Genetic programming-based symbolic regression (GPSR) is a machine learning method which produces symbolic models that can be readily interpreted. This study utilized GPSR to derive uniaxial texture-based constitutive models for an additively manufactured alloy which were evaluated in post hoc analyses. Training data consisted of microscopy and mechanical testing data provided by the Air Force Research Laboratory (AFRL) which was supplemented using a viscoplastic model calibrated to the observed data. The validity of the calibrated crystal plasticity viscoplastic model is demonstrated as part of the 2019 AFRL Additive Manufacturing Modeling Challenge Series. Additionally, an expression evaluator was developed to integrate the constitutive models into the topology optimization software package Plato. A significant aspect of this paper is the presentation of these topics as components within a highly automated framework that allows efficient incorporation of microstructural characteristics into design activities. A topology optimization example was conducted using the GPSR results that constitutes application of the automated framework and post hoc analyses of the GPSR models demonstrate interpretability, suitability, and a probabilistic method to quantify domain bounds.
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The authors acknowledge Sandia National Laboratories, a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the US Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. The support and resources from the Center for High Performance Computing at the University of Utah are gratefully acknowledged. The authors also recognize the developers of Bingo, Dr. Geoff Bomarito and Dr. Patrick Lesser, for their contributions and support. The efforts which contributed to data collection and organization of the challenge are gratefully appreciated. Professor A. Rollett acknowledges support from US Department of Energy, Office of Science, Basic Energy Sciences, under Award # DE-SC0019096.
Conflict of Interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.
Appendix 1: Genetic Programming-Based Symbolic Regression Hyper-Parameter Summary
Appendix 1: Genetic Programming-Based Symbolic Regression Hyper-Parameter Summary
See Table 2.
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Garbrecht, K., Aguilo, M., Sanderson, A. et al. Interpretable Machine Learning for Texture-Dependent Constitutive Models with Automatic Code Generation for Topological Optimization. Integr Mater Manuf Innov 10, 373–392 (2021). https://doi.org/10.1007/s40192-021-00231-6
- Symbolic regression
- Constitutive model
- Topology optimization
- Parameter homogenization