Special CMX Seminar

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 approximation methods using free knot splines and carefully chosen collocation points. 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, Lisa Kreusser, and Carola Schoenlieb