提出新方法推断非梯度型随机系统演化，提升分布拟合精度。
Leveraging Gauge Freedom for Learning Non-Gradient Population Dynamics of Stochastic Systems
- 基于连续性方程弱形式，参数化一般向量场
- 在多类物理问题上显著优于梯度约束基线
- 适合研究非势能驱动的复杂传输过程
现有群体动态推断方法多聚焦于由标量势能梯度生成的流。在所有与群体动态相容的流中，梯度流在特定意义上最优——它最小化动能。基于不同准则选择场对应于确定群体动态时的规范自由度，本文即利用此自由度。我们提出非梯度推断流（NGIF）算法，通过连续性方程的弱形式推断非梯度群体动态，可参数化一般向量场，并采用超越最小动能的其他选择准则。我们在多种低维与高维物理问题上验证，该更通用方法在分布精度上优于梯度受限基线，更好地捕捉非势能传输现象。
原文摘要 · Abstract (English)
Existing work on population dynamics inference often focuses on flows arising from vector fields that are the gradients of scalar potentials. Among all admissible flows that are compatible with the population dynamics, gradient flows are optimal in a specific sense: they minimize kinetic energy. The selection of fields based on different criteria corresponds to a gauge freedom when determining population dynamics, which we leverage in this work. We propose Non-Gradient Inference Flows (NGIF), an algorithm to infer non-gradient population dynamics using a weak formulation of the continuity equation. This allows us to parameterize general vector fields and choose other selection criteria beyond minimal kinetic energy. We demonstrate on a variety of low- and high-dimensional physics problems that this more general approach improves distributional accuracy over gradient-restricted baselines and better captures non-potential transport.
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