Mathematical Foundations & Methodologies for Artificial Intelligence and Data-Driven Scientific Computing

Overview

Artificial Intelligence (AI) is revolutionizing scientific computing, with applications spanning from drug discovery and molecular dynamics to natural language processing and weather forecasting. Despite these successes, the theoretical foundations underpinning modern AI models–such as transformers, diffusion models, and operator learning architectures–remain incomplete and fragmented. This poses challenges to reliability, interpretability, and robust deployment, particularly in high-stakes scientific and industrial domains.

This program, hosted at the Institute for Mathematical Sciences (IMS),  aims to address this gap by bringing together leading experts in mathematics, computer science, and engineering to investigate and advance the mathematical foundations of AI and its application in data-driven scientific computing.

Core topics include expressivity, optimization, generalization, explainability, and principled AI model design. Emphasis will also be placed on bridging academic advances with industrial applications and fostering interdisciplinary collaboration.