4 papers · 1 filter
Extended Walk-on-Spheres Algorithm for Linear and Nonlinear Elliptic Problems of Divergence-type
Iulian Cîmpean, Andreea Grecu, Arghir Zarnescu
The Walk-on-Spheres algorithm, introduced by M. E. Muller in 1956, is a well known Monte Carlo method that leverages Brownian exit distributions from spheres to solve the Laplace e…
A probabilistic approach to spectral analysis of Cauchy-type inverse problems: Convergence and stability analysis
Iulian Cîmpean, Andreea Grecu, Liviu Marin
A comprehensive convergence and stability analysis of some probabilistic numerical methods designed to solve Cauchy-type inverse problems is performed in this study. Such inverse p…
Error analysis for the deep Kolmogorov method
Iulian Cîmpean, Thang Do, Lukas Gonon +2
The deep Kolmogorov method is a simple and popular deep learning based method for approximating solutions of partial differential equations (PDEs) of the Kolmogorov type. In this w…
Numerical spectral analysis of Cauchy-type inverse problems: A probabilistic approach
Iulian Cîmpean, Andreea Grecu, Liviu Marin
We investigate the inverse Cauchy and data completion problems for elliptic partial differential equations in a bounded domain , , with a special e…