5 papers · 1 filter
An introduction to finite element methods for inverse coefficient problems in elliptic PDEs
Bastian Harrach
Several novel imaging and non-destructive testing technologies are based on reconstructing the spatially dependent coefficient in an elliptic partial differential equation from mea…
Multilevel Monte Carlo learning
Thomas Gerstner, Bastian Harrach, Daniel Roth +1
In this work, we study the approximation of expected values of functional quantities on the solution of a stochastic differential equation (SDE), where we replace the Monte Carlo e…
Convergence of Milstein Brownian bridge Monte Carlo methods and stable Greeks calculation
Thomas Gerstner, Bastian Harrach, Daniel Roth
We consider the pricing and the sensitivity calculation of continuously monitored barrier options. Standard Monte Carlo algorithms work well for pricing these options. Therefore th…
Beyond the Bakushinskii veto: Regularising linear inverse problems without knowing the noise distribution
Bastian Harrach, Tim Jahn, Roland Potthast
This article deals with the solution of linear ill-posed equations in Hilbert spaces. Often, one only has a corrupted measurement of the right hand side at hand and the Bakushinski…
A learning-based method for solving ill-posed nonlinear inverse problems: a simulation study of Lung EIT
Jin Keun Seo, Kang Cheol Kim, Ariungerel Jargal +2
This paper proposes a new approach for solving ill-posed nonlinear inverse problems. For ease of explanation of the proposed approach, we use the example of lung electrical impedan…