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Goal oriented error estimation for adaptive sampling of PINNS
Medard Govoeyi, Thomas Richter
Physics-Informed Neural Networks (PINNs) are mesh-free approaches for the numerical approximation of partial differential equations, where a neural network is trained by minimizing…
Error analysis for hybrid finite element/neural network discretizations
Uladzislau Kapustsin, Utku Kaya, Johannes Pfefferer +1
We describe and analyze a hybrid finite element/neural network method for predicting solutions of partial differential equations. The methodology is designed for obtaining fine sca…
An adaptive finite element multigrid solver using GPU acceleration
Manuel Liebchen, Robert Jendersie, Utku Kaya +2
Adaptive finite elements combined with geometric multigrid solvers are one of the most efficient numerical methods for problems such as the instationary Navier-Stokes equations. Ye…
Application of a Temporal Multiscale Method for Efficient Simulation of Degradation in PEM Water Electrolysis under Dynamic Operation
Dayron Chang Dominguez, An Phuc Dam, Thomas Richter +2
Hydrogen is vital for sectors like chemicals and others, driven by the need to reduce carbon emissions. Proton Electrolyte Membrane Water Electrolysis (PEMWE) is a key technology f…
Error analysis of a pressure correction method with explicit time stepping
Utku Kaya, Thomas Richter
The pressure-correction method is a well established approach for simulating unsteady, incompressible fluids. It is well-known that implicit discretization of the time derivative i…