Mechanics-informed, model-free symbolic regression framework for solving fracture problems

Data-driven methods have recently been introduced to address complex mechanics problems. While model-based, data-driven approaches are predominantly used, they often fall short of providing generalizable solutions due to their inherent reliance on pre-selected models. Model-free approaches, such as symbolic regression, hold promise for overcoming this limitation by extracting solutions directly from datasets. However, these approaches remain unexplored when dealing with high-dimensional fracture mechanics problems and require significant customization to be effective. In this work, we propose a new symbolic regression framework that integrates mechanics knowledge to enhance the ability to generalize solutions. This framework also includes a model-free variable separation scheme to decouple high-dimensional problems into simpler sub-problems with manageable complexity while preserving data fidelity. We demonstrate the advantages of this framework through two fracture mechanics problems, showing that it can potentially provide generalizable, analytical solutions to novel, easy-to-use fracture testing configurations.