Weak Adversarial Neural Pushforward Method for the Wigner Transport Equation

• URL: http://arxiv.org/abs/2604.08763v1
• Date: Thu, 09 Apr 2026 20:58:15 GMT
• Title: Weak Adversarial Neural Pushforward Method for the Wigner Transport Equation
• Abstract summary: We extend the Weak Adversarial Neural Pushforward Method to the Wigner transport equation governing the phase-space dynamics of quantum systems.<n>We introduce a signed pushforward architecture that decomposes the solution into two non-negative phase-space distributions mixed with a learnable weight.<n>The resulting method inherits the mesh-free, Jacobian-free, and scalable properties of the original framework while extending it to the quantum setting.
• Score: 2.64811975262819
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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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