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Although broadly used, they allow for analytical treatment only in limited settings, and often is inevitable to resort to numerical solutions. Here, we develop a computational approach for simulating the time evolution of Fokker-Planck solutions in terms of a mean field limit of an interacting particle system. The interactions between particles are determined by the gradient of the logarithm of the particle density, approximated here by a novel statistical estimator. The performance of our method shows promising results, with more accurate and less fluctuating statistics compared to direct stochastic simulations of comparable particle number. Taken together, our framework allows for effortless and reliable particle-based simulations of Fokker-Planck equations in low and moderate dimensions. The proposed gradient-log-density estimator is also of independent interest, for example, in the context of optimal control.","url_abs":"https://arxiv.org/abs/2006.00702v1","url_pdf":"https://arxiv.org/pdf/2006.00702v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"interacting-particle-solutions-of-fokker","repo_url":"https://gitlab.com/dimitra-maoutsa/odes_for_sdes","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null},{"paper_slug":"interacting-particle-solutions-of-fokker","repo_url":"https://github.com/dimitra-maoutsa/odes_for_sdes","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2006.00702","atlas_url":"https://app.syntology.ai/?focus=2006.00702","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2006.00702"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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