Apply by sending an email to the organizer faprile@ucm.es
"An Introduction to Solving PDEs Using Neural Networks" by Jamie Taylor
| 26 May | 27 May | 28 May | |
| 10.30 to 11.45hr | lecture 1 | lecture 3 | video |
| Coffee break | Coffee break | Coffee break | |
| 12.30 to 13.30hr | lecture 2 | lecture 4 | video |
Speaker: Jamie Taylor [[ ordic.org and researchgate.net ]]
Key Words: Numerical PDEs, Deep Learning, PINNs
Abstract: In recent years, advances in machine learning techniques have begun to make their way into numerical analysis, offering new toolkits for tackling problems arising from partial differential equations (PDEs), with a wealth of new capabilities - and limitations - compared to more classical methods. Whilst many new ideas have been proposed for integrating neural networks (NNs) with PDE methods, the aim of this course is to consider simple test cases to introduce attendees to key concepts underlying such methodologies. In particular, we will focus on the most established methodology: Physics-Informed Neural Networks (PINNs). The three cornerstones of any such implementation are the choice of an appropriate loss function to be minimized, the NN architecture, and the optimization strategy employed, which will be the focus of this course. The course aims to be as self-contained as possible, however, familiarity with classical methods (e.g. FEM) and elementary concepts from data science-based machine learning (e.g. simple NNs, stochastic gradient descent) will be beneficial.
Hands-on material available at github.com/jamie-m-taylor