10 papers
Neural Vector Field Transformations: Learning the Flow of Autonomous Systems by Conjugation to Explicitly Integrable Reference Flows
Andrew Qing He
We represent the flow map of an autonomous ODE as a conjugate of an explicitly integrable reference flow by an invertible neural…
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…
Deep Kuratowski Embedding Neural Networks for Wasserstein Metric Learning
Andrew Qing He
Computing pairwise Wasserstein distances is a fundamental bottleneck in data analysis pipelines. Motivated by the classical Kuratowski embedding theorem, we propose two neural arch…
Weak Adversarial Neural Pushforward Method for the Wigner Transport Equation
Andrew Qing He, Wei Cai, Sihong Shao
We extend the Weak Adversarial Neural Pushforward Method to the Wigner transport equation governing the phase-space dynamics of quantum systems. The central contribution is a struc…
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…
DeepMartNet -- A Martingale Based Deep Neural Network Learning Method for Dirichlet BVPs and Eigenvalue Problems of Elliptic PDEs in R^d
Wei Cai, Andrew He, Daniel Margolis
In this paper, we propose DeepMartNet - a Martingale based deep neural network learning method for solving Dirichlet boundary value problems (BVPs) and eigenvalue problems for elli…