22-24 September 2021
Alpen-Adria-Universität Klagenfurt
Europe/Vienna timezone

Parameter identification for PDEs: From neural-network-based learning to discretized inverse problems

22 Sep 2021, 16:10
HS 1 (Alpen-Adria-Universität Klagenfurt)

HS 1

Alpen-Adria-Universität Klagenfurt


Tram Nguyen


We investigate the problem of learning an unknown nonlinearity in parameter-dependent PDEs. The nonlineartiy is represented via a neural network of an unknown state. The learning-informed PDE model has three unknowns: physical parameter, state and nonlinearity. We propose an all-at-once approach to the minimization problem. (Joint work: Martin Holler, Christian Aarset)
More generally, the representation via neural networks can be realized as a discretization scheme. We study convergence of Tikhonov and Landweber methods for the discretized inverse problems, and prove convergence when the discretization error approaches zero. (Joint work: Barbara Kaltenbacher)

Primary authors

Tram Nguyen Barbara Kaltenbacher (MATH) Prof. Martin Holler (University of Graz) Christian Aarset (University of Graz)

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