Inferring constitutive forces from noisy Allen-Cahn movies with moment equations
Abstract
Inferring an Allen-Cahn constitutive force from images requires more than an accurate optimizer: nonlinear observation noise alters the mean of force features, shared noise couples instruments to the response, and a temporal balance borrowed from another solver can remain biased even on clean data. We develop observation-aware, noise-adjusted moment equations that address these effects before inversion. The surface-tension-calibrated constitutive transformer (SCCT) couples the resulting moments to a positive Bernstein inverse and can adapt its prior and precision from images and moments. A conditional stability bound separates moment residuals from prior error. Synthetic tests show that correcting the estimating equation matters more than increasing regularizer flexibility; the benefit of learned adaptation is smaller and depends on the training comparison. Forces inferred from planar movies predict unseen planar and three-dimensional evolutions. A ring-cage breakup shows why diffuse-interface accuracy distinguishes forces even when their topological predictions agree, while external surface tension sets the energy scale separately.
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BibTeX
@misc{jung2026inferring,
title = {{Inferring constitutive forces from noisy Allen-Cahn movies with moment equations}},
author = {Soobeen Jung and Hyunju Kim},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02672},
eprint = {2610.02672},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02672},
}
RIS
TY - UNPB
TI - Inferring constitutive forces from noisy Allen-Cahn movies with moment equations
AU - Soobeen Jung
AU - Hyunju Kim
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.02672
UR - https://arxiv.org/abs/2610.02672
AB - Inferring an Allen-Cahn constitutive force from images requires more than an accurate optimizer: nonlinear observation noise alters the mean of force features, shared noise couples instruments to the response, and a temporal balance borrowed from another solver can remain biased even on clean data. We develop observation-aware, noise-adjusted moment equations that address these effects before inversion. The surface-tension-calibrated constitutive transformer (SCCT) couples the resulting moments to a positive Bernstein inverse and can adapt its prior and precision from images and moments. A conditional stability bound separates moment residuals from prior error. Synthetic tests show that correcting the estimating equation matters more than increasing regularizer flexibility; the benefit of learned adaptation is smaller and depends on the training comparison. Forces inferred from planar movies predict unseen planar and three-dimensional evolutions. A ring-cage breakup shows why diffuse-interface accuracy distinguishes forces even when their topological predictions agree, while external surface tension sets the energy scale separately.
ER -