抄録
Simulation-based optimization often requires many simulations, which can be challenging to adapt due to time constraints. To address this issue, constructing approximators for simulations, such as the finite element method using machine learning, has gained attention. However, constructing these approximators requires a significant amount of training data. For this problem, we proposed an integration neural network as a highly accurate approximator with small data. Our method is based on Weierstrass’ approximation theorem, which uses a polynomial approximation. We constructed the integration neural network by integrating a linear approximator, which uses deductive knowledge to constrain the shape of the approximation curve between training points through multiple regression analysis, with a nonlinear approximator, which uses inductive learning to reduce overlearning of the linear approximator and correct errors. In this paper, by applying the approximator theorem one step further, we reduced the computational complexity of the learning process by simplifying and improving the network structure. Our experiments show that we can construct approximators with almost the same accuracy as previous methods while reducing the number of weight updates in the learning process to about 5%. Furthermore, by analyzing the weights of the approximators, we confirmed that the basic concept drove and that the improved integration neural network could learn with appropriate weights.
