Learning to Emulate Chaos: Adversarial Optimal Transport Regularization

2026-04-22

AI Summary

Existing data-driven simulators of chaotic systems struggle to accurately reproduce the long-term statistical properties of attractors under noisy conditions. This work proposes an adversarial optimal transport regularization framework that, for the first time, integrates Sinkhorn divergence (approximating 2-Wasserstein distance) and a WGAN-style dual formulation (1-Wasserstein) into chaotic system modeling. By jointly learning high-quality statistical summaries and physically consistent dynamical models, the method matches trajectory distributions in an end-to-end manner to enhance long-term statistical fidelity. Combining adversarial training, optimal transport theory, and neural operator architectures, the approach significantly outperforms existing methods—particularly those relying on handcrafted features or predefined statistics—across a range of chaotic systems, including those with high-dimensional attractors.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Multiagent Systems: Adversarial Agents
• Machine Learning: Adversarial Learning & Robustness

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Web Mining and Content Analysis: Web data generation and simulation
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

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.

Problem

• chaos
• emulator
• statistical fidelity
• chaotic attractor
• long-term forecasting

Innovation

• adversarial optimal transport
• chaotic systems
• neural operators
• Wasserstein distance
• statistical fidelity