Accuracy of Surrogate Solutions of Integral Equations by Feedforward Networks

Deep neural network processing of DEER data

“…An important practical test of correctness, intended to distinguish a neural network that merely fits a few Gaussians to the data set from a network that is a Fredholm solver, would be to present a DEER trace with four distances to a network that was trained on a database with at most three. A network that has learned to be a Fredholm solver in the sense discussed in ( 51 , 52 , 54 , 55 , 57 ) should still return the right answer. As Fig.…”

“…At a more general level, neural network “surrogate” solutions to Fredholm equations are well researched in their own right ( 51 ), with rigorous accuracy bounds available ( 52 , 53 ). In 2013, Jafarian and Nia ( 54 ) proposed a two-layer feedback network built around a Taylor expansion of the solution; Effati and Buzhabadi ( 55 ) published a feedforward network proposition.…”