Improved deep learning of chaotic dynamical systems with multistep penalty losses

• URL: http://arxiv.org/abs/2410.05572v1
• Date: Tue, 8 Oct 2024 00:13:57 GMT
• Title: Improved deep learning of chaotic dynamical systems with multistep penalty losses
• Authors: Dibyajyoti Chakraborty, Seung Whan Chung, Ashesh Chattopadhyay, Romit Maulik,
• Abstract summary: Predicting the long-term behavior of chaotic systems remains a formidable challenge. This paper introduces a novel framework that addresses these challenges by leveraging the recently proposed multi-step penalty operators.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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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