Department Mathematik
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Mathematisches Kolloquium


Am Donnerstag, 24. Juni 2021, um 16:30 Uhr spricht

Philipp Grohs
(Uni Wien )

im Zoom Meeting über das Thema

Deep Learning in Numerical Analysis

Abstract: The development of new classification and regression algorithms based on deep neural networks
coined Deep Learning have had a dramatic impact in the areas of artificial intelligence, machine learning, and
data analysis. More recently, these methods have been applied successfully to the numerical solution of partial
differential equations (PDEs). However, a rigorous analysis of their potential and limitations is still largely open.
In this talk we will survey recent results contributing to such an analysis.In particular I will present recent
empirical and theoretical results supporting the capability of Deep Learning based methods to break the curse
of dimensionality for several high dimensional PDEs,including nonlinear Black Scholes equations used in
computational finance, Hamilton Jacobi Bellman equations used in optimal control, and stationary Schrödinger
equations used in quantum chemistry. Despite these encouraging results, it is still largely unclear for which
problem classes a Deep Learning based ansatz can be beneficial. To this end I will, in a second part,present
recent work establishing fundamental limitations on the computational efficiency of Deep Learning based
numerical algorithms that, in particular, confirm a previously empirically observed "theory-to-practice gap".

Join Zoom Meeting: https://lmu-munich.zoom.us/j/99946902916?pwd=UWM5SGtIL091NmdjU3BHVVpOU0lEdz09 Meeting ID: 999 4690 2916
Passcode: 695211