On Predicting Material Fracture from Persistence Homology: Or, Which Topological Features Are Informative Covariates?

James Amarel, Nicolas Hengartner, Robyn Miller, Benjamin Migliori, Daniel Hope, Emily Casleton, Alexei Skurikhin, Earl Lawrence, Gerd J. Kunde
Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), PMLR 321:375-388, 2026.

Abstract

We apply topological data analysis to characterize the simulated evolution of cracks in heterogeneous materials. Using persistence homology, we derive covariates for survival analysis, enabling lifetime prediction within a generalized linear modeling framework. Zeroth-homology features alone reproduce the ensemble survival curves of distinct materials, revealing that coarse topological statistics retain predictive signal even when important geometric details are abstracted away. We further compare the predictive capability of neural networks trained directly on damage fields with those trained on persistence-homology-derived representations, finding that the latter achieve superior accuracy. Finally, we investigate patched persistence homology, which encodes local topological information by computing persistence within spatial subdomains. This localized variant bridges global and geometric perspectives, capturing the collective mechanisms that govern fracture and may eventually yield representations better suited to the design and evaluation of fracture emulators.

Cite this Paper

BibTeX
@InProceedings{pmlr-v321-amarel26a, title = {On Predicting Material Fracture from Persistence Homology: Or, Which Topological Features Are Informative Covariates?}, author = {Amarel, James and Hengartner, Nicolas and Miller, Robyn and Migliori, Benjamin and Hope, Daniel and Casleton, Emily and Skurikhin, Alexei and Lawrence, Earl and Kunde, Gerd J.}, booktitle = {Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025)}, pages = {375--388}, year = {2026}, editor = {Bernardez Gil, Guillermo and Black, Mitchell and Cloninger, Alexander and Doster, Timothy and Emerson, Tegan and Garcı́a-Rodondo, Ińes and Holtz, Chester and Kotak, Mit and Kvinge, Henry and Mishne, Gal and Papillon, Mathilde and Pouplin, Alison and Rainey, Katie and Rieck, Bastian and Telyatnikov, Lev and Yeats, Eric and Wang, Qingsong and Wang, Yusu and Wayland, Jeremy}, volume = {321}, series = {Proceedings of Machine Learning Research}, month = {01--02 Dec}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v321/main/assets/amarel26a/amarel26a.pdf}, url = {https://proceedings.mlr.press/v321/amarel26a.html}, abstract = {We apply topological data analysis to characterize the simulated evolution of cracks in heterogeneous materials. Using persistence homology, we derive covariates for survival analysis, enabling lifetime prediction within a generalized linear modeling framework. Zeroth-homology features alone reproduce the ensemble survival curves of distinct materials, revealing that coarse topological statistics retain predictive signal even when important geometric details are abstracted away. We further compare the predictive capability of neural networks trained directly on damage fields with those trained on persistence-homology-derived representations, finding that the latter achieve superior accuracy. Finally, we investigate patched persistence homology, which encodes local topological information by computing persistence within spatial subdomains. This localized variant bridges global and geometric perspectives, capturing the collective mechanisms that govern fracture and may eventually yield representations better suited to the design and evaluation of fracture emulators.} }
Endnote
%0 Conference Paper %T On Predicting Material Fracture from Persistence Homology: Or, Which Topological Features Are Informative Covariates? %A James Amarel %A Nicolas Hengartner %A Robyn Miller %A Benjamin Migliori %A Daniel Hope %A Emily Casleton %A Alexei Skurikhin %A Earl Lawrence %A Gerd J. Kunde %B Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025) %C Proceedings of Machine Learning Research %D 2026 %E Guillermo Bernardez Gil %E Mitchell Black %E Alexander Cloninger %E Timothy Doster %E Tegan Emerson %E Ińes Garcı́a-Rodondo %E Chester Holtz %E Mit Kotak %E Henry Kvinge %E Gal Mishne %E Mathilde Papillon %E Alison Pouplin %E Katie Rainey %E Bastian Rieck %E Lev Telyatnikov %E Eric Yeats %E Qingsong Wang %E Yusu Wang %E Jeremy Wayland %F pmlr-v321-amarel26a %I PMLR %P 375--388 %U https://proceedings.mlr.press/v321/amarel26a.html %V 321 %X We apply topological data analysis to characterize the simulated evolution of cracks in heterogeneous materials. Using persistence homology, we derive covariates for survival analysis, enabling lifetime prediction within a generalized linear modeling framework. Zeroth-homology features alone reproduce the ensemble survival curves of distinct materials, revealing that coarse topological statistics retain predictive signal even when important geometric details are abstracted away. We further compare the predictive capability of neural networks trained directly on damage fields with those trained on persistence-homology-derived representations, finding that the latter achieve superior accuracy. Finally, we investigate patched persistence homology, which encodes local topological information by computing persistence within spatial subdomains. This localized variant bridges global and geometric perspectives, capturing the collective mechanisms that govern fracture and may eventually yield representations better suited to the design and evaluation of fracture emulators.
APA
Amarel, J., Hengartner, N., Miller, R., Migliori, B., Hope, D., Casleton, E., Skurikhin, A., Lawrence, E. & Kunde, G.J.. (2026). On Predicting Material Fracture from Persistence Homology: Or, Which Topological Features Are Informative Covariates?. Proceedings of the 1st Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2025), in Proceedings of Machine Learning Research 321:375-388 Available from https://proceedings.mlr.press/v321/amarel26a.html.

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