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.

中文翻译：

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用于解决断裂问题的力学信息、无模型的符号回归框架


最近引入了数据驱动的方法来解决复杂的力学问题。虽然主要使用基于模型的数据驱动方法，但由于它们固有地依赖于预先选择的模型，因此它们通常无法提供可推广的解决方案。无模型方法（例如符号回归）有望通过直接从数据集中提取解决方案来克服这一限制。然而，在处理高维断裂力学问题时，这些方法仍未得到探索，需要大量定制才能有效。在这项工作中，我们提出了一个新的符号回归框架，该框架整合了力学知识，以增强泛化解的能力。该框架还包括一个无模型的变量分离方案，用于将高维问题解耦为更简单的子问题，这些子问题具有可管理的复杂性，同时保持数据保真度。我们通过两个断裂力学问题展示了该框架的优势，表明它有可能为新颖、易于使用的断裂测试配置提供通用的分析解决方案。