提出新方法学习非梯度扩散系统的物理规律，适用于复杂噪声数据。
Moment Estimate and Variational Approach for Learning Generalized Diffusion with Non-gradient Structures
- 分两阶段结合能量耗散与一阶矩演化，识别非梯度漂移的势能与旋转分量
- 在含噪声、粗糙势能和耗散-旋转耦合系统中均实现准确建模
- 适合研究非平衡物理系统、随机动力学建模的研究者
本文提出一种数据驱动的学习框架，用于识别具有非梯度项的广义扩散过程的控制规律。通过结合能量耗散律与物理一致的惩罚项，以及一阶矩演化方程，设计了两阶段方法，以恢复一类广义扩散中非梯度漂移在点对点正交分解下的伪势能与旋转分量。该方法应用于复杂的广义扩散过程，包括耗散-旋转动力学、粗糙伪势能及含噪声数据。代表性数值实验表明，该方法在学习非梯度广义扩散的物理规律方面具有有效性。
原文摘要 · Abstract (English)
This paper proposes a data-driven learning framework for identifying governing laws of generalized diffusions with non-gradient components. By combining energy dissipation laws with a physically consistent penalty and first-moment evolution, we design a two-stage method to recover the pseudo-potential and rotation in the pointwise orthogonal decomposition of a class of non-gradient drifts in generalized diffusions. Our two-stage method is applied to complex generalized diffusion processes including dissipation-rotation dynamics, rough pseudo-potentials and noisy data. Representative numerical experiments demonstrate the effectiveness of our approach for learning physical laws in non-gradient generalized diffusions.
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