Equation Informed Neural Networks with Bayesian Inference Improvement for the Coefficient Extraction of the Empirical Formulas

Equation-informed neural networks (EINS) method provides an efficient way for the coefficient extraction of the complicated empirical function from large observation data. The Bayesian inference is applied to improve the extraction from a statistical point of view. The empirical material model with multiple coefficients is first converted into a neural network representation, and the aforementioned coefficients are assigned as the weightings of the neural network. The training of this neural network provides a continuous improvement of the weighting.This paper presents the framework of EINS and Bayesian inference. The coefficient extraction of the Chaboche function for the material plasticity of SAC 305 is used as the test scenario for EINS, to investigate its applicability. Moreover, Bayesian inference is realized by the Monte Carlo Markov Chain method (MCMC) with Gibbs sampling to validate the robustness of the coefficients obtained by EINS.