论文标题
从最可能的过渡轨迹的数据中识别随机管理方程
Identifying stochastic governing equations from data of the most probable transition trajectories
论文作者
论文摘要
从难以捉摸的数据中提取管理随机微分方程模型对于理解和预测复杂系统的动力学至关重要。我们从其最可能的过渡轨迹的时间序列数据中设计了一种提取漂移术语并估算管理随机动力学系统的扩散系数的方法。通过Onsager-Machlup理论，最可能的过渡轨迹满足相应的Euler-Lagrange方程，这是涉及漂移项和扩散系数的二阶确定性普通微分方程。我们首先根据最可能的轨迹数据估算Euler-Lagrange方程的系数，然后计算管理随机动力学系统的漂移和扩散系数。这两个步骤涉及稀疏回归和优化。最后，我们用一个示例和一些讨论来说明我们的方法。
Extracting governing stochastic differential equation models from elusive data is crucial to understand and forecast dynamics for complex systems. We devise a method to extract the drift term and estimate the diffusion coefficient of a governing stochastic dynamical system, from its time-series data of the most probable transition trajectory. By the Onsager-Machlup theory, the most probable transition trajectory satisfies the corresponding Euler-Lagrange equation, which is a second order deterministic ordinary differential equation involving the drift term and diffusion coefficient. We first estimate the coefficients of the Euler-Lagrange equation based on the data of the most probable trajectory, and then we calculate the drift and diffusion coefficients of the governing stochastic dynamical system. These two steps involve sparse regression and optimization. Finally, we illustrate our method with an example and some discussions.
