8 papers
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 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…
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 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…