用多步惩罚损失提升神经网络对混沌系统长期预测的稳定性
Improved deep learning of chaotic dynamical systems with multistep penalty losses
- 引入多步惩罚损失，缓解混沌系统训练中梯度不连续问题
- 在二维湍流和海洋动力学预测中实现更稳定长期模拟
- 适用于傅里叶神经算子等复杂架构，适合气候与流体建模研究者
由于对初值极度敏感及传统数据驱动建模方法的固有局限，预测混沌系统的长期行为仍具挑战。本文提出一种新框架，利用近期提出的多步惩罚（MP）优化技术，将该方法扩展至傅里叶神经算子、UNET等多种深度学习架构。通过在预测轨迹中引入惩罚性局部不连续项，有效应对训练混沌系统神经网络时常见的非凸损失景观问题。我们在两个挑战性场景中验证了该方法：基于再分析数据预测二维湍流中的流速演化与海洋动力学。结果表明，该方法能实现准确且稳定的长期预测，为复杂自然现象的数据驱动建模带来新可能。
原文摘要 · Abstract (English)
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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