Learning to Solve PDEs: Scientific Machine Learning from Principles to Practice

Speaker: Minseok Choi

Venue: Room 102, Haina Building 2, Zijingang Campus

Abstract: Scientific Machine Learning (SML) is rapidly emerging as a powerful paradigm for addressing complex problems in science and engineering by integrating machine learning with real-world data and the fundamental laws of physics. This talk will provide a concise overview of the core concepts and algorithmic foundations of SML. In particular, it will introduce methodologies such as Physics-Informed Neural Networks (PINNs), which incorporate physical constraints directly into the learning process, and Operator Learning, which seeks to learn mappings between function spaces and thereby enables fast and efficient prediction of system responses under varying input conditions. The talk will also discuss recent developments aimed at overcoming key limitations of early PINN and operator learning approaches, including issues of long-time integration, data efficiency, generalization, and computational stability. Finally, several examples will be presented to illustrate how SML can lead to innovative and effective solutions in practical applications, often providing substantial speed-ups over traditional numerical simulations.