Physics inputs speed up glacier flow simulations on single GPUs
Physics-enriched neural solvers for transient ice-flow simulation
Machine Learning
Summary
Glacier flow simulations can be very slow because they require solving complex physics equations repeatedly as the glacier shape changes. The authors improved a neural network-based solver by giving it simple physics-based hints as inputs, which helps the network solve these equations faster and more accurately without needing extra training data. Their method runs fast enough to simulate hundreds of years of glacier movement in just minutes using a single GPU. This work shows a way to make advanced glacier models much more efficient for real-world use.
What this means in practice
- •For climate modelers: Run faster and more accurate glacier flow models to improve predictions of ice dynamics and melt impacts within climate simulations.
- •For earth system model developers: Integrate efficient neural solvers using physics-informed inputs to reduce computational cost of glacier components in large-scale Earth system models.
Authors
Thomas Gregov, Sebastian Rosier, Brandon Finley, Andreas Vieli, Guillaume Jouvet
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 $10^4$--$10^5$ 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.