Siddhartha Mishra, ETH Zurich
YouTube Stream: https://youtube.com/live/hiu-Ii2cwUA
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Abstract:
Partial Differential Equations (PDEs) are often described as the language of Physics as they describe a wide array of physical phenomena over a vast range of scales. Despite their remarkable success over many decades, numerical methods for approximating PDEs can incur a very high computational cost. This limitation has provided the impetus for the design of fast and accurate Machine Learning/AI based neural PDE surrogates which can learn the PDE solution operator from data. In this talk, we review some latest developments in the field of Neural Operators, which are widely used as an ML paradigm for PDEs and discuss state of the art neural operators based on convolutions or attention. We will discuss graph and transformer based architectures for PDEs on arbitrary domains and conditional Diffusion models for PDEs with chaotic multiscale solutions. Finally, the issue of sample complexity is addressed by the design of general purpose Foundation models for PDEs.
Bio:
Prof. Siddhartha Mishra is a Professor in the Seminar for Applied Mathematics at ETH Zurich, where he leads the Computational and Applied Mathematics Laboratory and serves as core faculty at the ETH AI Center and an executive board member of the Swiss National AI Institute. His research focuses on the development and analysis of numerical methods and AI/ML algorithms for simulating complex physical systems, with applications spanning astrophysics, geophysics, climate science, engineering, and biological systems. He is an elected fellow of the European Academy of Sciences and the recipient of numerous prestigious honors, including the GAMM Richard von Mises Prize, the ECCOMAS Jacques Louis Lions Medal, the ICIAM Collatz Prize, the Infosys Prize in Mathematical Sciences, the SIAM Germund Dahlquist Prize, and the ETH Zurich Rössler Prize. He has delivered keynote lectures at major international conferences, including the International Congress of Mathematicians (ICM) and the SIAM Annual Meeting.