- Series
- Stochastics Seminar
- Time
- Thursday, November 10, 2022 - 3:30pm for 1 hour (actually 50 minutes)
- Location
- ONLINE
- Speaker
- Ionel Popescu – University of Bucharest and Simion Stoilow Institute of Mathematics – ioionel@gmail.com – https://sites.google.com/site/ioionel/home
- Organizer
- Mayya Zhilova
Zoom link to the seminar: https://gatech.zoom.us/j/91330848866
I will show how to construct a numerical scheme for solutions to linear Dirichlet-Poisson boundary problems which does not suffer of the curse of dimensionality. In fact we show that as the dimension increases, the complexity of this scheme increases only (low degree) polynomially with the dimension. The key is a subtle use of walk on spheres combined with a concentration inequality. As a byproduct we show that this result has a simple consequence in terms of neural networks for the approximation of the solution. This is joint work with Iulian Cimpean, Arghir Zarnescu, Lucian Beznea and Oana Lupascu.