Physics-informed smooth operator learning for high-dimensional systems prediction and control
An operator learning model generator is provided for training a smooth 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 solution trajectories of airflow in the room for various times series of control actions given to the HVAC system, a memory configured to store the smooth operator learning model comprising an auto-encoder and a neural ordinary differential equation, the training dataset, and training instructions for the smooth operator learning model, and a processor configured to train the smooth operator learning model stored in the memory, wherein the training instructions comprise a jerk regularization that enforces smoothness of the dynamics predicted by the smooth operator learning model.
1 . An operator learning model generator for training a smooth operator learning model including an auto-encoder and a neural ordinary differential equation (ODE) used by a controller connected to a heating, ventilation and air conditioning (HVAC) system installed in a room, comprising:
an interface circuit configured to receive a training dataset via a network connected to a simulation computer, wherein the training dataset includes solution trajectories of airflow in the room for various times series of control actions given to the HVAC system;
a memory configured to store a smooth operator learning model for predicting dynamics of airflow in the room, the training dataset, and training instructions for the smooth operator learning model; and
a processor configured to train the smooth operator learning model stored in the memory, wherein the training instructions comprise steps of:
training the auto-encoder to learn a mapping from a high-dimensional state of the system to a low-dimensional latent vector 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;
training the neural ODE to learn the solution trajectories belonging to the training dataset mapped through the encoder to the low-dimensional latent space generating in real time optimal control actions to minimize a user-defined cost objective function by applying an open-loop control policy to the trained smooth operator learning model; and
transmitting the generated optimal control actions to the actuators of the HV AC system via an interface circuit, to control the airflow in the room.
2 . The operator learning model generator of claim 1 , further comprising:
generating in real time optimal control actions to minimize a user-defined cost objective function by applying an estimation and closed-loop control policy to the trained smooth operator learning model, and using the sensor measurements collected in real time; and
transmitting the generated optimal control actions to the actuators of the HVAC system via an interface circuit, to control the airflow in the room.
3 . The operator learning model generator of claim 2 , wherein the training loss for the neural ODE includes a physics-informed term that enforces partial differential equations (PDEs) describing the physical model of system dynamics.
4 . The operator learning model generator of claim 1 , wherein the training loss for the neural ODE includes a physics-informed term that enforces partial differential equations (PDEs) describing the physical model of system dynamics.
5 . The operator learning model generator of claim 1 , wherein parameters of the trained operator learning model are fine-tuned in real-time using sensor measurements collected during online operation of the system.
6 . The operator learning model generator of claim 1 , wherein the training loss for the neural ODE includes a physics-informed term that enforces partial differential equations (PDEs) describing the physical model of system dynamics.
7 . A computer-implemented method for training a smooth operator learning model including an auto-encoder and a neural ordinary differential equation (ODE) used by a controller for a continuously operating dynamical system in an engineered process or a machine, comprising:
receiving, using an interface circuit, a training dataset via a network connected to a simulation computer, wherein the training dataset include a collection of solution trajectories of the system for various time series of control actions;
uploading a smooth operator learning model for predicting the dynamics of the continuously operating dynamical system, the training dataset, and training instructions to a processor from a memory; and
training, using the processor, the smooth operator learning model based on the training instructions, wherein the training instructions comprise steps of:
training the auto-encoder 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;
training the neural ODE to learn the solution trajectories belonging to the training dataset mapped through the encoder to the low-dimensional latent space;
generating in real time optimal control actions to minimize a user-defined cost objective function by applying an open-loop control policy to the trained smooth operator learning model; and
transmitting the generated optimal control actions to actuators via an interface circuit, to control the dynamical system in the engineered process or the machine.
8 . The computer-implemented method of claim 7 , further comprising:
generating control actions by applying an estimation and closed-loop control policy to the trained smooth operator learning model, using the states measured from sensors; and
transmitting the generated optimal control actions to actuators via an interface circuit, to control the dynamical system in the engineered process or the machine.
9 . The computer-implemented method of claim 8 , wherein the training loss for the neural ODE includes a physics-informed term that enforces partial differential equations (PDEs) describing the physical model of the system dynamics.
10 . The computer-implemented method of claim 7 , wherein the training loss for the neural ODE includes a physics-informed term that enforces partial differential equations (PDEs) describing the physical model of the system dynamics.
11 . The computer-implemented method of claim 7 , wherein the training loss for the neural ODE includes a physics-informed term that enforces partial differential equations (PDEs) describing the physical model of the system dynamics.
12 . The computer-implemented method of claim 7 , wherein parameters of the trained operator learning model are fine-tuned in real-time using sensor measurements collected during online operation of the system.