Crack detection by holomorphic neural networks and transfer-learning-enhanced genetic optimization

A physics-informed machine learning framework based on holomorphic neural networks is introduced for detecting cracks in two-dimensional solids from strain or displacement data. Crack detection is formulated as an inverse problem in which the crack size, orientation, and location are treated as unknowns. The problem is solved using genetic optimization, where the fitness function is evaluated by expressing the solution of the corresponding plane elasticity problem in terms of holomorphic potentials, which are then determined through the training of two holomorphic neural networks. As the potentials satisfy equilibrium and traction-free conditions along the crack faces a priori, the training proceeds quickly based solely on boundary information. Training efficiency is further improved by splitting the genetic search into long-range and short-range stages, enabling the use of transfer learning in the latter. The new strategy is tested on three benchmark problems, showing that an optimal number of training epochs exists that provides the best overall performance. A comparison is also made with a popular crack detection approach that uses XFEM to compute the model response. Under the assumption of identical stress-field representation accuracy, the proposed method is found to be between 7 and 23 times faster than the XFEM-based approach. Furthermore, the proposed method appears to be less sensitive to noise in the input data. Overall, the present findings demonstrate that combining genetic optimization with holomorphic neural networks and transfer learning offers a promising avenue for developing crack detection strategies with higher efficiency than those currently available. • Crack detection formulated as an inverse problem and solved via genetic optimization. • Fitness evaluated by expressing the elastic solution in terms of complex potentials. • Complex potentials are determined by training two holomorphic neural networks. • Long-range and short-range searches are decoupled to leverage transfer learning. • Approach is 1 order of magnitude faster than common XFEM-based crack detection method.