Physical deep symbolic regression to learn crack tip correction formulas

<p>This repository publishes the data generated in the article "A universal crack tip correction algorithm discovered by physical deep symbolic regression" (see preprint: <a title="arXiv.2403.10320" href="https://doi.org/10.48550/arXiv.2403.10320" target="_blank" rel="noopener">arXiv.2403.10320</a>).</p> <p>This repository is structured with the following subfolders:</p> <ul> <li><strong><em>01_Simulation_Output</em></strong>: The results of the finite element (FE) simulations described in the paper</li> <li><strong><em>02_CrackPy_single_evaluation</em></strong>: For each FE simulation, the fracture analysis results of&nbsp;<a href="https://github.com/dlr-wf/crackpy" target="_blank" rel="noopener">CrackPy</a> performed with the crack tip as origin</li> <li><strong><em>04_CrackPy_random_evaluation_pipeline</em></strong>: For each FE simulation, the fracture analysis is performed at 1000 random perturbations of the crack tip position as origin and the results are stored in the subfolder&nbsp;<em>samples</em></li> <li><strong><em>05_1_PhySO_log_mode_I</em>,<em> 05_2_PhySO_log_mode_II, 05_3_PhySO_log_mixed_mode</em></strong>: These folders contain the logs of three distinct training runs of <a href="https://github.com/WassimTenachi/PhySO" target="_blank" rel="noopener">PhySO</a> - mode I, mode II, and mixed mode. For each of these three load cases, we train symbolic regression models for the x-correction and y-correction separately. The symbolic regression results are stored in the files <em>curves_pareto.csv&nbsp;</em></li> <li><strong><em>06_Pareto_Plots</em></strong>: The visualization of the Pareto front for each training run of PhySO</li> <li><strong><em>07_Plots_vector_fields</em></strong>: The correction vector fields for each discovered Pareto formula</li> <li><strong><em>08_Convergence_study_FEA</em></strong>: The iterative convergence behavior for the FE simulations data</li> <li><strong><em>13_Application</em></strong>: We applied the most promising formulas to experimental DIC data from uniaxial and biaxial fatigue crack growth experiments. The results are contained in this folder.</li> </ul> <p>The code to reproduce these results can be fould on our GitHub page at the following link: <a href="https://github.com/dlr-wf/crack_tip_correction_symbolic_regression" target="_blank" rel="noopener">https://github.com/dlr-wf/crack_tip_correction_symbolic_regression</a></p>