Date: Wednesday, February 16, 2022
Location: Zoom Virtual (4:00 PM to 5:00 PM)
Title: Convergence of Deep Solvers for Semilinear PDEs
Abstract: We derive convergence rates for a deep learning algorithm for semilinear partial differential equations which is based on a FeynmanKac representation in terms of an uncoupled forwardbackward stochastic differential equation and a discretization in time of the stochastic equation. We show that the error of the deep learning algorithm is bounded in terms of its loss functional, hence yielding a direct measure to judge the quality of the deep solver in numerical applications, and that the loss functional converges sufficiently fast to zero to guarantee that the error of the deep learning algorithm vanishes in the limit. As a consequence of these results, we argue that the deep solver has a strong convergence rate of order 1/2. The talk is based on joint work with Oliver Hager, Lotte Schnell, Charlotte Reimers (TU Berlin) and Maximilian Würschmidt (Trier University).
Files: 7642_Belak.pdf
Speaker: Christoph Belak
Institution: TU Berlin
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