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Optimal Dirichlet Boundary Control by Fourier Neural Operators Applied to Nonlinear Optics by Margenberg, Nils; Kärtner, Franz X.; Bause, Markus is a scholarly article available to read on EtoBox.

What is Optimal Dirichlet Boundary Control by Fourier Neural Operators Applied to Nonlinear Optics about?

We present an approach for solving optimal Dirichlet boundary control problems of nonlinear optics by using deep learning. For computing high resolution approximations of the solution to the nonlinear wave model, we propose higher order space-time finite element methods in combination with collocation techniques. Thereby, $C^{l}$-regularity in time of the global discrete is ensured. The resulting simulation data is used to train solution operators that effectively leverage the higher regularity of the training data. The solution operator is represented by Fourier Neural Operators and Gated Recurrent Units and can be used as the forward solver in the optimal Dirichlet boundary control problem. The proposed algorithm is implemented and tested on modern high-performance computing platforms, with a focus on efficiency and scalability. The effectiveness of the approach is demonstrated on the problem of generating Terahertz radiation in periodically poled Lithium Niobate, where the neural network is used as the solver in the optimal control setting to optimize the parametrization of the optical input pulse and maximize the yield of $0.3\,$THz-frequency radiation. We exploit the periodic

Author

Margenberg, Nils; Kärtner, Franz X.; Bause, Markus

Published

2023

Language

EN