用对抗最优传输学习混沌系统，仅靠一条噪声轨迹就能建模长期统计特性。
Learning to Emulate Chaos: Adversarial Optimal Transport Regularization
- 设计对抗式最优传输目标，自动学习高质量统计特征与物理一致的模拟器
- 在多个混沌系统上实现显著提升的长期统计保真度，包括高维时空混沌
- 无需多环境数据或人工统计量，适合仅有一条观测轨迹的场景
混沌现象广泛存在于天气、电网等复杂动力系统中，但数据驱动方法（如机器学习模拟器）难以准确建模。尽管模拟器能加速仿真并解决反问题，却仍难以捕捉敏感依赖初始条件的混沌动态，尤其在存在噪声数据时。现有方法尝试通过匹配混沌吸引子的统计特性来训练模拟器，但通常依赖人工构造的摘要统计量或大规模多样化的多环境数据集。本文提出一类对抗式最优传输目标，可从单一噪声轨迹中联合学习高质量摘要统计量与物理一致的模拟器。我们理论分析并实验验证了基于Sinkhorn散度（2-沃瑟斯坦）和WGAN风格对偶形式（1-沃瑟斯坦）的方案。在多种混沌系统上的数值实验表明，使用所提目标训练的模拟器具有显著提升的长期统计保真度。
原文摘要 · Abstract (English)
Chaos arises in many complex dynamical systems, from weather to power grids, but is difficult to accurately model with data-driven methods such as machine learning emulators. While emulators are promising tools for accelerating simulations and solving inverse problems, they still struggle to learn chaotic dynamics, where sensitivity to initial conditions renders exact long-term forecasts infeasible, especially given noisy data. Recent work instead trains emulators to match the statistical properties of chaotic attractors, but these approaches often rely on handcrafted summary statistics or large, diverse multi-environment datasets. In this work, we propose a family of adversarial optimal transport objectives that can jointly learn high-quality summary statistics and a physically consistent emulator from a single noisy trajectory. We theoretically analyze and experimentally validate a Sinkhorn divergence formulation (2-Wasserstein) and a WGAN-style dual formulation (1-Wasserstein) of our approach. Numerical experiments across a variety of chaotic systems, including ones with high-dimensional spatiotemporal chaos, show that emulators trained using our proposed objectives have significantly improved long-term statistical fidelity.
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