Solution-space heterogeneity shapes federated learning dynamics across partial differential equations
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 ...
| Authors | Ping Luo, Jiahuan Wang, Ziqing Wen et al. |
|---|---|
| Primary category | cs.LG |
| Published | 4 September 2026 |
| Last updated at source | 4 September 2026 |
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