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.

本研究解决了混沌系统长期行为预测的难题，特别是初始条件的极端敏感性和传统数据驱动建模方法的局限。文章提出了一种新框架，利用多步惩罚优化技术，扩展至多种深度学习架构，并通过对预测轨迹的局部惩罚不连续性处理训练中的非凸损失景观。研究显示该方法在两种复杂用例中的有效性，为复杂自然现象的数据驱动建模开辟了新的可能性。

改进的混沌动力系统深度学习方法与多步惩罚损失