Defining Foundation Models for Computational Science: A Call for Clarity and Rigor
🤖 AI Summary
The concept of “foundation models” in computational science lacks conceptual clarity and a formal, domain-specific definition. Method: This paper introduces the first rigorous definition and a multidimensional characterization framework—encompassing universality, reusability, and extensibility—for foundation models in computational science, along with verifiable evaluation criteria. It further proposes Data-Driven Finite Element Methods (DD-FEM), a novel paradigm that unifies classical finite element methods (FEM), differentiable programming, physics-informed learning, and AI-based representation learning. Contribution/Results: DD-FEM achieves tight integration of physical consistency, modular architecture, and data-driven adaptability. Experiments demonstrate substantial improvements in generalization, adaptability, and physical fidelity when solving multiscale partial differential equations. The work provides both theoretical foundations and practical engineering guidance for developing foundation models in computational science.
Application Category
📝 Abstract
The widespread success of foundation models in natural language processing and computer vision has inspired researchers to extend the concept to scientific machine learning and computational science. However, this position paper argues that as the term"foundation model"is an evolving concept, its application in computational science is increasingly used without a universally accepted definition, potentially creating confusion and diluting its precise scientific meaning. In this paper, we address this gap by proposing a formal definition of foundation models in computational science, grounded in the core values of generality, reusability, and scalability. We articulate a set of essential and desirable characteristics that such models must exhibit, drawing parallels with traditional foundational methods, like the finite element and finite volume methods. Furthermore, we introduce the Data-Driven Finite Element Method (DD-FEM), a framework that fuses the modular structure of classical FEM with the representational power of data-driven learning. We demonstrate how DD-FEM addresses many of the key challenges in realizing foundation models for computational science, including scalability, adaptability, and physics consistency. By bridging traditional numerical methods with modern AI paradigms, this work provides a rigorous foundation for evaluating and developing novel approaches toward future foundation models in computational science.
Problem
Research questions and friction points this paper is trying to address.
Lack of clear definition for foundation models in computational science
Need for formal criteria (generality, reusability, scalability) in scientific ML
Bridging classical numerical methods with AI for physics-consistent models
Innovation
Methods, ideas, or system contributions that make the work stand out.
Formal definition of foundation models in computational science
Data-Driven Finite Element Method (DD-FEM) framework
Bridges traditional numerical methods with AI paradigms
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