Improved deep learning of chaotic dynamical systems with multistep penalty losses

TL;DR

This paper presents a new deep learning framework using multi-step penalty optimization to improve long-term predictions of chaotic systems like turbulence and ocean dynamics, addressing stability and accuracy challenges.

Contribution

It extends multi-step penalty optimization to various neural network architectures for better chaotic system modeling, introducing penalized local discontinuities to handle non-convex loss landscapes.

Findings

Enhanced long-term prediction accuracy for chaotic systems.

Effective handling of non-convex loss landscapes in neural networks.

Demonstrated success on turbulence and ocean dynamics datasets.

Abstract

Predicting the long-term behavior of chaotic systems remains a formidable challenge due to their extreme sensitivity to initial conditions and the inherent limitations of traditional data-driven modeling approaches. This paper introduces a novel framework that addresses these challenges by leveraging the recently proposed multi-step penalty (MP) optimization technique. Our approach extends the applicability of MP optimization to a wide range of deep learning architectures, including Fourier Neural Operators and UNETs. By introducing penalized local discontinuities in the forecast trajectory, we effectively handle the non-convexity of loss landscapes commonly encountered in training neural networks for chaotic systems. We demonstrate the effectiveness of our method through its application to two challenging use-cases: the prediction of flow velocity evolution in two-dimensional turbulence and ocean dynamics using reanalysis data. Our results highlight the potential of this approach for accurate and stable long-term prediction of chaotic dynamics, paving the way for new advancements in data-driven modeling of complex natural phenomena.