MAE Seminar: Toward a “GPT” Moment for Scientific Computing

Details

MAE Seminar: Toward a “GPT” Moment for Scientific Computing
Date: February 17, 2026
Time: 12:50 PM Location: MAE-A 303

Dr. Sifan Wang
Postdoctoral Fellow
Yale University

Abstract
Foundation models such as ChatGPT have reshaped AI by learning reusable representations that transfer across tasks. This talk asks whether a similar shift is possible in scientific computing: moving beyond solvers for a single partial differential equation (PDE) toward foundation models for families of PDE-governed systems. A central obstacle is that high-fidelity PDE data are expensive—often requiring hours to millions of CPU-hours per simulation—making purely data-driven scaling impractical. I present a physics-first roadmap that replaces data scale with physical structure, using governing equations as supervision.

I will first focus on the single-PDE setting and show how physics-informed neural networks (PINNs) can be made reliable by diagnosing and addressing key training pathologies, leading to substantial accuracy improvements and successful simulations of challenging problems including 3D turbulence. I will then extend physics supervision from learning individual PDE solutions to learning solution operators for parametric PDE families. I will introduce the framework of physics-informed DeepONet and improve its scalability with continuous vision transformers. Finally, I will discuss how these advances motivate a longer-term direction toward unified models that can generalize across heterogeneous PDEs. Together, these results provide practical and theoretical steps toward PDE foundation models, with implications for accelerated simulation, design and control in computational science and engineering.

Biography
Sifan Wang is a Postdoctoral Fellow at Yale University’s Institute for Foundations of Data Science. He earned his Ph.D. in Applied Mathematics & Computational Science from the University of Pennsylvania (2023), advised by Paris Perdikaris. His research focuses on building reliable learning-based methods for physical systems governed by partial differential equations.

Faculty Host: Dr. Yu Wang