Confirmation of driving principle by weight analysis of Integration Neural Network and extension of deductive approximator

Simulation-based optimization often requires many simulations and can be difficult to adapt due to time constraints. To solve this problem, constructing approximators for simulations, such as the finite element method using machine learning, has attracted attention. However, creating these approximators requires a huge amount of training data. Therefore, we propose an integral neural network to construct highly accurate approximators with a small amount of data. The integral neural network is a linear approximator using deductive knowledge that constrains the shape of the approximate curve between learning points by multiple regression analysis in which the basis function is determined by deductive information and an inductive learning method that suppresses overlearning of the linear approximator by compensating factors that are not expressed in the basis function by deductive information of the linear approximator. The nonlinear approximator with inductive learning is integrated with the linear approximator by compensating for the influence of factors that cannot be formulated. In this paper, to apply this method to constructing approximators for thermal analysis of power devices, we extended the method to models other than multiple regression analysis for deductive information and constructed approximators. We showed that they can be approximated with high accuracy even by nontraditional models.