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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…