Learning to Emulate Chaos: Adversarial Optimal Transport Regularization

TL;DR

This paper introduces adversarial optimal transport regularization methods to improve data-driven emulators of chaotic systems, enhancing their long-term statistical accuracy.

Contribution

It proposes a novel adversarial optimal transport framework that learns summary statistics and physically consistent emulators for chaotic systems.

Findings

Sinkhorn divergence (2-Wasserstein) improves statistical fidelity.

WGAN-style dual formulation (1-Wasserstein) effectively captures chaotic attractors.

Approach outperforms traditional methods on high-dimensional chaotic systems.

Abstract

Chaos arises in many complex dynamical systems, from weather to power grids, but is difficult to accurately model using data-driven emulators, including neural operator architectures. For chaotic systems, the inherent sensitivity to initial conditions makes exact long-term forecasts theoretically infeasible, meaning that traditional squared-error losses often fail when trained on noisy data. Recent work has focused on training emulators to match the statistical properties of chaotic attractors by introducing regularization based on handcrafted local features and summary statistics, as well as learned statistics extracted from a diverse dataset of trajectories. In this work, we propose a family of adversarial optimal transport objectives that jointly learn high-quality summary statistics and a physically consistent emulator. We theoretically analyze and experimentally validate a Sinkhorn divergence formulation (2-Wasserstein) and a WGAN-style dual formulation (1-Wasserstein). Our experiments across a variety of chaotic systems, including systems with high-dimensional chaotic attractors, show that emulators trained with our approach exhibit significantly improved long-term statistical fidelity.