BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Philipp Grohs (University of Vienna) DTSTART:20210610T130000Z DTEND:20210610T140000Z DTSTAMP:20260423T035925Z UID:SNPDEA/31 DESCRIPTION:Title: Deep Learning in Numerical Analysis\nby Philipp Grohs (University of V ienna) as part of "Partial Differential Equations and Applications" Webina r\n\n\nAbstract\nThe development of new classification and regression algo rithms based on deep neural networks coined Deep Learning have had a drama tic impact in the areas of artificial intelligence\, machine learning\, an d data analysis. More recently\, these methods have been applied successfu lly to the numerical solution of partial differential equations (PDEs). Ho wever\, a rigorous analysis of their potential and limitations is still la rgely open. In this talk we will survey recent results contributing to suc h an analysis. In particular I will present recent empirical and theoretic al results supporting the capability of Deep Learning based methods to bre ak the curse of dimensionality for several high dimensional PDEs\, includi ng nonlinear Black Scholes equations used in computational finance\, Hamil ton Jacobi Bellman equations used in optimal control\, and stationary Schr ödinger equations used in quantum chemistry. Despite these encouraging re sults\, it is still largely unclear for which problem classes a Deep Learn ing based ansatz can be beneficial. To this end I will\, in a second part\ , present recent work establishing fundamental limitations on the computat ional efficiency of Deep Learning based numerical algorithms that\, in par ticular\, confirm a previously empirically observed "theory-to-practice ga p".\n LOCATION:https://researchseminars.org/talk/SNPDEA/31/ END:VEVENT END:VCALENDAR