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

Abstract

AbstractA 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 five‐fold 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.