为计算科学中的基础模型定义标准,推动AI与传统数值方法融合。
Defining Foundation Models for Computational Science: A Call for Clarity and Rigor
- 提出计算科学基础模型的正式定义,强调通用性、可复用性和可扩展性。
- 构建数据驱动有限元法(DD-FEM),融合经典方法与数据学习优势。
- 适合关注AI+科学计算融合的研究者,为未来模型设计提供评估框架。
基础模型在自然语言处理和计算机视觉领域的成功,促使研究者将其拓展至科学机器学习与计算科学领域。然而,本文指出,由于“基础模型”这一概念仍在演进,其在计算科学中的应用缺乏统一定义,可能引发混淆并削弱其科学意义。为此,本文基于通用性、可复用性和可扩展性等核心价值,提出计算科学中基础模型的正式定义,并列出必要与理想特性,类比传统有限元法、有限体积法等奠基性方法。同时,提出数据驱动有限元法(DD-FEM)框架,将经典有限元的模块化结构与数据驱动学习的表征能力相结合。实证表明,该框架有效应对了可扩展性、适应性与物理一致性等关键挑战。通过连接传统数值方法与现代AI范式,本工作为评估和开发计算科学中的未来基础模型提供了严谨基础。
原文摘要 · Abstract (English)
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.
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