Data-Driven Computational Methods for Quasi-Stationary Distribution and Sensitivity Analysis
Data-Driven Computational Methods for Quasi-Stationary Distribution and Sensitivity Analysis
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DOI：
10.1007/s10884-022-10137-2
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发表时间：
2022-02
影响因子：
1.3
通讯作者：
Yao Li;Yaping Yuan
中科院分区：
文献类型：
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作者：
Yao Li;Yaping Yuan
本文研究了准平稳分布的计算方法。我们首先提出了一个数据驱动的求解器，解决了福克-普朗克方程的QSD。类似于不变概率测度的Fokker-Planck方程的情况，我们建立了一个优化问题，该问题在满足离散化Fokker-Planck算子给出的线性关系的约束下，最小化与低精度参考解的距离。然后我们用耦合方法研究了QSD对边界条件和扩散系数变化的敏感性。QSD和相应的不变概率测度之间的1-Wasserstein距离可以定量估计。给出了QSD计算及其灵敏度分析的数值结果。
This paper studies computational methods for quasi-stationary distributions (QSDs). We first proposed a data-driven solver that solves Fokker–Planck equations for QSDs. Similar to the case of Fokker–Planck equations for invariant probability measures, we set up an optimization problem that minimizes the distance from a low-accuracy reference solution, under the constraint of satisfying the linear relation given by the discretized Fokker–Planck operator. Then we use coupling method to study the sensitivity of a QSD against either the change of boundary condition or the diffusion coefficient. The 1-Wasserstein distance between a QSD and the corresponding invariant probability measure can be quantitatively estimated. Some numerical results about both computation of QSDs and their sensitivity analysis are provided.