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Solution-space heterogeneity shapes federated learning dynamics across partial differential equations — arXiv:2609.05012

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.05012
License (as archived): CC0-1.0
Archived: 2026-10-16T22:41:28.818Z
SHA-256 of the archived text: 16175b605bf7915adb68b73f754449fc04641f8a7d71b6e737f77f4387585643
Stable URL of this page: https://metraipolis.com/documento/dc_18656c2affa2

How to cite

Solution-space heterogeneity shapes federated learning dynamics across partial differential equations — arXiv:2609.05012 — arXiv (en), https://arxiv.org/abs/2609.05012 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_18656c2affa2 (Metraipolis archive dc_18656c2affa2, sha256 16175b605bf7915adb68b73f754449fc04641f8a7d71b6e737f77f4387585643)

BibTeX

@misc{dc18656c2affa2,
  title = {Solution-space heterogeneity shapes federated learning dynamics across partial differential equations — arXiv:2609.05012},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.05012},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_18656c2affa2; sha256 16175b605bf7915adb68b73f754449fc04641f8a7d71b6e737f77f4387585643},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.05012. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Federated scientific machine learning enables institutions to train neural surrogates without centralizing local physical data, yet studies of partial differential equations (PDEs) lack a transferable definition of non-independent and identically distributed data. Existing protocols partition coordinates, coefficients, boundary conditions, or geometries according to equation-specific rules. Here, we introduce solution-space PDE-Dirichlet, a protocol that converts continuous supervised responses into reusable solution bins and quantifies the realized separation between clients through optimal transport over the geometry of these bins. We derive an exact inverse relation between population allocation heterogeneity and the Dirichlet concentration, and we establish conditions under which response heterogeneity induces gradient disagreement, local-update dispersion, and parameter divergence. Across seven controlled and public PDE tasks, three neural-operator families, and five random seeds, a lower concentration consistently increases the realized solution distance and optimization heterogeneity. The degradation in final error is task dependent: the largest effect occurs for low-viscosity Burgers, reaching 4.157 percentage points under the most heterogeneous setting, whereas additional communication or smoother dynamics can reduce the final gap despite persistent parameter separation. These results distinguish a reproducible geometric mechanism from task-dependent generalization outcomes and provide a common basis for evaluating non-IID federated PDE learning.

Tema degli esploratori: calcolo e infrastrutture (retro-catalogo arXiv: annunci del 2026-09-07 in cs.DC).
Categorie arXiv: Machine Learning (cs.LG) ; Distributed, Parallel, and Cluster Computing (cs.DC).
Pagina del lavoro: https://arxiv.org/abs/2609.05012 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-16T22:26:34.132Z dalla pagina https://arxiv.org/catchup/cs.DC/2026-09-07?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).