Langtangen Seminar (May 6, 2025) Siddhartha Mishra скачать в хорошем качестве

Langtangen Seminar (May 6, 2025) Siddhartha Mishra

Learning PDEs Siddhartha Mishra, Eidgenössische Technische Hochschule Zürich Abstract: 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 of the 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.