从轨迹数据中学习非平衡耗散系统，可解析能量景观与熵产生。
Identifiable learning of dissipative dynamics
- 构建可识别的神经框架，直接从轨迹学习耗散动力学。
- 首次实现能量景观唯一性识别，量化熵产生率与不可逆性。
- 适用于高分子拉伸、随机梯度动态等场景，揭示新物理规律。
复杂耗散系统广泛存在于科学与工程领域，如聚合物、活性物质及学习算法。这些系统远离平衡态，能量耗散与时间不可逆性主导其行为，但难以从数据中量化。本文提出一种通用且可识别的神经框架，可直接从轨迹中学习耗散随机动力学，确保可解释性、表达力与唯一性。该方法能识别唯一能量景观，分离可逆与不可逆运动，并直接计算熵产生率，提供不可逆性的原则性度量及偏离平衡的程度。在拉伸流中的聚合物行为和随机梯度朗之万动力学中的应用揭示了新现象：势垒高度随应变速率呈超线性增长，熵产生率呈亚线性变化；批量大小增大可抑制不可逆性。本方法建立了一种通用的数据驱动框架，用于发现与解析非平衡动力学。
原文摘要 · Abstract (English)
Complex dissipative systems appear across science and engineering, from polymers and active matter to learning algorithms. These systems operate far from equilibrium, where energy dissipation and time irreversibility govern their behavior but are difficult to quantify from data. Here, we introduce a universal and identifiable neural framework that learns dissipative stochastic dynamics directly from trajectories while ensuring interpretability, expressiveness, and uniqueness. Our method identifies a unique energy landscape, separates reversible from irreversible motion, and allows direct computation of the entropy production, providing a principled measure of irreversibility and deviations from equilibrium. Applications to polymer stretching in elongational flow and to stochastic gradient Langevin dynamics reveal new insights, including super-linear scaling of barrier heights and sub-linear scaling of entropy production rates with the strain rate, and the suppression of irreversibility with increasing batch size. Our methodology thus establishes a general, data-driven framework for discovering and interpreting non-equilibrium dynamics.
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