Paper
Weak Adversarial Neural Pushforward Method for the McKean-Vlasov / Mean-Field Fokker-Planck Equation
Authors
Andrew Qing He, Wei Cai
Abstract
We extend the Weak Adversarial Neural Pushforward Method (WANPM) to the McKean-Vlasov mean-field Fokker-Planck equation. For the quadratic interaction kernel, the mean-field nonlinearity reduces to a batch sample mean, requiring no secondary sampling. We focus on the stationary problem, identifying key training subtleties: gradient flow through the self-consistent mean estimate is essential for uniqueness, and adversarial test function frequencies must be initialized at a sufficiently large scale to avoid spurious minimizers. A numerical benchmark on the 1D linear McKean-Vlasov equation confirms accurate recovery of the exact Gaussian stationary distribution.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.16186v1</id>\n <title>Weak Adversarial Neural Pushforward Method for the McKean-Vlasov / Mean-Field Fokker-Planck Equation</title>\n <updated>2026-03-17T07:13:14Z</updated>\n <link href='https://arxiv.org/abs/2603.16186v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.16186v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>We extend the Weak Adversarial Neural Pushforward Method (WANPM) to the McKean-Vlasov mean-field Fokker-Planck equation. For the quadratic interaction kernel, the mean-field nonlinearity reduces to a batch sample mean, requiring no secondary sampling. We focus on the stationary problem, identifying key training subtleties: gradient flow through the self-consistent mean estimate is essential for uniqueness, and adversarial test function frequencies must be initialized at a sufficiently large scale to avoid spurious minimizers. A numerical benchmark on the 1D linear McKean-Vlasov equation confirms accurate recovery of the exact Gaussian stationary distribution.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='math.NA'/>\n <published>2026-03-17T07:13:14Z</published>\n <arxiv:comment>10 pages, 2 figures</arxiv:comment>\n <arxiv:primary_category term='math.NA'/>\n <author>\n <name>Andrew Qing He</name>\n </author>\n <author>\n <name>Wei Cai</name>\n </author>\n </entry>"
}