Physics-Informed Neural State Space Models via Learning and Evolution

TL;DR

This paper introduces a method for discovering neural state space models for physical systems by combining structured design spaces with genetic algorithms, enabling accurate and physically consistent system identification.

Contribution

It proposes a novel approach that integrates physical priors, structured model design, and genetic search to identify neural state space models without complete prior knowledge.

Findings

Successfully modeled aerodynamics, reactor, and tank systems.

Achieved physically consistent and accurate models.

Demonstrated effectiveness of genetic search in model discovery.

Abstract

Recent works exploring deep learning application to dynamical systems modeling have demonstrated that embedding physical priors into neural networks can yield more effective, physically-realistic, and data-efficient models. However, in the absence of complete prior knowledge of a dynamical system's physical characteristics, determining the optimal structure and optimization strategy for these models can be difficult. In this work, we explore methods for discovering neural state space dynamics models for system identification. Starting with a design space of block-oriented state space models and structured linear maps with strong physical priors, we encode these components into a model genome alongside network structure, penalty constraints, and optimization hyperparameters. Demonstrating the overall utility of the design space, we employ an asynchronous genetic search algorithm that alternates between model selection and optimization and obtains accurate physically consistent models of three physical systems: an aerodynamics body, a continuous stirred tank reactor, and a two tank interacting system.