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Published at November 26

Training Hamiltonian neural networks without backpropagation

cs.LG

cs.NA

math.NA

Released Date: November 26, 2024

Authors: Atamert Rahma¹, Chinmay Datar², Felix Dietrich³

Aff.: ¹School of Computation, Information and Technology, Technical University of Munich, Munich, Germany; ²School of Computation, Information and Technology, Technical University of Munich, Munich, Germany; Institute for Advanced Study; ³School of Computation, Information and Technology, Technical University of Munich, Munich, Germany; Munich Data Science Institute

Arxiv: http://arxiv.org/abs/2411.17511v1

	Double pendulum		Hénon-Heiles
Method	Training time (s)	Rel. $L^{2}$ error	Training time (s)	Rel. $L^{2}$ error
HNN	10485.4	3.62E-03	13140.6	6.68E-04
ELM	43.1	5.69E-03	46.0	2.07E-02
U-SWIM	39.6	5.00E-03	41.7	8.22E-08
A-SWIM	85.2	4.08E-03	89.4	6.80E-08
SWIM	40.0	4.18E-03	41.9	6.80E-08