A data-driven method for the steady state of randomly perturbed dynamics
A data-driven method for the steady state of randomly perturbed dynamics
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DOI：
10.4310/cms.2019.v17.n4.a9
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发表时间：
2018-05
影响因子：
1
通讯作者：
Yao Li
中科院分区：
文献类型：
--
作者：
Yao Li
我们演示了一种数据驱动的方法来求解随机扰动动力系统的不变概率密度函数。其关键思想是将数值格式的边界条件替换为与参考解相对应的最小二乘问题，该参考解是通过蒙特卡罗模拟生成的。利用这种方法，无论吸引子是否被数值域覆盖，我们都可以高精度地求解任意局部区域内的不变概率密度函数。
We demonstrate a data-driven method to solve for the invariant probability density function of a randomly perturbed dynamical system. The key idea is to replace the boundary condition of numerical schemes by a least squares problem corresponding to a reference solution, which is generated by Monte Carlo simulation. With this method we can solve for the invariant probability density function in any local area with high accuracy, regardless of whether the attractor is covered by the numerical domain.