Weak Adversarial Neural Pushforward Method for the Wigner Transport Equation
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Quantum Physics arXiv:2604.08763 (quant-ph) [Submitted on 9 Apr 2026] Title:Weak Adversarial Neural Pushforward Method for the Wigner Transport Equation Authors:Andrew Qing He, Wei Cai, Sihong Shao View a PDF of the paper titled Weak Adversarial Neural Pushforward Method for the Wigner Transport Equation, by Andrew Qing He and 2 other authors View PDF HTML (experimental) 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. Comments: 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 arXiv-issued DOI via DataCite (pending registration) Submission history From: Qing He [view email] [v1] Thu, 9 Apr 2026 20:58:15 UTC (10 KB) Full-text links: Access Paper: View a PDF of the paper titled Weak Adversarial Neural Pushforward Method for the Wigner Transport Equation, by Andrew Qing He and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 Change to browse by: cs cs.LG cs.NA math math.NA References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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 Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)