On Predicting Material Fracture from Persistent 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

Track: Full Paper (8 pages)

Keywords: Fracture, Persistence Homology

Abstract:

We apply topological data analysis to characterize the simulated evolution of
cracks in heterogeneous materials. Using persistent 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 significant predictive signal even when geometric detail is
abstracted away. We further compare the predictive capability of neural networks trained
directly on damage fields with those trained on persistent homology-derived
representations, finding that the latter achieve superior accuracy. Finally, we investigate
patched persistent 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.

Submission Number: 38