1 citations · 1 across the 7 of their papers we have counts for
9 papers
An overview of machine learning-enhanced iterative methods for systems of linear and nonlinear equations
Yuhuang Meng, Jing Zhao, Alexander Heinlein
Systems of equations arise in a wide range of scientific and engineering applications. The present work focuses on solvers for general systems of equations, including but not limit…
Model reduction of port-Hamiltonian systems via neural networks
Silke Glas, Alexander Heinlein, Harald Monsuur +1
In this paper, we consider structure-preserving model reduction of port-Hamiltonian (pH) systems which extend classical Hamiltonian systems with dissipation and an input-output por…
Domain decomposition architectures and Gauss-Newton training for physics-informed neural networks
Alexander Heinlein, Taniya Kapoor
Approximating the solutions of boundary value problems governed by partial differential equations with neural networks is challenging, largely due to the difficult training process…
Resolving Extreme Data Scarcity by Explicit Physics Integration: An Application to Groundwater Heat Transport
Julia Pelzer, Corné Verburg, Alexander Heinlein +1
Real-world flow applications in complex scientific and engineering domains, such as geosciences, challenge classical simulation methods due to large spatial domains, high spatio-te…
Numerical study on hyper parameter settings for neural network approximation to partial differential equations
Hee Jun Yang, Alexander Heinlein, Hyea Hyun Kim
Approximate solutions of partial differential equations (PDEs) obtained by neural networks are highly affected by hyper parameter settings. For instance, the model training strongl…
Overlapping Schwarz Preconditioners for Randomized Neural Networks with Domain Decomposition
Yong Shang, Alexander Heinlein, Siddhartha Mishra +1
Randomized neural networks (RaNNs), in which hidden layers remain fixed after random initialization, provide an efficient alternative for parameter optimization compared to fully p…
PACMANN: Point Adaptive Collocation Method for Artificial Neural Networks
Coen Visser, Alexander Heinlein, Bianca Giovanardi
Physics-Informed Neural Networks (PINNs) have emerged as a tool for approximating the solution of Partial Differential Equations (PDEs) in both forward and inverse problems. PINNs…
High-order discretized ACMS method for the simulation of finite-size two-dimensional photonic crystals
Elena Giammatteo, Alexander Heinlein, Philip Lukas Lederer +1
The computational complexity and efficiency of the approximate mode component synthesis (ACMS) method is investigated for the two-dimensional heterogeneous Helmholtz equations, aim…
Improving Pseudo-Time Stepping Convergence for CFD Simulations With Neural Networks
Anouk Zandbergen, Tycho van Noorden, Alexander Heinlein
Computational fluid dynamics (CFD) simulations of viscous fluids described by the Navier-Stokes equations are considered. Depending on the Reynolds number of the flow, the Navier-S…