用神经网络求解量子相空间方程，无需导数信息且可处理负概率分布。
Weak Adversarial Neural Pushforward Method for the Wigner Transport Equation
- 将弱对抗神经前推法扩展到量子系统的相空间演化方程
- 通过平面波测试函数使非局部算子退化为两点差分，避免级数截断
- 设计带符号前推结构，可处理负的准概率分布，适合量子模拟研究者
我们将弱对抗神经前推法扩展至描述量子系统相空间动力学的威格纳传输方程。核心贡献在于一项结构观察：将非局部伪微分势算子与平面波测试函数积分，可产生一个狄拉克δ函数，精确反转定义威格纳势核的傅里叶变换，从而使算子简化为在两个平移参数处的势能点值差分。该方法在任意维度下成立，无需对莫亚尔级数进行截断，且将势能视为不需导数信息的黑箱函数接口。为处理威格纳准概率分布的负性，我们引入一种带符号的前推架构，将解分解为两个非负相空间分布，并以可学习权重混合。新方法继承了原框架的无网格、无雅可比、可扩展特性，同时拓展至量子场景。
原文摘要 · Abstract (English)
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 structural observation: integrating the nonlocal pseudo-differential potential operator against plane-wave test functions produces a Dirac delta that exactly inverts the Fourier transform defining the Wigner potential kernel, reducing the operator to a pointwise finite difference of the potential at two shifted arguments. This holds in arbitrary dimension, requires no truncation of the Moyal series, and treats the potential as a black-box function oracle with no derivative information. To handle the negativity of the Wigner quasi-probability distribution, we introduce a signed pushforward architecture that decomposes the solution into two non-negative phase-space distributions mixed with a learnable weight. The resulting method inherits the mesh-free, Jacobian-free, and scalable properties of the original framework while extending it to the quantum setting.
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