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GLENN: Neural network-enhanced computation of Ginzburg-Landau energy minimizers
Michael Crocoll, Christian Döding, Benjamin Dörich +1
In this work, we propose a neural network-enhanced finite element strategy to compute the minimizer of the Ginzburg-Landau energy based on an unsupervised deep Ritz-type strategy.…
Complexity bounds on neural networks for the solution of structured linear systems of equations
Benjamin Dörich, Roland Maier, Lukas Ullmer
We derive upper bounds on the complexity of ReLU neural networks approximating the solution of a linear system given the matrix and the right-hand side. We focus on matrices which…
Gautschi-type and implicit-explicit integrators for constrained wave equations
R. Altmann, B. Dörich, C. Zimmer
This paper deals with the construction and analysis of two integrators for (semi-linear) second-order partial differential-algebraic equations of semi-explicit type. More precisely…
Finite element discretization of nonlinear models of ultrasound heating
Julio Careaga, Benjamin Dörich, Vanja Nikolić
Heating generated by high-intensity focused ultrasound waves is central to many emerging medical applications, including non-invasive cancer therapy and targeted drug delivery. In…