Neural networks can be FLOP-efficient integrators of 1D oscillatory integrands

arXiv:2404.05938v1 Announce Type: new
Abstract: We demonstrate that neural networks can be FLOP-efficient integrators of one-dimensional oscillatory integrands. We train a feed-forward neural network to compute integrals of highly oscillatory 1D functions. The training set is a parametric combination of functions with varying characters and oscillatory behavior degrees. Numerical examples show that these networks are FLOP-efficient for sufficiently oscillatory integrands with an average FLOP gain of 1000 FLOPs. The network calculates oscillatory integrals better than traditional quadrature methods under the …

abstract arxiv behavior characters combination compute cs.ce cs.lg cs.na examples functions math.na network networks neural network neural networks numerical parametric set train training type