Foundation models have already reshaped fields like natural language processing and computer vision, powering tools such as ChatGPT and enabling broad generalization across diverse tasks. The excitement is now spilling into computational science, where the potential impact is enormous, spanning fluid dynamics, materials design, climate modeling, and beyond. But what exactly qualifies as a foundation model in this domain? Without a shared definition, the term risks becoming a buzzword rather than a rigorous scientific concept. In this talk, I will present our recent position paper that seeks to address this gap. I will outline a set of necessary and desirable characteristics for foundation models in computational science, emphasizing principles such as generalization, reusability, and scalability. I will also introduce the Data-Driven Finite Element Method (DD-FEM) as one concrete path toward realizing these ideas, combining the modular structure and mathematical rigor of classical numerical methods with the adaptability of modern machine learning. The goal is not to prescribe a single solution, but to spark community-wide discussion and help establish standards for evaluating and developing foundation models in high-consequence scientific domains. I will close by sharing open questions and opportunities for collaboration, as we collectively shape what foundation models should mean for computational science.

Zoom link: https://snu-ac-kr.zoom.us/my/youngjoonhong

The seminar homepage can be found at the following link: https://sites.google.com/view/acms-snu/