提出一种新方法，从噪声数据中学习复杂系统的能量耗散与保守演化。
Moment Estimates and DeepRitz Methods on Learning Diffusion Systems with Non-gradient Drifts
- 分两阶段：先估计系统矩，再用DeepRitz求解漂移分解
- 在含噪声、粗糙势能和振荡旋转的条件下仍有效
- 适合研究复杂开放系统的动力学建模
保守-耗散动力学广泛存在于各类复杂开放系统中。本文提出一种数据驱动的两阶段方法——矩-DeepRitz方法，用于学习包含保守-耗散动力学的广义扩散系统中的漂移分解。该方法对噪声数据具有鲁棒性，可适应粗糙势能和振荡旋转。通过多个数值实验验证了其有效性。
原文摘要 · Abstract (English)
Conservative-dissipative dynamics are ubiquitous across a variety of complex open systems. We propose a data-driven two-phase method, the Moment-DeepRitz Method, for learning drift decompositions in generalized diffusion systems involving conservative-dissipative dynamics. The method is robust to noisy data, adaptable to rough potentials and oscillatory rotations. We demonstrate its effectiveness through several numerical experiments.
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