Weak Adversarial Neural Pushforward Method for the Wigner Transport Equation

Quantum Physics [Submitted on 9 Apr 2026] 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 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. Comments: 9 pages, 1 algorithm Subjects: Quantum Physics (quant-ph); Machine Learning (cs.LG); Numerical Analysis (math.NA) MSC classes: 65N75, 68T07, 81Q05, 81S30 Cite as: arXiv:2604.08763 [quant-ph]   (or arXiv:2604.08763v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.08763 Focus to learn more Submission history From: Qing He [view email] [v1] Thu, 9 Apr 2026 20:58:15 UTC (10 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 Change to browse by: cs cs.LG cs.NA math math.NA References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)