Physics-Informed Smooth Operator Learning for High-Dimensional Systems Prediction and Control
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Solution Overview
Problem
High-dimensional dynamical systems pose computational challenges for model-based control policies due to the complexity of their physical models described by partial differential equations (PDEs), and data-driven techniques lack performance guarantees and require large datasets.
Innovation Solution
A computer-implemented method and system for training a smooth operator learning surrogate model that incorporates the smoothness property of dynamics to regularize the training procedure, using an autoencoder architecture with an encoder, a neural ordinary differential equation (ODE) propagator, and a decoder, to predict the future state of the system given an initial state and control sequence.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a physical model described by PDEs is used for model-based control, then performance guarantees are achieved, but computational cost becomes too expensive for high-dimensional systems
Solution Approach 1:
The patent creates a simplified copy (surrogate model) of the complex physical system described by PDEs. This surrogate model uses neural networks to approximate the system dynamics, maintaining performance guarantees while reducing computational complexity to enable real-time control of high-dimensional systems.
Solution Approach 2:
The patent introduces an intermediary component (surrogate model with neural network) that bridges the gap between the complex physical model and the control algorithm. This intermediary captures essential system dynamics without requiring full PDE solving, enabling model-based control with reduced computational burden.
2Device complexity
If data-driven techniques are used to construct control policies, then computational cost is reduced, but large quantities of data are required and performance guarantees are lacking
Solution Approach 1:
The patent changes the parameters and structure of the surrogate model during training to incorporate physical constraints and smoothness properties. This allows the model to achieve good performance with less data while maintaining reliability through physics-informed regularization terms in the loss function.
Solution Approach 2:
The patent incorporates feedback mechanisms where the surrogate model is trained using operational data while being regularized by physical principles. The training process continuously adjusts model parameters to satisfy both data fidelity and physical consistency, ensuring performance guarantees without requiring large datasets.
3Device complexity
If a simplified surrogate model is constructed using operational data, then computational cost is reduced for online control, but large quantities of data are required to ensure sufficient accuracy
Solution Approach 1:
The patent modifies the training approach by changing the loss function parameters to include physics-informed regularization terms. This allows the surrogate model to learn accurate system dynamics with fewer data points by constraining the solution space to physically plausible behaviors.
Solution Approach 2:
The patent performs preliminary action by pre-training the surrogate model offline with available operational data and physical constraints. This preliminary training phase creates a robust model that requires minimal additional data for adaptation, reducing the overall data requirement while maintaining accuracy for online control applications.
Data Source
AI summary
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.