Learning to Emulate Chaos: Adversarial Optimal Transport Regularization

2026-04-24 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences, Engineering & Applied Sciences · Depth: Expert, extended

Summary

This research introduces a novel family of adversarial optimal transport (OT) objectives designed to improve data-driven emulators for chaotic dynamical systems, which are notoriously difficult to model due to their sensitivity to initial conditions. Traditional squared-error losses often fail in these systems, leading to catastrophic degradation in long-term forecasts. The proposed method jointly learns high-quality summary statistics and a physically consistent emulator, addressing limitations of prior approaches that relied on handcrafted features or diverse multi-environment datasets. The framework utilizes either a Sinkhorn divergence formulation (2-Wasserstein) or a WGAN-style dual formulation (1-Wasserstein) to regularize the standard mean squared error (MSE) loss. Experiments on high-dimensional chaotic systems like Lorenz-96, Kuramoto-Sivashinsky, and Kolmogorov flow demonstrate significantly improved long-term statistical fidelity, outperforming MSE-only baselines and methods using fixed summary statistics, especially in spectral distance and leading Lyapunov exponent reproduction.

Key takeaway

For Machine Learning Engineers developing emulators for chaotic dynamical systems, your reliance on traditional MSE loss for long-term forecasting is fundamentally limited by noise sensitivity. You should integrate adversarial optimal transport regularization, such as the Sinkhorn or WGAN-style objectives, to achieve superior long-term statistical fidelity and accurately capture invariant measures, even from single, noisy trajectories. This approach will prevent attractor collapse and improve the reproduction of critical dynamical properties like the leading Lyapunov exponent.

Key insights

Adversarial optimal transport regularization enables emulators to learn chaotic system statistics from noisy, single-trajectory data.

Principles

• MSE loss is insufficient for long-term chaotic system emulation.
• Distributional objectives are robust to initial condition noise.
• Adversarial learning can discover informative summary statistics.

Method

The method trains an emulator and a summary map simultaneously. The emulator minimizes MSE and an OT cost, while the summary map maximizes the OT cost to identify discriminative statistics, using Sinkhorn or WGAN formulations.

In practice

• Use adversarial OT for chaotic system emulation.
• Prioritize spectral distance and L1 histogram error for evaluation.
• Consider warm-start pretraining with MSE before OT regularization.

Topics

• Chaotic Systems Emulation
• Adversarial Optimal Transport
• Neural Operators
• Sinkhorn Divergence
• Wasserstein GAN

Best for: AI Scientist, Machine Learning Engineer, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.