Blending data and physics for reduced-order modeling of systems with spatiotemporal chaotic dynamics

TL;DR

This paper introduces a hybrid reduced-order modeling approach combining data and physics for chaotic systems, improving predictions especially when data is limited or the physics model is imperfect.

Contribution

The paper develops a physics-informed hybrid ROM using autoencoders and neural ODEs, enhancing chaotic system predictions over data-only methods.

Findings

Hybrid model outperforms data-only approaches in various data scenarios.

Incorporating physics improves robustness against model errors.

Method validated on Kuramoto-Sivashinsky and Ginzburg-Landau equations.

Abstract

While data-driven techniques are powerful tools for reduced-order modeling of systems with chaotic dynamics, great potential remains for leveraging known physics (i.e. a full-order model (FOM)) to improve predictive capability. We develop a hybrid reduced order model (ROM), informed by both data and FOM, for evolving spatiotemporal chaotic dynamics on an invariant manifold whose coordinates are found using an autoencoder. This approach projects the vector field of the FOM onto the invariant manifold; then, this physics-derived vector field is either corrected using dynamic data, or used as a Bayesian prior that is updated with data. In both cases, the neural ordinary differential equation approach is used. We consider simulated data from the Kuramoto-Sivashinsky and complex Ginzburg-Landau equations. Relative to the data-only approach, for scenarios of abundant data, scarce data, and even an incorrect FOM (i.e. erroneous parameter values), the hybrid approach yields substantially improved time-series predictions.