Fracture-Bench: A Controlled Benchmark Suite for Machine Learning Surrogates in Phase-Field Fracture Mechanics
Abstract
Machine-learning surrogates are increasingly proposed to replace phase-field fracture simulations in many-query tasks such as uncertainty quantification, inverse analysis and design. Little controlled evidence shows which architectures are reliable, for which fracture problems and how far beyond their training data. We introduce Fracture-Bench, an open benchmark of two phase-field datasets with fixed splits, common test metrics and a description of each dataset's physical regime. Dataset~1 contains 1,000 AT2 simulations of multiple cracks growing from a notched hole in a hyperelastic plate under random non-uniform biaxial boundary displacements (44 load steps, 128×128 grid). Dataset~2 contains 4,000 PF-CZM simulations of a pre-cracked plate with two inclusions, each ten times stiffer or more compliant than the matrix (128×256 grid). We train a Fourier neural operator (FNO), DeepONet, Latent DeepONet, a UNet and a conditional diffusion model on identical splits and compare one test metric per dataset, training time, inference time and model size. On Dataset~1, FNO and Latent DeepONet attain mean test errors of order 10−6, about ten times lower than UNet and DeepONet. On Dataset~2, the diffusion model is most accurate, with about one sixth of the UNet error, but requires \SI{706}{s} per prediction versus \SI{6}{ms} for UNet. For all architectures, most of the error occurs in the final load steps, after crack localization. Dataset~2 contains initial cracks less than one grid cell apart that produce qualitatively different paths. Architecture rankings therefore depend on the task, and errors averaged over densely sampled inputs reveal little about near-bifurcation cases. Data, codes, splits, regime descriptors and generalization splits are public, with a protocol for adding under-represented regimes such as mixed-mode, three-dimensional and experimentally paired fracture.
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BibTeX
@misc{krishnan2026fracturebench,
title = {{Fracture-Bench: A Controlled Benchmark Suite for Machine Learning Surrogates in Phase-Field Fracture Mechanics}},
author = {Meenu Krishnan U. and Maryam Hakimzadeh and Indrashish Saha and Meer Mehran Rashid and Lori Graham-Brady and Somdatta Goswami},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03473},
eprint = {2611.03473},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03473},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fracture-Bench: A Controlled Benchmark Suite for Machine Learning Surrogates in Phase-Field Fracture Mechanics
AU - Meenu Krishnan U.
AU - Maryam Hakimzadeh
AU - Indrashish Saha
AU - Meer Mehran Rashid
AU - Lori Graham-Brady
AU - Somdatta Goswami
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03473
UR - https://arxiv.org/abs/2611.03473
AB - Machine-learning surrogates are increasingly proposed to replace phase-field fracture simulations in many-query tasks such as uncertainty quantification, inverse analysis and design. Little controlled evidence shows which architectures are reliable, for which fracture problems and how far beyond their training data. We introduce Fracture-Bench, an open benchmark of two phase-field datasets with fixed splits, common test metrics and a description of each dataset's physical regime. Dataset~1 contains 1,000 AT2 simulations of multiple cracks growing from a notched hole in a hyperelastic plate under random non-uniform biaxial boundary displacements (44 load steps, 128×128 grid). Dataset~2 contains 4,000 PF-CZM simulations of a pre-cracked plate with two inclusions, each ten times stiffer or more compliant than the matrix (128×256 grid). We train a Fourier neural operator (FNO), DeepONet, Latent DeepONet, a UNet and a conditional diffusion model on identical splits and compare one test metric per dataset, training time, inference time and model size. On Dataset~1, FNO and Latent DeepONet attain mean test errors of order 10^−6, about ten times lower than UNet and DeepONet. On Dataset~2, the diffusion model is most accurate, with about one sixth of the UNet error, but requires \SI{706}{s} per prediction versus \SI{6}{ms} for UNet. For all architectures, most of the error occurs in the final load steps, after crack localization. Dataset~2 contains initial cracks less than one grid cell apart that produce qualitatively different paths. Architecture rankings therefore depend on the task, and errors averaged over densely sampled inputs reveal little about near-bifurcation cases. Data, codes, splits, regime descriptors and generalization splits are public, with a protocol for adding under-represented regimes such as mixed-mode, three-dimensional and experimentally paired fracture.
ER -