Recurrent localization networks applied to the Lippmann-Schwinger equation. Kelly, C. & Kalidindi, S. R. Computational Materials Science, 192:110356, May, 2021. ![Recurrent localization networks applied to the Lippmann-Schwinger equation [link]](https://bibbase.org/img/filetypes/link.svg "link")
Paper doi abstract bibtex The bulk of computational approaches for modeling physical systems in materials science derive from either analytical (i.e., physics based) or data-driven (i.e., machine-learning based) origins. In order to combine the strengths of these two approaches, we advance a novel machine learning approach for solving equations of the generalized Lippmann-Schwinger (L-S) type. In this paradigm, a given problem is converted into an equivalent L-S equation and solved as an optimization problem, where the optimization procedure is calibrated to the problem at hand. As part of a learning-based loop unrolling, we use a recurrent convolutional neural network to iteratively solve the governing equations for a field of interest. This architecture leverages the generalizability and computational efficiency of machine learning approaches, but also permits a physics-based interpretation. We demonstrate our learning approach on the two-phase elastic localization problem, where it achieves excellent accuracy on the predictions of the local (i.e., voxel-level) elastic strains. Since numerous governing equations can be converted into an equivalent L-S form, the proposed architecture has potential applications across a range of multiscale materials phenomena.
@article{kelly_recurrent_2021,
title = {Recurrent localization networks applied to the {Lippmann}-{Schwinger} equation},
volume = {192},
issn = {0927-0256},
url = {https://www.sciencedirect.com/science/article/pii/S0927025621000811},
doi = {10.1016/j.commatsci.2021.110356},
abstract = {The bulk of computational approaches for modeling physical systems in materials science derive from either analytical (i.e., physics based) or data-driven (i.e., machine-learning based) origins. In order to combine the strengths of these two approaches, we advance a novel machine learning approach for solving equations of the generalized Lippmann-Schwinger (L-S) type. In this paradigm, a given problem is converted into an equivalent L-S equation and solved as an optimization problem, where the optimization procedure is calibrated to the problem at hand. As part of a learning-based loop unrolling, we use a recurrent convolutional neural network to iteratively solve the governing equations for a field of interest. This architecture leverages the generalizability and computational efficiency of machine learning approaches, but also permits a physics-based interpretation. We demonstrate our learning approach on the two-phase elastic localization problem, where it achieves excellent accuracy on the predictions of the local (i.e., voxel-level) elastic strains. Since numerous governing equations can be converted into an equivalent L-S form, the proposed architecture has potential applications across a range of multiscale materials phenomena.},
language = {en},
urldate = {2023-07-10},
journal = {Computational Materials Science},
author = {Kelly, Conlain and Kalidindi, Surya R.},
month = may,
year = {2021},
keywords = {Convolutional neural networks, Learned optimization, Localization, Machine learning},
pages = {110356},
}
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