用神经网络推演玻尔兹曼方程，高效求解时间演化问题。
Weak Adversarial Neural Pushforward Method for Boltzmann Equation
- 通过可逆神经网络生成符合方程的分布样本
- 在弱形式下训练网络，逼近玻尔兹曼方程解
- 适合需要快速求解复杂输运问题的研究者
本文将弱对抗神经网络前向映射方法拓展至求解时变玻尔兹曼方程。提出一种弱形式的碰撞算子，利用可逆神经前向映射生成由玻尔兹曼方程控制的分布样本。通过强制满足玻尔兹曼方程的弱形式来训练该前向映射。数值结果验证了所提方法的有效性。
原文摘要 · Abstract (English)
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.
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