Machine learning based framework for rapid forecasting of the crack propagation

Motivated by avoiding the high computational cost of the phase field simulations, this paper proposes machine-learning based frameworks to implement the rapid forecasting of crack propagations. Three specific frameworks, namely the framework with dimensionality reduction and series forecasting (DS), the Auto-encoder and LSTM based framework (AL), and the U-net and LSTM based framework (UL), are proposed and examined. The DS provides accurate forecast of training data, but with poor generalization. The main reason is that the DS consists of a 3-step process, dimensionality reduction by principal components analysis (PCA), forecast by long short term memory (LSTM) networks and reconstruction for phase-field images, and the unsupervised dimensionality reduction possesses weak generalization. The AL implements the end-toend forecasting by integrating the Auto-encoder and LSTM in network architecture, which enhances the generalization of the framework. The UL introduces the skip connections of the U-net into the AL to improve the image processing capability. Hence the UL achieves more accurate prediction to the cracks compared with the AL and greater generalization compared with the DS. The phase field evolution is converted into image sequences with phase-field value, and a specific loss function is proposed for phase-field value to strengthen the forecast of crack propagation. By comparing the prediction effects of all frameworks, it can be found that the UL is the optimal framework for its generalization and accurate forecasts, and the proposed loss function improves the accuracy of the prediction. The proposed UL implement the accurate and rapid forecasting of crack propagation, and can be extended to practical engineering issues e.g. fracture and fatigue of composites.