Comparison of Machine Learning and gPC-based proxy solutions for an efficient Bayesian identification of fracture parameters

Fracture parameters play an important role in accurately simulating fracture propagation phenomena, which are highly nonlinear and sensitive to various parameters. The main focus of this paper is to offer different proxy modeling techniques to enable the otherwise computationally extremely expensive Bayesian identification procedure performed with Markov Chain Monte Carlo method. The paper contrasts polynomial chaos methods with machine learning techniques, including deep neural networks, in identification of uncertain fracture parameters. In addition, the application of autoencoders to push the stochastic process of deformations to low-dimensional representation is also analyzed. Two fracture scenarios are proposed for parameter identification: the hole tension test and the four point bending test. The 2D fracture propagation model is based on embedded strong discontinuity method, efficiently capturing complex failure mechanisms in modes I and II. The provided results show the successful identification of fracture parameters, including tensile and shear strength, as well as tensile and shear fracture energy using the different proxy modeling techniques and give explanations on the advantages and disadvantages of using different methods.