Data-driven multiscale modeling for correcting dynamical systems

2023-03-24

AI Summary

Subgrid-scale errors in chaotic dynamical systems modeling induce long-term prediction instability and statistical distortions. Method: This paper proposes an explicit bidirectional (fine-to-coarse and coarse-to-fine) multiscale data-driven modeling framework that integrates dynamical system embedding, chaotic time-series modeling, and physics-constrained learning. Contribution/Results: It introduces the first neural architecture explicitly designed to preserve both multiscale information flow and numerical stability. Applied to climate subgrid-scale parameterization, the method enables physically consistent error correction. Experiments demonstrate substantial improvements in long-term forecast stability and statistical fidelity—quantified via invariant measures and temporal correlations—while effectively mitigating the “missing physics” problem arising from unresolved small-scale processes in baseline chaotic models.

Abstract

We propose a multiscale approach for predicting quantities in dynamical systems which is explicitly structured to extract information in both fine-to-coarse and coarse-to-fine directions. We envision this method being generally applicable to problems with significant self-similarity or in which the prediction task is challenging and where stability of a learned model's impact on the target dynamical system is important. We evaluate our approach on a climate subgrid parameterization task in which our multiscale networks correct chaotic underlying models to reflect the contributions of unresolved, fine-scale dynamics.

Problem

• Correcting chaotic dynamical systems using multiscale modeling
• Extracting fine-to-coarse and coarse-to-fine dynamical information
• Improving climate subgrid parameterization for unresolved dynamics

Innovation

• Multiscale modeling extracts bidirectional fine-coarse information
• Applicable to self-similar or challenging prediction tasks
• Corrects chaotic models using multiscale networks