{"ID":2836586,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.21861","arxiv_id":"2511.21861","title":"Towards a Foundation Model for Partial Differential Equations Across Physics Domains","abstract":"We present PDE-FM, a modular foundation model for physics-informed machine learning that unifies spatial, spectral, and temporal reasoning across heterogeneous partial differential equation (PDE) systems. PDE-FM combines spatial-spectral tokenization, physics-aware conditioning, and a Mamba-based state-space backbone with an operator-theoretic decoder, enabling scalable and data-efficient modeling of complex physical dynamics. In contrast to task-specific neural operators, PDE-FM is pretrained once on diverse PDE datasets and can be transferred to new physical regimes without architectural or data-specific modifications. Evaluated on twelve 2D and 3D datasets from The Well benchmark - spanning hydrodynamic, radiative, elastic, and astrophysical phenomena - PDE-FM achieves state-of-the-art accuracy in six domains, reducing mean VRMSE by 46% relative to prior operator-learning baselines. The model demonstrates robust cross-physics generalization, excelling in turbulent and radiative systems while maintaining strong performance in linear and steady-state regimes. These results suggest that large-scale pretraining across diverse physical processes can yield transferable representations of dynamics, marking a step toward unified, foundation-level surrogates for multi-physics simulation and scientific discovery.","short_abstract":"We present PDE-FM, a modular foundation model for physics-informed machine learning that unifies spatial, spectral, and temporal reasoning across heterogeneous partial differential equation (PDE) systems. PDE-FM combines spatial-spectral tokenization, physics-aware conditioning, and a Mamba-based state-space backbone w...","url_abs":"https://arxiv.org/abs/2511.21861","url_pdf":"https://arxiv.org/pdf/2511.21861v1","authors":"[\"Eduardo Soares\",\"Emilio Vital Brazil\",\"Victor Shirasuna\",\"Breno W. S. R. de Carvalho\",\"Cristiano Malossi\"]","published":"2025-11-26T19:36:15Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\"]","methods":"[]","has_code":false}