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arXiv · 2410.05572

Improved deep learning of chaotic dynamical systems with multistep penalty losses

Dibyajyoti Chakraborty·Seung Whan Chung·Ashesh Chattopadhyay·Romit Maulik
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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.

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Dibyajyoti Chakraborty, Seung Whan Chung, Ashesh Chattopadhyay, Romit Maulik. 2024-10-08. Improved deep learning of chaotic dynamical systems with multistep penalty losses. https://arxiv.org/abs/2410.05572

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