notesum.ai

Published at November 29

PACMANN: Point Adaptive Collocation Method for Artificial Neural Networks

math.NA

cs.LG

cs.NA

physics.comp-ph

65M22, 68T07, 65M50

Released Date: November 29, 2024

Authors: Coen Visser¹, Alexander Heinlein², Bianca Giovanardi³

Aff.: ¹Faculty of Aerospace Engineering, Delft University of Technology, 2629 HS Delft, The Netherlands; ²Delft Institute of Applied Mathematics, Faculty of Electrical Engineering, Mathematics and Computer; ³Delft Institute for Computational Science and Engineering, Delft University of Technology, 2628 CD, The Netherlands

Arxiv: http://arxiv.org/pdf/2411.19632v1

Sampling method	$L_{2}$ relative error		Mean runtime [s]
Sampling method	Mean	1 SD	Mean runtime [s]
Uniform grid	25.9%	14.2%	425
Hammersley grid	0.61%	0.53%	443
Random resampling	0.40%	0.35%	423
RAR	0.11%	0.05%	450
RAD	0.16%	0.10%	463
RAR-D	0.24%	0.21%	503
*Adam	0.07%	0.05%	461