27 citations · 67 across the 13 of their papers we have counts for
15 papers
A hybrid physics-informed neural network based multiscale solver as a partial differential equation constrained optimization problem
Michael Hintermüller, Denis Korolev
In this work, we study physics-informed neural networks (PINNs) constrained by partial differential equations (PDEs) and their application in approximating PDEs with two characteri…
Optimal boundary control of the isothermal semilinear Euler equation for gas dynamics on a network
Marcelo Bongarti, Michael Hintermüller
The analysis and boundary optimal control of the nonlinear transport of gas on a network of pipelines is considered. The evolution of the gas distribution on a given pipe is modele…
Risk-averse optimal control of random elliptic variational inequalities
Amal Alphonse, Caroline Geiersbach, Michael Hintermüller +1
We consider a risk-averse optimal control problem governed by an elliptic variational inequality (VI) subject to random inputs. By deriving KKT-type optimality conditions for a pen…
Optimality Conditions and Moreau--Yosida Regularization for Almost Sure State Constraints
Caroline Geiersbach, Michael Hintermüller
We analyze a potentially risk-averse convex stochastic optimization problem, where the control is deterministic and the state is a Banach-valued essentially bounded random variable…
Dualization and Automatic Distributed Parameter Selection of Total Generalized Variation via Bilevel Optimization
Michael Hintermüller, Kostas Papafitsoros, Carlos N. Rautenberg +1
Total Generalized Variation (TGV) regularization in image reconstruction relies on an infimal convolution type combination of generalized first- and second-order derivatives. This…
Existence, iteration procedures and directional differentiability for parabolic QVIs
Amal Alphonse, Michael Hintermüller, Carlos N. Rautenberg
We study parabolic quasi-variational inequalities (QVIs) of obstacle type. Under appropriate assumptions on the obstacle mapping, we prove the existence of solutions of such QVIs b…