On scientific foundation models: Rigorous definitions, key applications, and a comprehensive survey

Scientific Foundation Models (SciFMs) represent a transformative paradigm for addressing complex scientific and engineering problems by leveraging large-scale pretraining and deep learning architectures. Unlike traditional numerical solvers, which require problem-specific discretization and extensive parameter tuning, SciFMs aim to learn generalizable representations of physical laws, thereby enabling broad applicability with minimal retraining. In the absence of a rigorous definition, this work categorizes their capabilities into four key dimensions-domain adaptation, domain generalization, problem adaptation, and problem generalization; thereby providing rigorous definitions for SciFMs, which we refer to as…