Physics-enriched neural solvers for transient ice-flow simulation
Abstract
Transient glacier simulations with higher-order ice flow require the repeated solution of a nonlinear problem as the geometry evolves. In the online mode of the Instructed Glacier Model, the velocity field is represented by a neural network whose weights are warm-started from the previous time step and updated with a few optimizer iterations. We show that supplying the network with inexpensive input fields derived from low-order ice-flow balances improves this online solver. Unlike residual-based physics-informed neural networks, which incorporate physics through governing-equation penalties in the loss, our approach leaves the governing energy objective unchanged, adding physical structure through the network inputs. Across three real-world glacier configurations, the enriched solver is markedly more robust to solver settings. On the two alpine cases, it also improves the tuned accuracy--runtime trade-off, reducing surface-velocity errors by factors of two to four at fixed runtime and reaching few-percent relative errors with only 104--105 trainable parameters, far fewer than comparable raw-input baselines. A 300-year Aletsch simulation then completes in under one minute, and the larger Valais domain in about two minutes, on a single GPU---a budget once reserved for much simpler shallow-ice models. Gains are smaller for the fast marine-terminating glacier, where nonlocal stress coupling favors larger or spectral networks. More broadly, the results suggest that enriching a neural solver's inputs with reduced-order physics can make repeated higher-order solves much cheaper, with no training data and no offline training.
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BibTeX
@misc{gregov2026physicsenriched,
title = {{Physics-enriched neural solvers for transient ice-flow simulation}},
author = {Thomas Gregov and Sebastian Rosier and Brandon Finley and Andreas Vieli and Guillaume Jouvet},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12900},
eprint = {2609.12900},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12900},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Physics-enriched neural solvers for transient ice-flow simulation
AU - Thomas Gregov
AU - Sebastian Rosier
AU - Brandon Finley
AU - Andreas Vieli
AU - Guillaume Jouvet
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.12900
UR - https://arxiv.org/abs/2609.12900
AB - Transient glacier simulations with higher-order ice flow require the repeated solution of a nonlinear problem as the geometry evolves. In the online mode of the Instructed Glacier Model, the velocity field is represented by a neural network whose weights are warm-started from the previous time step and updated with a few optimizer iterations. We show that supplying the network with inexpensive input fields derived from low-order ice-flow balances improves this online solver. Unlike residual-based physics-informed neural networks, which incorporate physics through governing-equation penalties in the loss, our approach leaves the governing energy objective unchanged, adding physical structure through the network inputs. Across three real-world glacier configurations, the enriched solver is markedly more robust to solver settings. On the two alpine cases, it also improves the tuned accuracy--runtime trade-off, reducing surface-velocity errors by factors of two to four at fixed runtime and reaching few-percent relative errors with only 10^4--10^5 trainable parameters, far fewer than comparable raw-input baselines. A 300-year Aletsch simulation then completes in under one minute, and the larger Valais domain in about two minutes, on a single GPU---a budget once reserved for much simpler shallow-ice models. Gains are smaller for the fast marine-terminating glacier, where nonlocal stress coupling favors larger or spectral networks. More broadly, the results suggest that enriching a neural solver's inputs with reduced-order physics can make repeated higher-order solves much cheaper, with no training data and no offline training.
ER -