A deep learning method for solving Fokker-Planck equations

被引：0
|
作者：
Zhai, Jiayu [1 ]
Dobson, Matthew [1 ]
Li, Yao [1 ]
机构：
[1] Univ Massachusetts, Dept Math & Stat, Amherst, MA 01002 USA
来源：
MATHEMATICAL AND SCIENTIFIC MACHINE LEARNING, VOL 145 | 2021年 / 145卷
关键词：
Stochastic differential equation; Monte Carlo simulation; invariant measure; coupling method; data-driven and machine learning methods; APPROXIMATION; ALGORITHMS;
D O I：
暂无
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
The time evolution of the probability distribution of a stochastic differential equation follows the Fokker-Planck equation, which usually has an unbounded, high-dimensional domain. Inspired by Li (2019), we propose a mesh-free Fokker-Planck solver, in which the solution to the Fokker-Planck equation is now represented by a neural network. The presence of the differential operator in the loss function improves the accuracy of the neural network representation and reduces the demand of data in the training process. Several high dimensional numerical examples are demonstrated.
引用
收藏
页码：568 / 597
页数：30
相关论文
共 50 条
  • [21] Application of He's Homotopy Perturbation Method for Solving Fractional Fokker-Planck Equations
    Mousa, Mohamed M.
    Kaltayev, Aidarkhan
    ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES, 2009, 64 (12): : 788 - 794
  • [22] φ-Entropies: convexity, coercivity and hypocoercivity for Fokker-Planck and kinetic Fokker-Planck equations
    Dolbeault, Jean
    Li, Xingyu
    MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2018, 28 (13): : 2637 - 2666
  • [23] Solving Fokker-Planck Equations on Cantor Sets Using Local Fractional Decomposition Method
    Yan, Shao-Hong
    Chen, Xiao-Hong
    Xie, Gong-Nan
    Cattani, Carlo
    Yang, Xiao-Jun
    ABSTRACT AND APPLIED ANALYSIS, 2014,
  • [24] Maximum Entropy Method for Solving Fokker-Planck Equations Driven by Fractional Brownian Motion
    Peng L.
    Xie F.
    Xie, Fuji (xiefuji@sjtu.edu.cn), 2017, Shanghai Jiaotong University (51): : 1443 - 1447
  • [25] Composite Laguerre Pseudospectral Method for Fokker-Planck Equations
    Wang, Chuan
    Wang, Tianjun
    Shang, Youlin
    MATHEMATICAL MODELLING AND ANALYSIS, 2023, 28 (04) : 542 - 560
  • [26] Solving Fokker-Planck equations using deep KD-tree with a small amount of data
    Zhang, Hao
    Xu, Yong
    Liu, Qi
    Wang, Xiaolong
    Li, Yongge
    NONLINEAR DYNAMICS, 2022, 108 (04) : 4029 - 4043
  • [27] FORMULATION OF A MOMENT METHOD FOR MULTIDIMENSIONAL FOKKER-PLANCK EQUATIONS
    HUANG, HC
    GHONIEM, NM
    PHYSICAL REVIEW E, 1995, 51 (06) : 5251 - 5260
  • [28] A new efficient method for solving the nonlinear Fokker-Planck equation
    Aminikhah, H.
    Jamalian, A.
    SCIENTIA IRANICA, 2012, 19 (04) : 1133 - 1139
  • [29] THE OPERATOR METHOD FOR SOLVING THE MOMENT EQUATION OF FOKKER-PLANCK EQUATION
    CHU, FM
    FANG, FK
    JIANG, L
    COMMUNICATIONS IN THEORETICAL PHYSICS, 1987, 7 (02) : 187 - 194
  • [30] A POLYNOMIAL EXPANSION METHOD FOR SOLVING THE LASER FOKKER-PLANCK EQUATION
    RISKEN, H
    VOLLMER, HD
    ZEITSCHRIFT FUR PHYSIK B-CONDENSED MATTER, 1980, 39 (01): : 89 - 93
12345