混沌现象广泛存在于诸多复杂动力系统中，如天气系统与电网，但利用机器学习等数据驱动方法构建高精度模拟器（emulator）仍面临巨大挑战。尽管模拟器在加速数值模拟与求解反问题方面展现出潜力，其在建模混沌动力学时仍表现不佳——初始条件的敏感性使得长期精确预测难以实现，尤其当观测数据含有噪声时。近期研究转而训练模拟器以匹配混沌吸引子的统计特性，但此类方法往往依赖人工设计的汇总统计量或大规模、多环境的多样化数据集。本文提出一类对抗式最优传输目标函数，可仅凭单条含噪轨迹，同步学习高质量的汇总统计量与物理上自洽的模拟器。我们从理论上分析并实验验证了该方法的两种形式：基于Sinkhorn散度（2-Wasserstein距离）的公式，以及类WGAN的对偶公式（1-Wasserstein距离）。在多种混沌系统（包括具有高维时空混沌的系统）上的数值实验表明，采用本文所提目标函数训练的模拟器，在长期统计保真度方面显著提升。

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.