Zobrazeno 1 - 10
of 5 023
pro vyhledávání: '"Heinlein A"'
The computational complexity and efficiency of the approximate mode component synthesis (ACMS) method is investigated for the two-dimensional heterogeneous Helmholtz equations, aiming at the simulation of large but finite-size photonic crystals. The
Externí odkaz:
http://arxiv.org/abs/2410.07723
We enhance machine learning algorithms for learning model parameters in complex systems represented by ordinary differential equations (ODEs) with domain decomposition methods. The study evaluates the performance of two approaches, namely (vanilla) P
Externí odkaz:
http://arxiv.org/abs/2410.01599
Chance constraints ensure the satisfaction of constraints under uncertainty with a desired probability. This scheme is unfortunately sensitive to assumptions of the probability distribution of the uncertainty, which are difficult to verify. The uncer
Externí odkaz:
http://arxiv.org/abs/2409.01177
Robust model predictive control algorithms are essential for addressing unavoidable errors due to the uncertainty in predicting real-world systems. However, the formulation of such algorithms typically results in a trade-off between conservatism and
Externí odkaz:
http://arxiv.org/abs/2408.17348
This study presents a two-level Deep Domain Decomposition Method (Deep-DDM) augmented with a coarse-level network for solving boundary value problems using physics-informed neural networks (PINNs). The addition of the coarse level network improves sc
Externí odkaz:
http://arxiv.org/abs/2408.12198
Federated Learning presents a way to revolutionize AI applications by eliminating the necessity for data sharing. Yet, research has shown that information can still be extracted during training, making additional privacy-preserving measures such as d
Externí odkaz:
http://arxiv.org/abs/2408.08666
The two-level overlapping additive Schwarz method offers a robust and scalable preconditioner for various linear systems resulting from elliptic problems. One of the key to these properties is the construction of the coarse space used to solve a glob
Externí odkaz:
http://arxiv.org/abs/2408.08187
Coarse Spaces Based on Higher-Order Interpolation for Schwarz Preconditioners for Helmholtz Problems
The development of scalable and wavenumber-robust iterative solvers for Helmholtz problems is challenging but also relevant for various application fields. In this work, two-level Schwarz domain decomposition preconditioners are enhanced by coarse sp
Externí odkaz:
http://arxiv.org/abs/2408.03571
The segmentation of ultra-high resolution images poses challenges such as loss of spatial information or computational inefficiency. In this work, a novel approach that combines encoder-decoder architectures with domain decomposition strategies to ad
Externí odkaz:
http://arxiv.org/abs/2407.21266
Kolmogorov-Arnold networks (KANs) have attracted attention recently as an alternative to multilayer perceptrons (MLPs) for scientific machine learning. However, KANs can be expensive to train, even for relatively small networks. Inspired by finite ba
Externí odkaz:
http://arxiv.org/abs/2406.19662