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

2025-07-21

AI Summary

Reduced-order modeling of spatiotemporal chaotic systems faces dual challenges—physics model mismatch and scarce training data. Method: We propose a physics-informed, data-driven hybrid framework: (i) an autoencoder learns a low-dimensional invariant manifold; (ii) the full-order model’s vector field is orthogonally projected onto this manifold; (iii) a differentiable neural ordinary differential equation (Neural ODE) predictor is constructed on the manifold and augmented with a Bayesian error correction mechanism for uncertainty quantification and online adaptation. Results: Experiments on the Kuramoto–Sivashinsky and complex Ginzburg–Landau equations demonstrate that our method significantly outperforms purely data-driven approaches, maintaining high-fidelity long-term predictions under adverse conditions—including parametric mismatch and sparse observations. This work establishes a new paradigm for robust physics-informed deep learning in chaotic system modeling.

Technology Category

Machine Learning: Learning with ManifoldsCognitive Modeling & Cognitive Systems: Neural Spike CodingSearch and Optimization: Learning to Search

Application Category

Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingSystems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applicationsUser Modeling, Personalization and Recommendation: User privacy protection in personalized systems

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.

Problem

• Blending data and physics for chaotic dynamics modeling
• Improving predictions with hybrid reduced-order models
• Addressing data scarcity and model inaccuracies

Innovation

• Hybrid ROM blending data and physics
• Autoencoder finds invariant manifold coordinates
• Neural ODE corrects physics with data