Physics-informed smooth operator learning for high-dimensional systems prediction and control

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.