# Learning to Emulate Chaos: Adversarial Optimal Transport Regularization

arXiv: https://arxiv.org/abs/2604.21097 · HTML: https://mlsanity.com/paper/2604.21097/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 46 references that are in the map.
- First posted on arXiv 22 Apr 2026.

## Builds on (most cited first, 7 of 7)

- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [ACE: A fast, skillful learned global atmospheric model for climate prediction](https://mlsanity.com/paper/2310.02074/) (2023)
- [Wasserstein GANs Work Because They Fail (to Approximate the Wasserstein Distance)](https://mlsanity.com/paper/2103.01678/) (2021)
- [Challenges of learning multi-scale dynamics with AI weather models: Implications for stability and one solution](https://mlsanity.com/paper/2304.07029/) (2023)
- [How Well Do WGANs Estimate the Wasserstein Metric?](https://mlsanity.com/paper/1910.03875/) (2019)
- [Optimal Transport for Machine Learners](https://mlsanity.com/paper/2505.06589/) (2025)

## Built on by (most cited first, 1 of 1)

- [Primal-Dual Flow Matching for Sample-Wise Constrained Generation](https://mlsanity.com/paper/2610.12699/) (2026)

## Abstract (arXiv)

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.