Numerical solution of the Fokker–Planck equation using physics-based mixture models

A review and assessment of importance sampling methods for reliability analysis

(2022) Armin Tabandeh et al.   STRUCTURAL SAFETY

A structure preserving numerical scheme for Fokker-Planck equations of neuron networks: Numerical analysis and exploration

(2021) Jingwei Hu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A high-order semi-Lagrangian method for the consistent Monte-Carlo solution of stochastic Lagrangian drift–diffusion models coupled with Eulerian discontinuous spectral element method

(2021) H. Natarajan et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Nonlinear random vibration analysis: A Bayesian nonparametric approach

(2021) Armin Tabandeh et al.   PROBABILISTIC ENGINEERING MECHANICS

Solving Fokker-Planck equation using deep learning

(2020) Yong Xu et al.   CHAOS

Dissipative brackets for the Fokker–Planck equation in Hamiltonian systems and characterization of metriplectic manifolds

(2020) Naoki Sato   PHYSICA D-NONLINEAR PHENOMENA

New method for solving strong conservative odd parity nonlinear oscillators: Applications to plasma physics and rigid rotator

(2020) Ma’mon Abu Hammad et al.   AIP Advances

Neural network representation of the probability density function of diffusion processes

(2020) Wayne Isaac T. Uy et al.   CHAOS

PPINN: Parareal physics-informed neural network for time-dependent PDEs

(2020) Xuhui Meng et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Pseudospectral solutions of the Fokker-Planck equation for Pearson diffusion that yields a Kappa distribution; the associated SUSY Schrödinger equation

(2020) Hrishikesh Patel et al.   Computational and Theoretical Chemistry

Finite element solution of the Fokker–Planck equation for single domain particles

(2020) N.V. Peskov   PHYSICA B-CONDENSED MATTER

A conservative, free energy dissipating, and positivity preserving finite difference scheme for multi-dimensional nonlocal Fokker–Planck equation

(2019) Yiran Qian et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Morphogenesis as Bayesian inference: A variational approach to pattern formation and control in complex biological systems

(2019) Franz Kuchling et al.   Physics of Life Reviews

Non-linear Fokker-Planck equation solved with generalized finite differences in 2D and 3D

(2019) Francisco Ureña et al.   APPLIED MATHEMATICS AND COMPUTATION

Probabilistic solution to two-dimensional stochastic solute transport model by the Fokker-Planck equation approach

(2019) Tongbi Tu et al.   JOURNAL OF HYDROLOGY

Efficient statistically accurate algorithms for the Fokker–Planck equation in large dimensions

(2018) Nan Chen et al.   JOURNAL OF COMPUTATIONAL PHYSICS

DGM: A deep learning algorithm for solving partial differential equations

(2018) Justin Sirignano et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Solving high-dimensional partial differential equations using deep learning

(2018) Jiequn Han et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

(2018) M. Raissi et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Oligarchy as a phase transition: The effect of wealth-attained advantage in a Fokker–Planck description of asset exchange

(2017) Bruce M. Boghosian et al.   PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS

Multifidelity importance sampling

(2016) Benjamin Peherstorfer et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Numerical methods for high-dimensional probability density function equations

(2016) H. Cho et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Numerical methods for kinetic equations

(2014) G. Dimarco et al.   ACTA NUMERICA

The Hysteresis Bouc-Wen Model, a Survey

(2009) Mohammed Ismail et al.   ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING

Normal forms for reduced stochastic climate models

(2009) A. J. Majda et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA