Weak Adversarial Neural Pushforward Method for Boltzmann Equation
Jenia Fardousi Koly, Andrew Qing He, Wei Cai
math.NA, cs.LG, cs.NA
Submitted: 2026-08-07
Updated: 2026-08-10
License: http://creativecommons.org/licenses/by/4.0/
The gist: 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 proposed where an
Terminology
Abstract
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 proposed where an invertible neural pushforward mapping is used to generating samples given by the distribution governed by the Boltzmann equation. The training of the pushforward mapping is learnt by enforcing the weak form of the Boltzmann equation. Numerical results have demonstrated the effectiveness of the proposed method.
Sources
- Learning Neural Pushforward Samplers for Distributions from Fokker-Planck Equations by Weak Adversarial Training
- Weak Adversarial Neural Pushforward Method for Fractional Fokker-Planck Equations
- Weak Adversarial Neural Pushforward Method for the McKean-Vlasov / Mean-Field Fokker-Planck Equation
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