Year: 2026
Type: article
Abstract: The termfoundation modelis rapidly entering scientific machine learning, yet its meaning in computational science remains inconsistent. Models are increasingly labeled foundational without evidence of broad generalization across physical systems, geometries, boundary/initial conditions, tasks, or operating regimes. We propose a definition of foundation models tailored to computational science and identify core and desirable characteristics, drawing inspiration from classical foundational methods (FEM/FVM/FDM) that achieve wide reuse through problem-independent structure and principled enforcement of governing equations. We argue that scientific foundation models face unique barriers relative to language and vision models, including field-valued data, mesh and geometry dependence, heterogeneous physics, expensive adaptation, limited benchmarks, and strict requirements for interpretability and physical consistency. To make claims measurable, we introduce a reviewer- and author-friendly checklist for reporting training breadth, generalization axes, adaptation cost, extrapolation protocols, and scientific consistency checks. We also highlight a constructive hybrid path: local learning with global physics enforcement.
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G1088636562, G1356433355, G14554683, G2145270357, G217780377, Collaborative Research: Data-Driven Variational Multiscale Reduced Order Models for Biomedical and Engineering Applications, G3279819049, G3390444915, G3629910294, G3669113783, G4094752214, G4744444288, G5630301777, G5660175478, G5685548091, G574795485, G5946024249, G8110683607, G8397015973, G895790057, G991281326
OpenAlex ID: W7161821616