Adaptive Deep Density Approximation for Fractional Fokker–Planck Equations

Adaptive deep density approximation for Fokker-Planck equations

(2022) Kejun Tang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Normalizing field flows: Solving forward and inverse stochastic differential equations using physics-informed flow models

(2022) Ling Guo et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Monte Carlo fPINNs: Deep learning method for forward and inverse problems involving high dimensional fractional partial differential equations

(2022) Ling Guo et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

On a structure-preserving numerical method for fractional Fokker-Planck equations

(2022) Nathalie Ayi et al.   MATHEMATICS OF COMPUTATION

DAS-PINNs: A deep adaptive sampling method for solving high-dimensional partial differential equations

(2022) Kejun Tang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks

(2021) N. Sukumar et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Discovering Physical Concepts with Neural Networks

(2020) Raban Iten et al.   PHYSICAL REVIEW LETTERS

Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations

(2020) Maziar Raissi et al.   SCIENCE

Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations

(2020) Liu Yang et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Weak adversarial networks for high-dimensional partial differential equations

(2020) Yaohua Zang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Stochastic dynamics driven by combined Lévy-Gaussian noise: fractional Fokker-Planck-Kolmogorov equation and solution

(2020) wanrong zan et al.   Journal of Physics A-Mathematical and Theoretical

B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data

(2020) Liu Yang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

PFNN: A penalty-free neural network method for solving a class of second-order boundary-value problems on complex geometries

(2020) Hailong Sheng et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data

(2019) Yinhao Zhu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Adversarial uncertainty quantification in physics-informed neural networks

(2019) Yibo Yang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Path integral solutions of the governing equation of SDEs excited by Lévy white noise

(2019) Yong Xu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Machine Learning for Fluid Mechanics

(2019) Steven L. Brunton et al.   Annual Review of Fluid Mechanics

A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems

(2019) Xuhui Meng et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Deep Potential Molecular Dynamics: A Scalable Model with the Accuracy of Quantum Mechanics

(2018) Linfeng Zhang et al.   PHYSICAL REVIEW LETTERS

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

Fokker–Planck equations for stochastic dynamical systems with symmetric Lévy motions

(2016) Ting Gao et al.   APPLIED MATHEMATICS AND COMPUTATION

Finite Element Method for the Space and Time Fractional Fokker–Planck Equation

(2008) Weihua Deng   SIAM JOURNAL ON NUMERICAL ANALYSIS