nonlinear

Overcoming the curse of dimensionality: from nonlinear Monte Carlo to deep learning

Arnulf Jentzen, Professor, Applied Mathematics Münster: Institute for Analysis and Numerics, University of Münster

Jan 10, 14:00 - 15:00

KAUST

nonlinear Deep learning monte carlo algorithms

In this talk we prove that suitable deep neural network approximations do indeed overcome the curse of dimensionality in the case of a general class of semilinear parabolic PDEs and we thereby prove, for the first time, that a general semilinear parabolic PDE can be solved approximatively without the curse of dimensionality.

On some nonlinear elliptic/parabolic systems arising in mechanics and turbulence

Prof. Luigi Carlo Berselli

May 9, 16:00 - 17:00

B2 L5 R5220

nonlinear linear elliptic parabolic Systems Mechanics Turbulence

I consider the vector counterpart of the classical p-Laplace and p-heat equations which are some of the building blocks for the mathematical description of non-linear plasticity, non-Newtonian fluids, and turbulent eddy viscosity models. I will discuss results of “natural regularity” and their role in the study of the well-posedness of the nonlinear pdes as well as in the theory of convergence for space-time discretisation methods. In particular, I will present the “A-approximation" method which generalises results by Necas and which reduces the problem to a family of linear ones. Coffee Time: 15:30 - 16:00