Reduction of training computation by network optimization of Integration Neural Network approximator

In constructing approximators for simulations, such as the finite element method using machine learning, there is a conflict between reducing training data generation time and improving approximation accuracy. To solve this problem, we proposed a Hybrid Neural Network and Integration Neural Network as an approximator for simulations with high accuracy, even with a small number of data. This method combines a simple perceptron approximator that mimics multiple regression analysis created based on deductive knowledge (linear approximator) and a neural network approximator created based on inductive knowledge (nonlinear approximator). This combination is based on Weierstrass' approximation theorem. In this study, by applying the approximator theorem one step further, we investigated the reduction of learning computational complexity by simplifying the network structure of the Integration Neural Network and improving the network structure. As a result, we found that approximators with almost the same accuracy can be constructed, and the number of weight updates in the learning process can be reduced to about 5%.