基于平稳分布观测的随机支配律检测
Detecting Stochastic Governing Laws with Observation on Stationary Distributions
AI总结：
本文提出基于神经网络的方法，通过观测平稳概率分布学习随机微分方程的漂移项和扩散项，引入含Hellinger距离的新损失函数，经数值实验验证能有效近似数据驱动动力系统。
摘要：
复杂系统的数学模型常伴随不确定性。本文旨在通过观测平稳概率分布提取随机微分方程支配模型。我们开发了一种神经网络方法学习随机微分方程的漂移项和扩散项。引入包含观测数据与所学平稳概率密度函数之间Hellinger距离的新损失函数。我们发现，在训练方法中最小化此损失函数后，所学随机微分方程能对数据驱动动力系统提供良好近似。数值实验验证了本方法的有效性。
英文摘要：
Mathematical models for complex systems are often accompanied with uncertainties. The goal of this paper is to extract a stochastic differential equation governing model with observation on stationary probability distributions. We develop a neural network method to learn the drift and diffusion terms of the stochastic differential equation. We introduce a new loss function containing the Hellinger distance between the observation data and the learned stationary probability density function. We discover that the learnt stochastic differential equation provides a fair approximation of the data-driven dynamical system after minimizing this loss function during the training method. The effectiveness of our method is demonstrated in numerical experiments.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
