Physical information smoothing operator learning for high-dimensional system prediction and control

Abstract

An operator learning model generator is provided for training a smoothed operator learning model for predicting airflow dynamics in a room used by a controller connected to a heating, ventilation, and air conditioning (HVAC) system. The operator learning model generator includes an interface circuit configured to receive a training dataset via a network connected to a simulation computer, wherein the training dataset includes un-trajectories of airflow in the room for various time series of control actions applied to the HVAC system; a memory configured to store the smoothed operator learning model including an autoencoder and a neural ordinary differential equation, the training dataset, and training instructions for the smoothed operator learning model; and a processor configured to train the smoothed operator learning model stored in the memory, wherein the training instructions include jerk regularization that constrains smoothness of dynamics predicted by the smoothed operator learning model.

Description

Technical Field

[0001] This disclosure generally relates to system modeling, prediction, and control, and more specifically to systems and methods for reducing the order of high-dimensional physical systems to model and control using neural network models. Background Technology

[0002] Control theory in control systems engineering is a subfield of mathematics that deals with the control of continuously operating dynamic systems in engineering processes and machines. The goal is to develop a control strategy for controlling and regulating the behavior of such systems. The control strategy specifies appropriate control actions for the system at each time step to achieve the desired outcome defined by an objective function. Examples of desired outcomes specified by the objective function include stabilizing the system or tracking a desired state trajectory while minimizing certain costs.

[0003] The control strategy can be open-loop, in which case the control action at a given time is not a function of the system's current state. The control strategy can also be closed-loop, in which case the control action at a given time is a function of the system's current state, reconstructed in real-time from physical sensor data using an estimation algorithm.

[0004] The physical model of a system's dynamics, or physical model of a system, uses ordinary differential equations (ODEs) or partial differential equations (PDEs) to describe the system's dynamics. These ODEs or PDEs are constructed based on physical conservation laws and principles, and they can be linear or nonlinear. Given an initial state and an arbitrary sequence of control actions, the physical model of the system can be used to predict the future state of the system at any desired time.

[0005] Operator learning models of system dynamics, or system operator learning models, use neural network models to describe the dynamics of a system. Operator learning models are constructed using computational data generated by the system. Similar to physical models, operator learning models can be used to predict the future state of the system at any desired time, given an initial state and arbitrary control sequences. However, the computational cost of solving an operator learning model can be significantly lower than that of solving a physical model, especially in the case of a physical model described by a PDE.

[0006] One class of approaches for developing control strategies includes model-based techniques, where a physical model of the system is used directly when designing the control strategy. This approach can be open-loop or closed-loop and can be applied to control dynamical systems of varying complexity. Examples of such systems can include production lines, car engines, robots, CNC machining, electric motors, satellites, and generators. The advantage of model-based techniques is that the resulting control strategies have performance guarantees because they are designed based on system dynamics.

[0007] High-dimensional systems are systems whose states are of high dimensionality, meaning they are described by a large number of variables or by continuous functions of space. Examples of such systems include power grids, buildings, room airflow, and smart grids. Systems whose physical models are described by PDEs are always high-dimensional. Solving the physical model of a high-dimensional system can be computationally very expensive, especially when the physical model is described by a PDE. Therefore, model-based control strategies for high-dimensional systems may be computationally too expensive to implement in a computer architecture.

[0008] Therefore, another approach for developing control strategies includes data-driven techniques that utilize computational data generated by the system to construct control strategies that achieve the desired results.

[0009] In examples of data-driven techniques, control policies can be directly constructed based on computational data. The drawback of this approach is that it may require a large amount of data and lacks performance guarantees when the system's state during operation differs from the state present in the data used to construct the control policy.

[0010] In another example of data-driven techniques, a simplified surrogate model of the system can be constructed first using computational data generated by the system. This simplified model predicts the future state of the system at any desired time given an initial state and arbitrary control sequences, and can be in the form of an operator-learned model. A control policy can then be designed based on model-based techniques applied to the simplified model. When the computational cost of solving the simplified model is low, the control policy based on the generated model can be implemented online in a computer architecture. However, constructing a simplified surrogate model of the system with sufficient accuracy to ensure good control policy performance may require a large amount of data.

[0011] To address the aforementioned issues, some methods for constructing operator learning models incorporate the physical model represented by the PDE into the training process for the neural network. An advantage is that the resulting operator learning model may require less training data because it learns to satisfy the physical conservation laws of control system dynamics. However, these methods do not incorporate the inherent dynamical smoothness properties of most physical systems into the training process. Dynamical smoothness refers to the property of a system's state changing smoothly over sufficiently short timescales. Therefore, operator learning models constructed using these methods may not exhibit sufficient accuracy to ensure good performance of model-based control strategies designed based on these proxy models.

[0012] Therefore, there is a need for methods and systems for incorporating the smoothing properties of dynamics into operator-learning models, so that effective control strategies based on these operator-learning surrogate models can be implemented in computer architectures used to control high-dimensional dynamical systems. Summary of the Invention

[0013] Embodiments of the present invention provide a computer-implemented method and system for using a smooth operator learning surrogate model of a high-dimensional dynamical system trained with control inputs to regularize the training process by leveraging the smoothing properties of dynamics. The operator learning surrogate model can be used to predict the future state of the system at any desired time given an initial state and arbitrary control sequences. The operator learning surrogate model has an autoencoder architecture comprising an encoder neural network, a nonlinear propagator composed of neural ODEs, and a decoder neural network. The encoder is configured to encode a digital representation of the high-dimensional state into a low-dimensional latent vector belonging to the latent space at the initial time; the neural ODE propagator is configured to propagate the latent vector in the latent space using a nonlinear transformation; and the decoder is configured to decode the propagated latent vector in the latent space back into a digital representation of the high-dimensional state.

[0014] The computer-implemented method includes collecting digital representations of high-dimensional state sequences at different time instances during the system's operation, as well as digital representations of time sequences of control action values ​​applied to the system during its operation. This collection is performed multiple times, starting with different initial conditions of the states and using time sequences of control action values. For a given initial condition of the state, the sequence of states and the time sequence of control action values ​​at different time instances are called solution trajectories. The collection of collected solution trajectories is called the training set.

[0015] The computer-implemented method also includes training the operator learning model in two stages.

[0016] In the first training phase, the encoder and decoder are trained to compress high-dimensional states into low-dimensional latent vectors and vice versa. To achieve this, in each training iteration, a sequence of high-dimensional states belonging to randomly sampled solution trajectories in the training set is applied as input to the encoder, which outputs a corresponding sequence of low-dimensional latent vectors. These latent vectors are then applied as input to the decoder, which outputs a corresponding sequence of high-dimensional states. The loss consists of two parts. The first part penalizes the mean squared error between the state sequence returned as output by the decoder and the ground truth state sequence applied as input to the encoder. The second part penalizes the accelerometer along the curve drawn by the sequence of latent vectors in the latent space. Since this sequence of latent vectors is obtained from the state sequence belonging to a given solution trajectory, minimizing the accelerometer in the latent space is equivalent to the smoothing property of constrained dynamics.

[0017] In the second training phase, the neural ODE propagator is trained to learn the dynamics of the system in the latent space. To achieve this, each solution trajectory in the training set is first mapped to the latent space by passing a high-dimensional state sequence of each trajectory to the encoder, thus obtaining a corresponding ground truth latent vector sequence. Then, in each training iteration, the initial ground truth latent vector and the time series of control action values ​​corresponding to the randomly sampled trajectories are applied to the neural ODE propagator, which returns the corresponding latent vector sequence. The loss is then penalized by the mean squared error between the latent vector sequence predicted by the neural ODE propagator and the ground truth latent vector sequence.

[0018] In some implementations, the training set of solution trajectories is obtained by a numerical solver that solves the PDE defined by the physical model of the system. For example, if the system of interest is airflow in a room with air conditioning control, computational fluid dynamics (CFD) simulations can be used to compute the solution trajectories. CFD simulations solve the physical Navier-Stokes equations governing the fluid flow to obtain a sequence of states corresponding to the initial state and any sequence of control actions.

[0019] In some implementations, the method further includes incorporating the physical model represented by the PDE into a second training phase for the neural ODE propagator. In this case, the loss includes an additional physical information term penalizing the mean square error between the time derivative of the latent vectors predicted by the neural ODE and the ground truth time derivative of the PDE defined by the physical model. The second part can be evaluated on latent vectors corresponding to states in the training set trajectory, or on latent vectors corresponding to arbitrary states satisfying boundary conditions or other constraints associated with the system. This incorporation of the physical model into the training method yields a physical information manipulator learning model.

[0020] In some implementations, the method further includes generating control actions using a model-based control strategy to control the system in real time, wherein the model used to design the control strategy is a trained operator-learned surrogate model, and the objective of the control is to minimize a user-specified objective function.

[0021] In some implementations, the method further includes generating control actions to control the system based on a hybrid model-based and reinforcement learning control policy, wherein the model used to design the control policy is a trained operator-learning agent model. Starting with a model-based control policy as a warm start, the hybrid model-based and reinforcement learning approach iteratively refines the policy parameters to achieve better control performance by alternating between collecting data using the current control policy and updating the policy parameters to minimize a user-specified objective function.

[0022] According to some embodiments of the present invention, an operator learning model generator is provided for training a smooth operator learning model, the smooth operator learning model including an automatic encoder and a neural constant differential equation (ODE) used by a heating, ventilation and air conditioning (HVAC) controller in a system including airflow in a room with HVAC actuators. The operator learning model generator may include: an interface circuit configured to receive a training dataset via a network connected to an analog computer, wherein the training dataset includes solution trajectories of airflow in a room starting from different initial conditions of the state and controlled by HVAC actuators over different time series; a memory configured to store a smoothing operator learning model for predicting the dynamics of airflow in the room, the training dataset, and training instructions for the smoothing operator learning model; and a processor configured to train the smoothing operator learning model stored in the memory, wherein the training instructions include the following steps: training the autoencoder to learn a mapping from a high-dimensional state space to a low-dimensional latent space based on a training loss, wherein the training loss includes both a reconstruction loss and an acceleration loss evaluated on solution trajectories belonging to the training dataset; and training a neural ODE network to learn solution trajectories belonging to the training dataset mapped to the low-dimensional latent space by the encoder.

[0023] Furthermore, some embodiments of the present invention provide a computer-implemented method for training a smoothing operator learning model, the smoothing operator learning model comprising an autoencoder and a neural ordinary differential equation (ODE) for a continuously operating dynamic system in an engineering process or machine, controlled by a controller. The computer-implemented method may include the following steps: receiving a training dataset via a network connected to an analog computer using interface circuitry, wherein the training dataset comprises a set of solution trajectories of the system starting from different initial conditions of the state and using time series of different control actions; uploading the smoothing operator learning model for predicting the dynamics of the continuously operating dynamic system, the training dataset, and training instructions from memory to a processor; and training the smoothing operator learning model using the processor based on the training instructions, wherein the training instructions include the following steps: training the autoencoder to learn a mapping from a high-dimensional state space to a low-dimensional latent space based on a training loss, wherein the training loss comprises both a reconstruction loss and an accelerometer loss evaluated on solution trajectories belonging to the analog dataset; and training a neural ODE network to learn solution trajectories belonging to the training dataset mapped to the low-dimensional latent space by the encoder.

[0024] The accompanying drawings are included to provide a further understanding of the invention. The drawings illustrate embodiments of the invention and, together with the description, serve to explain the principles of the invention. The drawings are not necessarily drawn to scale, but generally focus on illustrating the principles of the currently disclosed embodiments. Attached Figure Description

[0025] [ Figure 1 ]

[0026] Figure 1 This is a flowchart of a method for offline construction of an operator learning model of a dynamic system and online fine-tuning and control system using the operator learning model, according to some embodiments of this disclosure; [ Figure 2 ] Figure 2 This is a schematic diagram of the architecture of an operator learning model according to an embodiment of the present disclosure; [ Figure 3A ] Figure 3A This is a schematic diagram illustrating the first training phase of an operator learning model according to an embodiment of the present disclosure; [ Figure 3B ] Figure 3B This is a schematic diagram illustrating the second training phase of an operator learning model according to an embodiment of the present disclosure; [ Figure 4 ] Figure 4This is a block diagram of parameters for online real-time fine-tuning of an operator learning model according to some embodiments of this disclosure; [ Figure 5A ] Figure 5A This is a block diagram illustrating online open-loop control of the operation of a dynamic system using an operator learning model according to some embodiments of the present disclosure; [ Figure 5B ] Figure 5B This is a block diagram illustrating online closed-loop control of the operation of a dynamic system using an operator learning model according to some embodiments of the present disclosure; [ Figure 6 ] Figure 6 This is a block diagram of a device for controlling the operation of a control system according to some embodiments of the present invention; and [ Figure 7 ] Figure 7 An exemplary real-time implementation of a device for controlling a system according to an embodiment of the present invention is shown, wherein the system is a room with an air conditioning and ventilation (HVAC) system. Detailed Implementation

[0027] While the accompanying drawings illustrate the embodiments currently disclosed, other embodiments are contemplated as indicated in the discussion. This disclosure presents illustrative embodiments in a purposive and not restrictive manner. Many other modifications and embodiments can be devised by those skilled in the art, falling within the scope and spirit of the principles of the embodiments currently disclosed.

[0028] In describing embodiments of this disclosure, the following definitions apply throughout the disclosure. "Control system" or "controller" can refer to a device or set of devices used to manage, command, direct, or regulate the behavior of other devices or systems. A control system can be implemented in software or hardware and may include one or more modules. A control system including feedback loops can be implemented using a microprocessor. A control system can be an embedded system.

[0029] "Air conditioning system" or heating, ventilation, and air conditioning (HVAC) system can refer to a system that uses a vapor compression cycle to move refrigerant between the system's components based on thermodynamic, fluid dynamics, and / or heat transfer principles. Air conditioning systems encompass a wide range of systems, from those that supply only outdoor air to the building's occupants, to those that control only the building's temperature, and even those that control both temperature and humidity.

[0030] "Central Processing Unit (CPU)" or "processor" can refer to a computer or computer component that reads and executes software instructions. Furthermore, a processor can be "at least one processor" or "one or more processors".

[0031] Figure 1 This is a flowchart (referred to as an operator learning model generator) of a method for constructing a surrogate smoothing operator learning model 103 of a high-dimensional dynamic system 100 in an offline phase 101 and using the operator learning model to fine-tune and / or control the system in an online phase 102, according to some embodiments of this disclosure. The dynamic system 100 may include actuators 111 and may include sensors 112. The physical model of the system may be described by a PDE. In some embodiments, the system may have control inputs. For simplicity, in the following description, we will refer to the surrogate smoothing operator learning model 103 as the operator learning model.

[0032] The offline phase 101 includes operator learning model 103. Figure 2 The operator learning model 103 described herein includes an encoder neural network 108, a neural ODE 109, and a decoder neural network 110. The offline phase 101 may further include an experimental module 104, a physical model 105 describing the dynamics of system 100 using an ODE or PDE, a high-fidelity numerical solver module 106, and a training dataset 107 consisting of a set of solution trajectories of the system. Each solution trajectory includes initial conditions of the state, a time series of control action values, and a sequence of states generated at different time instances during the operation of system 100. For example, the solution trajectory of airflow in a room might describe the velocity and temperature fields evolving over time from an initial state due to the forced action of the HVAC system. The solution trajectories in the training dataset 107 correspond to various initial conditions of the state and various time series of control action values. The online phase 102 may include a fine-tuning module 120, a prediction module 121, an estimation module 122, an open-loop control module 123, and a closed-loop control module 124 to control system 100 during online operation of system 100.

[0033] The encoder neural network 108, the neural ODE 109, and the decoder neural network 110 can be composed of a fully connected neural network (FNN) or a convolutional neural network (CNN), whose parameters are trained offline and tuned online based on the computer-implemented method of this disclosure. In the offline phase 101, the operator learning model generator trains the operator learning model 103 using solution trajectories contained in the training dataset 107. Training determines the parameter values ​​of the operator learning model 103 so that it can predict the state evolution of the system 100 given initial conditions and time series of control action values. The method of this disclosure improves prediction performance compared to the prior art by enhancing the smoothness of the dynamics during the training of the operator learning model. Furthermore, in some embodiments, the operator learning model 103 can be additionally trained using a physical model 105 so that the system dynamics predicted by the operator learning model 103 obey the PDE describing the physical model 105. In the online phase 102, according to some embodiments, the method can fine-tune the operator learning model 103 using sensor measurements obtained from online operation of a real system.

[0034] In practical applications, it may be necessary to use a surrogate operator to learn model 103 instead of the physical model 105 of the high-dimensional system 100. For example, solving the physical model 105 may be computationally difficult on platforms with limited computing power, such as embedded devices and autonomous devices. For instance, in an HVAC system, solving the physical model means solving the Navier-Stokes equations in real time on a fine grid, which may exceed the computing power of the HVAC system's CPU. On the other hand, solving the surrogate operator to learn model 103 may be inexpensive. Finally, even if solving the physical model 105 is possible (e.g., by utilizing a remote cluster), implementing control over the resulting model, which is the ultimate goal of the HVAC system, may be difficult to achieve. In fact, implementing control may require multiple iterative evaluations of the physical model 105 at each time step.

[0035] The computer-implemented method of this disclosure may include collecting solution trajectories contained in training dataset 107. The solution trajectories contained in training dataset 107 may be generated by performing experiments using experimental module 104 or by calculating numerical solutions to physical model 105 using high-fidelity numerical solver module 106 implemented on a simulation computer.

[0036] In some implementations, the numerical solver module 106 may consist of a computational fluid dynamics (CFD) solver that utilizes numerical analysis and data structures to solve the Navier-Stokes equations governing fluid flow dynamics. For example, a computer may be used to perform the calculations required to simulate the flow of a fluid interacting with a surface defined by boundary conditions. Furthermore, various software programs have been designed to provide good accuracy in complex simulation scenarios associated with transonic or turbulent flows that may occur in applications, such as describing airflow in an HVAC room. Initial validation of such software can typically be performed using experimental data. Additionally, prior analyses or empirical studies of specific airflow-related issues associated with the system can be used for comparison in CFD simulations.

[0037] According to some embodiments of this disclosure, in the online phase 102, the operator learning model 103 can be used with the open-loop control module 123 or the closed-loop control module 124 to control the system 100. Since the operator learning model 103 learns the dynamics of the system 100, it can be used to predict the evolution of states or to control the system's operation outside the time frame of the solution trajectories present in the training dataset 107.

[0038] The open-loop control module 123 includes an open-loop control strategy that generates commands to control the operation of the system 100 in order to achieve the desired result defined by the objective function. The prediction module 121 can be used to generate a trajectory of the state of the system 100, and the open-loop control module 123 can then use these trajectories to generate optimal control actions.

[0039] Alternatively, the closed-loop control module 124 includes a closed-loop control strategy that generates commands to control the operation of the system to achieve a desired result defined by an objective function, wherein each control action is calculated based on the current estimated state of the system 100. The estimation module 122 can be used to calculate the current estimated state of the system 100 based on historical, noisy sensor measurement data up to the current time, and the closed-loop control module 124 can then use this estimated state to generate optimal control actions. For example, for a room controlled by an HVAC system, sensors can record data such as temperature, velocity, and humidity at specific locations. The estimation module can then be used to reconstruct the spatial distribution of temperature and velocity in the room in real time based on the sensor measurements. The control module 124 can then use the reconstructed temperature and velocity model to generate HVAC control actions to achieve the desired distribution of velocity and temperature in the room.

[0040] Figure 2 This is a schematic diagram of the architecture of an operator learning model 103 according to some embodiments of this disclosure. The encoder neural network 108 is composed of... This indicates that the neural network defining neural ODE 109 is composed of... It is stated that the decoder neural network 110 is composed of It means, and This refers to the trainable parameters of all three neural networks. In some implementations, the system state is represented as... It is described by a continuous space function, where, It is a physical quantity. It is a spatial coordinate (or position), and For example, regarding airflow in a room, It can represent time The spatial distribution of velocity and temperature within a room. The system's state is high-dimensional because it is a continuous space function. Precise numerical representation requires a large number of spatial locations to Sampling is performed. From the initial time... Initial conditions of the state Start, and give control action values. The time series of the operator learning model 103 can be used to predict the system at any time. future state As described below. First, In a finite (but potentially large) number of spatial locations The digital representation of the initial conditions of the sampled sample is applied as input to encoder 108, which outputs a low-dimensional latent vector at the initial time.

[0041]

[0042] The latent vector is then passed to a neural ODE 109, which uses neural networks to... The defined ODE parameterizes the dynamics of the latent vector as follows:

[0043] By transferring neural ODE 109 from Points to To obtain the latent vector Decoder 110 is... and any spatial location The input is a neural network, and the output is:

[0044] This is the actual situation. An approximation of . By... As input, decoder 110 generates continuous states. continuous representation Such parameterization of continuous functions using neural networks is called implicit neural representation.

[0045] This disclosure provides a computer-implemented operator learning model generator method that provides training instructions to... Figure 3A and Figure 3B The operator learning model 103 is trained in a two-stage process described in the paper. This two-step training process determines the encoder neural network 108 ( ), neural ODE 109 ( ) and decoder neural network 110 ( ) parameter value So that From arbitrary initial conditions Start and given control action value In the case of any time series, for time The true state of being An accurate approximation.

[0046] We use Represents the solution trajectory in training dataset 107, where Refers to the training dataset One of the different solution trajectories, and In a finite number of spatial locations This is a time instance for sampling the state. Along with each solution trajectory, it also stores the time instance for... and Time series of control action values .

[0047] Figure 3A The first stage of a training operator learning model 103 according to some embodiments of the present disclosure is shown. The first stage determines the encoder neural network 108 ( ) and decoder neural network 1100 ( ) parameter value The goal is for the trained encoder to process continuous states. Compressing or mapping to low-dimensional latent vectors In the middle, and the trained decoder is able to process low-dimensional latent vectors Decompress or map back to the same continuous state Each training iteration includes a forward pass 301, where a given plot is drawn based on the training dataset 107. The entire solution trajectory This is then applied as input to encoder 108. Encoder 108 then outputs the corresponding trajectory of the low-dimensional latent vector as:

[0048] Then, the trajectory of the low-dimensional latent vector is applied as input to decoder 110, and decoder 110 outputs the reconstructed trajectory of the system state:

[0049] Then, each training iteration includes building loss. 302. This loss consists of two items. The first item is the reconstruction loss. 303, ensure encoder 108 ( ) and decoder 110 ( These are inverse mappings of each other. The mean square error is calculated as follows:

[0050] The second item is jerk loss. 304, ensuring low-dimensional latent vectors The transition from one time step to the next is smooth. (Jerk speed loss) This constitutes the main novelty of this disclosure, and its motivation is a high-dimensional state. The smooth evolution over time should also be transformed into a latent vector. The jerk loss evolves smoothly over time. It is constructed based on the norm of the jerk along the trajectory.

[0051] Finally, during each training iteration, the total loss is... This is used to update the parameters of encoder 108 and decoder 110 using gradient descent algorithms such as stochastic gradient descent or Adam optimizer. .

[0052] The reconstruction loss typically used when training an encoder-decoder (also known as an autoencoder) Conversely, assess jerk loss It is necessary to use many consecutive states along a given trajectory , , , Thus, the state is implicitly considered in the first stage of training the operator learning model 103. The dynamics.

[0053] It can be noted that, compared with other trajectories, each trajectory It can be used for different spatial locations and time instances Capture. In this case, the loss function should be modified accordingly. To simplify the symbolic representation without sacrificing its generality, it is assumed that all trajectories are recorded at the same spatial location and for the same temporal instance.

[0054] Figure 3B The second stage of a training operator learning model 103 according to some embodiments of this disclosure is shown. The second stage determines the neural ODE 109 ( ) parameter value The goal is for the trained neural ODE to reproduce the latent vectors in the latent space. The dynamics. Each training iteration includes a forward pass 303, where a plot is drawn based on the training dataset 107 for a given... The entire solution trajectory This is then applied as input to encoder 108. Encoder 108 then outputs the corresponding trajectory of the ground truth low-dimensional latent vector as:

[0055] Then the first potential vector in the trajectory Time series of control action values ​​for the same trajectory Together, they are applied as input to neural ODE 109. Then, neural ODE... from Points to The predicted potential vector trajectory is obtained. .

[0056] Then, each training iteration includes building the loss. 304, which includes a prediction loss term that ensures the trajectory of the predicted latent vector is similar to the trajectory of the ground truth latent vector. It is calculated based on the mean squared error as follows: .

[0057] Finally, during each training iteration, the loss This is used to update the parameters of neural ODE 109 using gradient descent algorithms such as stochastic gradient descent or the Adam optimizer. .

[0058] The method for training the operator learning model 103 may also include incorporating the PDE of the physical model 105 into the training loss of the neural ODE 109. In this case, the method may include generating at a finite number of spatial locations. Any state sampled Each state satisfies the system's boundary conditions and other constraints. Furthermore, the states... This should be physically achievable by the system. Then the item... Add to In these states The dynamics induced by the enhanced neural ODE 109 are consistent with the dynamics given by the PDE in physical model 105.

[0059] As is known in the art, the steps of the operator learning model generator described above can be performed in an apparatus including a processor connected to memory and interface circuitry. For example, the interface circuitry can be configured to receive training dataset 107 via a network connected to an analog computer containing numerical solver 106. The memory can be configured to store operator learning model 103, training dataset 107, and the training instructions described above for training operator learning model 103. The processor can be configured to train the operator learning model stored in memory using training dataset 107 and training instructions. Thanks to accelerometer regularization that enhances dynamic smoothness, the accuracy of the trained operator learning model is significantly improved compared to the prior art, and the trained operator learning model can be effectively used in compact control systems. This apparatus can form a standalone system that can be sold to customers as a single, complete unit.

[0060] Figure 4 This is a block diagram illustrating, according to some embodiments of the present disclosure, a method for real-time fine-tuning of the parameters of an operator learning model 103 using sensor measurements. In various locations Measurement status Sensors 112 of different components can be placed in the actual system 100 to collect sensor output measurements 402 during online operation of the system. In parallel, as... Figure 3A and Figure 3B After training the operator learning model 103 offline, the operator learning model can be used to calculate the sensor output prediction 403 at sensor 112. Then, the parameter values ​​of the operator learning model 103... Fine-tuning can be performed in real time in the fine-tuning module 120 based on the difference between the sensor output prediction 403 and the sensor output measurement value 402.

[0061] Figure 5A This is a block diagram illustrating online open-loop control of the operation of a dynamic system 100 using an operator learning model 103 according to some embodiments of this disclosure. Once as Figure 3A and Figure 3BThe operator learning model 103, trained offline, can then be used in the prediction module 121 to calculate the system's trajectory under various initial conditions and time series of control action values. Based on these trajectories and the operator learning model 103, the open-loop control strategy in the control module 123 can be used to calculate the time series of the optimal control action value 501 in real time. These time series can be applied to the actuator 111 to influence the online operation of the system 100, thereby achieving the desired result defined by the user-specified objective function.

[0062] Figure 5B This is a block diagram illustrating online closed-loop control of the operation of a dynamic system 100 using an operator learning model 103 according to some embodiments of the present disclosure. Sensors 112 can be placed in the actual system 100 at various locations during online operation of the system. Real-time collection status The measured values ​​of different components are 503. Furthermore, the actuator 111 can be placed in the actual system 100, allowing for measurement at various locations. The state of being acted upon To control the online operation of the system. Once such Figure 3A and Figure 3B The operator learning model 103, trained offline, can then be used in the estimation module 122 to calculate the current estimated state of the system 100 based on real-time collected sensor measurements 503. Based on the estimated state and the operator learning model 103, the closed-loop control strategy in the control module 124 can be used to calculate the time series of optimal control action values ​​501 in real time. These time series can be applied to the actuator 111 to control the online operation of the system 100 to achieve the desired result defined by the user-specified objective function.

[0063] Figure 6 A block diagram of a control device 600 (also referred to as a controller) for online closed-loop control of the operation of a power system 100, according to some embodiments, is shown. The device 600 includes an input interface 601 and an output interface 602 for connecting the device 600 to other systems and devices. In some embodiments, the device 600 may include multiple input interfaces and multiple output interfaces. The input interface 601 is configured to receive real-time sensor output measurements 503 from sensors 112 of the power system 100 using a network interface controller (NIC) 604 connected to a network 605. Through the input interface 601, the network interface controller (NIC) 604, and the network 605, the device 600 receives the real-time sensor output measurements 503 of the power system 100 wirelessly or via a wired connection.

[0064] Device 600 also includes a processor 606 and a memory 607, the memory 607 storing instructions executable by the processor 606. The processor 606 can be a single-core processor, a multi-core processor, a computing cluster, or any number of other configurations. The processor 606 is connected to one or more input and output devices. The memory 607 can include random access memory (RAM), read-only memory (ROM), flash memory, or any other suitable storage system. The memory 607 can be further extended to include a storage device 608. The storage device 608 can be configured to store a trained smoothing operator learning model 103, an estimation module 122, and a closed-loop control module 124. The processor 606 can execute the instructions stored in the trained operator learning model 103, the estimation module 122, and the closed-loop control module 124 to calculate the optimal control action value 501 based on sensor output measurements received from the input interface 601. Figure 3A and Figure 3B As described, due to the accelerometer loss included in the offline training process of the operator learning model 103, the operator learning model 103 can still achieve high accuracy despite operating under the limited computing power of the processor 606, thereby generating effective optimal control command values ​​501. The output interface 602 is configured to transmit the optimal control action value 501 to the actuator 111 of the system 100 to control its operation in a manner that minimizes the objective function specified by the user.

[0065] Figure 7 An exemplary real-time implementation of a control device 600 for controlling a power system 100 is shown, wherein, in this example, the power system 100 is a room 700 having a door 701 and at least one window 702. The temperature and airflow of the room 700 are controlled by the device 600 via a heating, ventilation, and air conditioning (HVAC) system 701 through a ventilation unit 703 (i.e., the ventilation unit 703 is the actuator of the room 700). Control actions specified by the device 600 may include the temperature, velocity magnitude, and velocity direction of the airflow generated by the HVAC system at each ventilation unit 703. A sensor set 704 is arranged in the room 700, which may include one or more sensors 704a for measuring the airflow velocity at a given point and one or more sensors 704b for measuring the airflow temperature at a given point. Other setups are also contemplated, such as a room with multiple HVAC systems or a house with multiple rooms.

[0066] First, according to Figure 3A and Figure 3BThe steps described herein involve offline training of the smoothing operator learning model 103 included in the control device 600 using jerk loss, thereby obtaining a smoothing operator learning model with high prediction accuracy, which can operate within the limited computing power of the processor 606 in the control device 600. Then, the control device 600 can be used online using real-time measurements from the speed and temperature sensors 704 to calculate and send optimal control actions to the air conditioning system 701 to control the airflow velocity and temperature in room 700 in a manner that achieves the desired result defined by the objective function. This result may include minimizing the airflow velocity or achieving the target temperature anywhere in the room. In some embodiments, such as Figure 3B The coupled Navier-Stokes equations and thermal PDEs describing the dynamics of controlling airflow velocity and temperature in room 700 can be included in the training process of operator learning model 103.

[0067] The control device 600 can be embedded in the device to form a standalone system that can be sold to customers as a single unit and can operate and perform the above functions when installed in an environment (such as a room with an HVAC system).

[0068] The above description provides only exemplary embodiments and is not intended to limit the scope, applicability, or configuration of this disclosure. Rather, the following description of exemplary embodiments will provide those skilled in the art with a description of the feasibility of implementing one or more exemplary embodiments. Various changes may be made to the function and arrangement of the elements without departing from the spirit and scope of the subject matter disclosed in the appended claims.

[0069] Although this disclosure has described the invention by way of examples of preferred embodiments, it should be understood that various other adjustments and modifications can be made within the spirit and scope of the invention. Therefore, the appended claims are intended to cover all such variations and modifications that fall within the true spirit and scope of the invention.

Claims

1. An operator learning model generator for training a smoothing operator learning model, the smoothing operator learning model comprising an autoencoder and a neural constant differential equation (ODE) used by a controller connected to a heating, ventilation, and air conditioning (HVAC) system installed in a room, the operator learning model generator comprising: An interface circuit configured to receive a training dataset via a network connected to an analog computer, wherein the training dataset includes solution trajectories of airflow in the room for various time series of control actions applied to the HVAC system; A memory configured to store a smoothing operator learning model for predicting the dynamics of airflow in the room, the training dataset, and training instructions for the smoothing operator learning model; and A processor configured to train the smoothing operator learning model stored in the memory, wherein the training instructions include the following steps: The autoencoder is trained to learn a mapping from the high-dimensional states of the system to low-dimensional latent vectors based on a training loss, wherein the training loss comprises both a reconstruction loss and a jerk loss evaluated on the solution trajectories belonging to the training dataset; and The neural ODE is trained to learn the solution trajectory belonging to the training dataset mapped to a low-dimensional latent space by the encoder.

2. The operator learning model generator according to claim 1, wherein the operator learning model generator further comprises: By applying estimation and closed-loop control strategies to a trained smoothing operator learning model and using real-time collected sensor measurements, optimal control actions are generated in real time to minimize the user-defined cost objective function. as well as The generated optimal control action is transmitted to the actuator of the HVAC system via an interface circuit to control the airflow in the room.

3. The operator learning model generator according to claim 1, wherein the operator learning model generator further comprises: By applying an open-loop control strategy to a trained smooth operator learning model, optimal control actions are generated in real time to minimize the user-defined cost objective function. as well as The generated optimal control action is transmitted to the actuator of the HVAC system via an interface circuit to control the airflow in the room.

4. The operator learning model generator according to claim 1, wherein, The training loss for the neural ODE includes the physical information term of the partial differential equation (PDE) that constrains the physical model of the system's dynamics.

5. The operator learning model generator according to claim 2, wherein, The training loss for the neural ODE includes the physical information term of the partial differential equation (PDE) that constrains the physical model of the system's dynamics.

6. The operator learning model generator according to claim 3, wherein, The training loss for the neural ODE includes the physical information term of the partial differential equation (PDE) that constrains the physical model of the system's dynamics.

7. The operator learning model generator according to claim 1, wherein, The parameters of the trained operator learning model are fine-tuned in real time using sensor measurements collected during the online operation of the system.

8. A computer-implemented method for training a smoothing operator learning model, the smoothing operator learning model comprising an automatic encoder and a neural ordinary differential equation (ODE) of a continuously operating dynamic system controlled by a controller in an engineering process or machine, the computer-implemented method comprising the following steps: The training dataset is received via a network connected to an analog computer using an interface circuit, wherein the training dataset comprises a set of solution trajectories for various time series of control actions of the system; The smoothing operator learning model used to predict the dynamics of the continuously operating dynamic system, the training dataset, and training instructions are uploaded from memory to the processor; and The processor is used to train the smoothing operator learning model based on the training instructions, wherein the training instructions include the following steps: The autoencoder is trained to learn a mapping from a high-dimensional state space to a low-dimensional latent space based on a training loss, wherein the training loss includes both a reconstruction loss and a jerk loss evaluated on the solution trajectories belonging to the training dataset; and The neural ODE is trained to learn the solution trajectory belonging to the training dataset mapped to the low-dimensional latent space by the encoder.

9. The computer-implemented method according to claim 8, further comprising the following steps: Control actions are generated by applying the estimated and closed-loop control strategy to a trained smooth operator learning model using the state measured from sensors. as well as The generated optimal control action is transmitted to the actuator via an interface circuit to control the power system in the engineering process or the machine.

10. The computer-implemented method according to claim 8, further comprising the following steps: By applying an open-loop control strategy to a trained smooth operator learning model, optimal control actions are generated in real time to minimize the user-defined cost objective function. as well as The generated optimal control action is transmitted to the actuator via an interface circuit to control the power system in the engineering process or the machine.

11. The computer-implemented method according to claim 8, wherein, The training loss for the neural ODE includes the physical information term of the partial differential equation (PDE) that constrains the physical model of the system's dynamics.

12. The computer-implemented method according to claim 9, wherein, The training loss for the neural ODE includes the physical information term of the partial differential equation (PDE) that constrains the physical model of the system's dynamics.

13. The computer-implemented method according to claim 10, wherein, The training loss for the neural ODE includes the physical information term of the partial differential equation (PDE) that constrains the physical model of the system's dynamics.

14. The computer-implemented method according to claim 8, wherein, The parameters of the trained operator learning model are fine-tuned in real time using sensor measurements collected during the online operation of the system.

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