6 papers · 1 filter
Weak Adversarial Neural Pushforward Method for Boltzmann Equation
Jenia Fardousi Koly, Andrew Qing He, Wei Cai
In this paper, we extend a weak adversary neural network pushforward method for solving time dependent Boltzmann equation and a weak formulation of the collision operator is propos…
Weak Adversarial Neural Pushforward Method for the McKean-Vlasov / Mean-Field Fokker-Planck Equation
Andrew Qing He, Wei Cai
We extend the Weak Adversarial Neural Pushforward Method (WANPM) to the McKean--Vlasov mean-field Fokker--Planck equation, covering both the stationary and time-dependent cases. Th…
Weak Adversarial Neural Pushforward Method for Fractional Fokker-Planck Equations
Andrew Qing He, Wei Cai
We extend the Weak Adversarial Neural Pushforward Method (WANPM) to fractional Fokker-Planck equations, in which the classical Laplacian diffusion operator is replaced by the fract…
Neural Pushforward Samplers for the Fokker-Planck Equation on Embedded Riemannian Manifolds
Andrew Qing He, Wei Cai
In this paper, we extend the Weak Adversarial Neural Pushforward Method to the Fokker--Planck equation on compact embedded Riemannian manifolds. The method represents the solution…
Learning Neural Pushforward Samplers for Distributions from Fokker-Planck Equations by Weak Adversarial Training
Andrew Qing He, Wei Cai
This paper presents a new method for solving Fokker-Planck equations (FPE) by learning a neural sampler for the distribution given by the FPE via an adversarial training based on a…
ARDO: A Weak Formulation Deep Neural Network Method for Elliptic and Parabolic PDEs Based on Random Differences of Test Functions
Wei Cai, Andrew Qing He
We propose ARDO method for solving PDEs and PDE-related problems with deep learning techniques. This method uses a weak adversarial formulation but transfers the random difference…