Seminar| Institute of Mathematical Sciences
Time：Friday, September 16th, 2022, 15:30-16:45
Location：R408, IMS; Online, Zoom
Speaker: Ariel Neufeld, NTU Singapore
Abstract: In this talk, we first present a deep-learning based algorithm which can solve nonlinear parabolic PDEs in up to 10’000 dimensions with short run times, and apply it to price high-dimensional financial derivatives under default risk.
Then, we discuss a general problem when training neural networks, namely that it typically involves non-convex stochastic optimization.
To that end, we present TUSLA, a gradient descent type algorithm (or more precisely : stochastic gradient Langevin dynamics algorithm) for which we can prove that it can solve non-convex stochastic optimization problems involving ReLU neural networks.
This talk is based on joint works with C. Beck, S. Becker, P. Cheridito, A. Jentzen, and D.-Y. Lim, S. Sabanis, Y. Zhang, respectively.
Zoom Meeting Link: https://us06web.zoom.us/j/2044972880
Password: 2044972880