R-adaptivity, deep learning and the deep ritz method
- đ¤ Speaker: Chris Budd (University of Bath) đ Website
- đ Date & Time: Thursday 19 October 2023, 15:00 - 16:00
- đ Venue: Centre for Mathematical Sciences, MR14
Abstract
PINNS (physics informed neural nets) are becoming increasingly popular methods for using deep learning techniques to solve a wide variety of differential equations. They have been advertised as ‘mesh free methods’ which can out perform traditional methods. But how good are they in practice? In this talk I will look at how they compare with traditional techniques such as the finite element method on different types of PDE , linking their performance to that of general nonlinear approximation methods such as Free Knot Splines. I will show that a combination of ‘traditional’ numerical analysis and deep learning can yield good results. But there is still a lot to be learned about the performance and reliability of a PINN based method.
Joint work with Simone Appela, Teo Deveney, and Lisa Kreusser.
Series This talk is part of the Applied and Computational Analysis series.
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Thursday 19 October 2023, 15:00-16:00