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R-adaptivity, deep learning and the deep ritz method

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If you have a question about this talk, please contact Nicolas Boulle.

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.

This talk is part of the Applied and Computational Analysis series.

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