF2026518661000252.tif4170, Increasing TIFF2026518661000253.tif5170) will increase its transparency This could negatively impact TIFF2026518661000254.tif6170. Therefore, molecular design Topological polar surface area (TPSA) of TIFF2026518661000255.tif4170, TIFF2026518661000256.tif5170) and its transparency TIFF2026518661000257.tif6170 is also a competing objective. To illustrate further, Figure 9A shows two examples of molecular designs with desirable combinations of topological polar surface area (TPSA), permeability, and lipophilicity (calculated logP) values. In contrast, Figure 9B shows an example of a molecular design with a poor combination of topological polar surface area (TPSA), permeability, and lipophilicity (calculated logP) values.

[0150] Considering these experimental tasks, the table in Figure 7 shows the changes in the values ​​of different utility metrics over multiple multi-objective Bayesian optimization (MOBO) processes. Referring to Figure 7, the changes in the hypervolume (HV) and cumulative distribution function (CDF) indices of molecular designs generated for the Branin-Currin task over 30 multi-objective Bayesian optimizations (MOBOs) are shown in Graphs 710 and 720. The changes in the hypervolume (HV) and cumulative distribution function (CDF) indices of molecular designs generated for the DTLZ task over 30 multi-objective Bayesian optimizations (MOBOs) are also shown in Graphs 710 and 720.

[0151] To further compare the hypervolume (HV) index and the cumulative distribution function (CDF) index, Table 2 below shows the mean and standard deviation of the hypervolume (HV) index values ​​calculated in their original units, and the values ​​of the cumulative distribution function (CDF) index for different tasks. It should be understood that higher mean and standard deviation are considered to indicate better performance. The two versions of the multivariate ranking-based acquisition function described herein are annotated as MVR v1 and MVR v2. As shown in Table 2, the performance of the Noisy Predictive Hypervolume Improvement (NEHVI) is as follows: The value of TIFF2026518661000258.tif4170 decreases as its value increases. Meanwhile, Graph 800 in Figure 8 compares the wall clock time per call of different acquisition functions for the Branin-Currin task and the DTLZ task. As shown in Figure 8, the multivariate ranking-based acquisition functions described herein achieved comparable performance in identifying Pareto optimals across different tasks, but their performance is faster due to the reduced computational complexity of using copulas to estimate the cumulative distribution function (CDF) index. Furthermore, it should be understood that the cumulative distribution function (CDF) index described herein has a more interpretable scale than hypervolume indexes whose scale does not carry any information about the internal order of molecular designs. For example, in some cases, the cumulative distribution function (CDF) index described herein may be bounded by values ​​between 0 and 1, with values ​​closer to 1 associated with Pareto optimals close to the Pareto frontier.

[0152] TIFF2026518661000259.tif108170

[0153] Figure 10 depicts a block diagram showing an example of a computing system 1100 according to several exemplary embodiments. Referring to Figures 1 to 10, the computing system 1100 may be used to implement a molecular design engine 110, a selection engine 120, laboratory equipment 130, client devices 140, and / or any components thereof.

[0154] As shown in Figure 10, the computing system 1100 may include a processor 1110, memory 1120, storage device 1130, and input / output device 1140. The processor 1110, memory 1120, storage device 1130, and input / output device 1140 may be interconnected via a system bus 1150. The processor 1110 is capable of processing instructions for execution within the computing system 1100. Such executed instructions may implement one or more components, such as a molecular design engine 110, a selection engine 120, laboratory equipment 130, or a client device 140. In some exemplary embodiments, the processor 1110 may be a single-threaded processor. Alternatively, the processor 1110 may be a multi-threaded processor. The processor 1110 is capable of processing instructions stored in memory 1120 and / or storage device 1130 to display graphical information for a user interface provided via the input / output device 1140.

[0155] Memory 1120 is a computer-readable medium, such as volatile or non-volatile, that stores information within the computing system 1100. Memory 1120 can store, for example, data structures representing a configuration object database. Storage device 1130 is capable of providing persistent storage for the computing system 1100. Storage device 1130 may be a floppy disk device, a hard disk device, an optical disk device, or a tape device, or other suitable persistent storage means. Input / output device 1140 provides input / output operations for the computing system 1100. In some exemplary embodiments, input / output device 1140 includes a keyboard and / or a pointing device. In various embodiments, input / output device 1140 includes a display unit for displaying a graphical user interface.

[0156] According to some exemplary embodiments, the input / output device 1140 may provide input / output operation for network devices. For example, the input / output device 1140 may include an Ethernet port or other networking port to communicate with one or more wired and / or wireless networks (e.g., a local area network (LAN), a wide area network (WAN), the Internet).

[0157] In some exemplary embodiments, the computing system 1100 may be used to run various interactive computer software applications that can be used for organizing, analyzing, and / or storing various forms of data. Alternatively, the computing system 1100 may be used to run any type of software application. These applications may be used to perform various functions, such as planning functions (e.g., generating, managing, and editing spreadsheet documents, word processing documents, and / or any other objects), computing functions, communication functions, etc. An application may include various add-in functions or may be a standalone computing product and / or function. When activated within an application, functionality may be used to generate a user interface provided via the input / output device 1140. The user interface may be generated by the computing system 1100 and presented to the user (e.g., on a computer screen monitor).

[0158] One or more aspects or features of the subject matter described herein may be realized in digital electronic circuits, integrated circuits, specially designed ASICs, field-programmable gate array (FPGA) computer hardware, firmware, software, and / or combinations thereof. These various aspects or features may include implementations in one or more computer programs executable and / or interpretable on a programmable system which includes at least one programmable processor, which may be special or general-purpose, coupled to receive data and instructions from a storage system, at least one input device, and at least one output device, and to transmit data and instructions to the storage system, at least one input device, and at least one output device. The programmable system or computing system may include clients and servers. Clients and servers are generally remote from each other and generally interact over a communication network. The relationship between clients and servers is brought about by computer programs running on each computer and having a client-server relationship with each other.

[0159] These computer programs, also called programs, software, software applications, applications, components, or code, contain machine instructions for a programmable processor and may be implemented in high-level procedural and / or object-oriented programming languages ​​and / or assembly / machine languages. As used herein, the term “machine-readable medium” means any computer program product, apparatus, and / or device used to provide machine instructions and / or data to a programmable processor, such as magnetic disks, optical disks, memory, and programmable logic devices (PLDs), and includes machine-readable medium that receives machine instructions as machine-readable signals. The term “machine-readable signals” means any signals used to provide machine instructions and / or data to a programmable processor. Machine-readable medium can store such machine instructions non-temporarily, such as non-temporarily solid-state memory, magnetic hard drives, or any equivalent storage medium. Machine-readable medium can, alternatively or additionally, store such machine instructions temporarily, such as processor caches or other random-access memories associated with one or more physical processor cores.

[0160] To provide user interaction, one or more aspects or features of the subject matter described herein may be implemented on a computer having, for example, a display device such as a cathode ray tube (CRT), liquid crystal display (LCD), or light-emitting diode (LED) monitor for displaying information to the user, and a keyboard and a pointing device such as a mouse or trackball, to which the user can provide input to the computer. User interaction may also be provided using other types of devices. For example, the feedback provided to the user may be any form of sensory feedback, such as visual feedback, auditory feedback, or tactile feedback, and input from the user may be received in any form, including acoustic, speech, or tactile input. Other possible input devices include touchscreens, or single-point or multi-point resistive or capacitive trackpads, speech recognition hardware and software, optical scanners, optical pointers, digital image capture devices, and other touch-sensitive devices such as associated interpretation software.

[0161] In the above description and claims, phrases such as “at least one of ~” or “one or more of ~” may appear, followed by a conjunctive list of elements or features. The term “and / or” may also be used in the enumeration of two or more elements or features. Unless implicitly or explicitly contradicted by the context in which it is used, such phrases are intended to mean either any of the enumerated elements or features individually, or any of the enumerated elements or features in combination with any of the other enumerated elements or features. For example, the phrases “at least one of A and B,” “one or more of A and B,” and “A and / or B” are intended to mean “A only,” “B only,” or “A and B together,” respectively. A similar interpretation is intended for lists containing three or more items. For example, the phrases “at least one of A, B, and C;”, “one or more of A, B, and C;”, and “A, B, and / or C” are intended to mean “A alone, B alone, C alone, A and B, A and C, B and C, or A, B and C,” respectively. The use of the term “based on” in the foregoing and in the claims is intended to mean “at least partially based,” so as to allow for features or elements that are not enumerated.

[0162] The subject matter described herein may be implemented in systems, apparatus, methods, and / or articles, depending on the desired configuration. The implementations described above do not necessarily represent all implementations of the subject matter described herein. Rather, those embodiments are merely examples that correspond to the aspects associated with the described subject matter. While several variations have been described in detail above, other modifications or additions are also possible. In particular, further features and / or variations may be provided in addition to those described herein. For example, the embodiments described herein may cover various combinations and partial combinations of the disclosed features, and / or combinations and partial combinations of some of the further features described herein. Furthermore, the logical flows shown in the accompanying drawings and / or described herein do not necessarily require a specific order or sequence shown to achieve the desired result. Other embodiments may fall within the scope of the following claims.

Claims

1. To generate multiple molecular designs, Applying one or more characteristic calculation models to determine the multiple characteristics exhibited by the multiple molecular designs, wherein the one or more characteristic calculation models are trained to approximate the probability distribution of each of the multiple characteristics. Determining a cumulative distribution function (CDF) index for each of the plurality of molecular designs based at least on the output of one or more characteristic calculation models, wherein the cumulative distribution function (CDF) index of the molecular design corresponds to the multivariate rank of the molecular design, and the multivariate rank of the molecular design quantifies and determines the probability that none of the plurality of characteristics present in the molecular design can be improved without degrading at least one other characteristic among the plurality of characteristics. Based at least on the cumulative distribution function (CDF) index of each molecular design, one or more molecular designs are selected from multiple molecular designs as candidates for wet lab evaluation. Computer implementation methods, including those mentioned above.

2. The method according to claim 1, wherein one or more characteristic calculation models are trained to approximate a first probability distribution of a first plurality of possible values ​​of a first characteristic among the plurality of characteristics, and the one or more characteristic calculation models are further trained to approximate a second probability distribution of a second plurality of possible values ​​of a second characteristic among the plurality of characteristics.

3. The method according to claim 2, wherein the output of the one or more characteristic calculation models includes a plurality of predicted samples from the first probability distribution and the second probability distribution, each predicted sample including a first value of the first characteristic and a second value of the second characteristic present in the molecular design.

4. The cumulative distribution function (CDF) index for each molecular design is at least: Based at least on the output of the one or more characteristic calculation models, the marginal distribution of each of the multiple characteristics is determined. Based at least on the output of the one or more characteristic calculation models, one or more copulas that describe the cross-correlations between the multiple characteristics are determined. The cumulative distribution function (CDF) index of each molecular design is determined based on the marginal distribution of each characteristic and at least one of the copulas. The method according to any one of claims 1 to 3, as determined by...

5. The cumulative distribution function (CDF) index for each molecular design is at least: Based at least on the output of the one or more characteristic calculation models, a first marginal distribution of the first characteristic among the plurality of characteristics is determined. Based at least on the output of the one or more characteristic calculation models, a second marginal distribution of the second characteristic among the plurality of characteristics is determined. A first copula that combines the first marginal distribution and the second marginal distribution is determined by at least describing the dependency between the first characteristic and the second characteristic based at least on the output of the one or more characteristic calculation models. The method according to any one of claims 1 to 4, as determined by...

6. The cumulative distribution function (CDF) index for each molecular design is further defined as, at least, Determining the third peripheral distribution of the third characteristic among the aforementioned multiple characteristics, Determining a second copula that combines the third marginal distribution with at least one of the first and second marginal distributions. The method according to claim 5, as determined by...

7. The method according to claim 6, wherein the first copula and the second copula are bivariate copulas that form a vine.

8. The method according to claim 7, wherein the vine is determined to exhibit a hierarchical structure corresponding to a suborder in which the first characteristic takes precedence over the second characteristic and / or the third characteristic.

9. The cumulative distribution function (CDF) index for each molecular design is at least: To determine one or more pairwise groupings of the aforementioned plurality of characteristics, a pairwise factorization of the multivariate joint distributions corresponding to the plurality of characteristics is performed, wherein each pairwise grouping of the plurality of characteristics corresponds to a bivariate joint distribution. To determine a bivariate copula that combines each pairwise grouping of the aforementioned multiple characteristics. The method according to any one of claims 1 to 8, as determined by...

10. The cumulative distribution function (CDF) index for each molecular design is at least: The method according to claim 9, determined by determining the type of the bivariate copula that combines each pairwise grouping of the plurality of characteristics, based at least on the tail behavior of the bivariate joint distribution.

11. The method according to claim 10, wherein the type of the bivariate copula is one of a Clayton copula, a Gambler copula, or a Gauss copula.

12. The cumulative distribution function (CDF) index for each molecular design is at least: The mean and covariance of the multiple characteristics are determined based at least on the measurement set, Determining a multivariate Gaussian distribution of multiple possible values ​​of the multiple characteristics, based at least on the mean and covariance of the multiple characteristics, The cumulative distribution function (CDF) index for each molecular design is determined based at least on the aforementioned multivariate Gaussian distribution. The method according to any one of claims 1 to 11, as determined by...

13. The cumulative distribution function (CDF) index for each molecular design is at least: Determining an empirical cumulative distribution function based at least on a set of measurements, wherein the empirical cumulative distribution function includes a step function that increases by 1 / n for each of the n data points in the set of measurements, and the empirical cumulative distribution function outputs a value corresponding to the proportion of measurements in the set that are less than or equal to the specified value for any specified value of the plurality of characteristics. Based at least on the aforementioned empirical cumulative distribution function, the cumulative distribution function (CDF) index for each molecular design is determined. The method according to any one of claims 1 to 12, as determined by...

14. The cumulative distribution function (CDF) index for each molecular design is at least: In order to estimate the multivariate joint distribution corresponding to the aforementioned multiple characteristics, kernel density estimation (KDE) is performed, Based at least on the estimates of the multivariate joint distribution, the cumulative distribution function (CDF) index for each molecular design is determined. The method according to any one of claims 1 to 13, as determined by...

15. The method according to any one of claims 1 to 14, wherein the cumulative distribution function (CDF) index for each molecular design is a predicted cumulative distribution function (CDF) index whose value is determined to explain the uncertainty of the output of one or more characteristic calculation models.

16. The method according to any one of claims 1 to 15, further comprising selecting the one or more molecular designs as candidates for wet lab evaluation based on at least one or more molecular designs having a better cumulative distribution function (CDF) index than one or more molecular designs generated during previous iterations of multi-objective Bayesian optimization.

17. Selecting a first molecular design as a candidate for wet lab evaluation based at least on a first cumulative distribution function (CDF) index of the first molecular design that satisfies one or more thresholds, The second molecular design is excluded from the wet lab evaluation candidates based at least on a second cumulative distribution function (CDF) index of the second molecular design that does not satisfy one or more of the thresholds. The method according to any one of claims 1 to 16, further comprising:

18. The method according to any one of claims 1 to 17, further comprising selecting the first molecular design as a candidate for wet lab evaluation instead of the second molecular design, at least on the basis that the first cumulative distribution function (CDF) index of the first molecular design is better than the second cumulative distribution function (CDF) index of the second molecular design.

19. The method according to any one of claims 1 to 18, further comprising selecting a threshold amount for a molecular design having the best cumulative distribution function (CDF) index as a candidate for wet lab evaluation, based at least on the cumulative distribution function (CDF) index of each molecular design.

20. Receiving a set of measurements related to multiple previous molecular designs, wherein each set of measurements includes one or more measurements of multiple properties exhibited by each previous molecular design. Training one or more characteristic calculation models to approximate the probability distribution of each of the multiple characteristics based at least on the measurement set. The method according to any one of claims 1 to 19, further comprising:

21. For the one or more molecular designs selected as candidates for wet lab evaluation, to receive one or more additional measurements of the multiple properties, Retraining the one or more characteristic calculation models based on at least one or more of the aforementioned additional measurements, Applying the one or more retrained property calculation models to determine the multiple properties exhibited by one or more subsequent molecular designs The method according to claim 19, further comprising:

22. The method according to claim 21, wherein the retraining of the one or more characteristic calculation models includes updating the probability distribution of each of the plurality of characteristics approximated by the one or more characteristic calculation models, based on at least the one or more additional measurements.

23. The method according to any one of claims 21 to 22, wherein the plurality of prior molecular designs are generated during a previous iteration of multi-objective Bayesian optimization (MOBO), the plurality of molecular designs are generated during the current design iteration of multi-objective Bayesian optimization (MOBO), and the one or more subsequent molecular designs are generated during a subsequent iteration of multi-objective Bayesian optimization (MOBO).

24. The method according to any one of claims 1 to 23, wherein the one or more characteristic calculation models include at least one ensemble of characteristic calculation models, in which the multiple characteristic calculation models are trained to determine a single characteristic among the multiple characteristics.

25. At least one data processor, A memory that stores instructions which, when executed by the at least one data processor, result in an operation including the method according to any one of claims 1 to 24, A system that includes these features.

26. A non-temporary computer-readable medium storing instructions that, when executed by at least one data processor, result in an operation comprising the method according to any one of claims 1 to 24.

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