Meta‐modeling of fractional constitutive relationships for rocks based on physics‐induced machine learning

Abstract

A fractional constitutive meta-model for the mechanical behavior of rocks is proposed to bypass complex integration algorithms and consider the uncertainty of model/material parameters. First, a physics-induced database is constructed with the aid of a fractional constitutive model and two developed input-output strategies. Then three machine algorithms (i.e., random forests, extreme gradient boosting, and multilayer perceptron) together with two input-output strategies are employed to formulate six different meta-models. The grid-search and fivefold cross-validation methods are utilized to optimize key hyperparameters of meta-models. Through the comparisons of evaluation metrics and prediction results, the multilayer perceptron algorithm with strategy II becomes an optimal combination to construct the meta-model. The results of the feature's importance and sensitivity analyses indicate that the parameters' influences in this data-driven paradigm are in line with physical reality. The effectiveness of the proposed meta-model is validated by comparing the predicted results with experimental observations from the literature. Additionally, the uncertainty analyses from the meta-model and material/model parameters can be conducted based on a linear regression model and the Monte Carlo simulation. The study results show that the presented meta-model based on physics-guided synthetic data has the potential to replace the general fractional constitutive model.