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Session Chair: Jörg Schröder, UDE Session Chair: Alexander Schwarz, University of Duisburg-Essen
Location:Auditorium Wolfsburg
Presentations
Neural Networks as Discretization for Full Waveform Inversion
Leon Herrmann, Tim Bürchner, Divya Singh, Stefan Kollmannsberger
Chair of Computational Modeling and Simulation, TUM School of Engineering and Design, Technische Universität München, Germany
Neural networks have recently gained attention in solving inverse problems. One prominent methodology are Physics-Informed Neural Networks (PINNs) which can solve both forward and inverse problems. In this presentation, we consider full waveform inversion as an example of an inverse problem. The performance of PINNs is compared against classical adjoint optimization, focusing on three key aspects: the forward-solver, the neural network Ansatz for the inverse field, and the sensitivity computation for the gradient-based minimization. Starting from PINNs, each of these key aspects is adapted individually until the classical adjoint optimization emerges. It is shown that it is beneficial to use the neural network only for the discretization of the unknown material field, where the neural network produces reconstructions without oscillatory artifacts as typically encountered in classical full waveform inversion approaches. Due to this finding, a hybrid approach is proposed. It exploits both the efficient gradient computation with the continuous adjoint method as well as the neural network Ansatz for the unknown material field. This new hybrid approach outperforms Physics-Informed Neural Networks and the classical adjoint optimization in settings of two and three-dimensional examples [1]. [1] https://arxiv.org/abs/2303.03260
