Deep learning speeds up ice flow modelling by several orders of magnitude

Abstract

This paper introduces the Instructed Glacier Model (IGM) – a model that simulates ice dynamics, mass balance and its coupling to predict the evolution of glaciers, icefields or ice sheets. The novelty of IGM is that it models the ice flow by a Convolutional Neural Network, which is trained from data generated with hybrid SIA + SSA or Stokes ice flow models. By doing so, the most computationally demanding model component is substituted by a cheap emulator. Once trained with representative data, we demonstrate that IGM permits to model mountain glaciers up to 1000 × faster than Stokes ones on Central Processing Units (CPU) with fidelity levels above 90% in terms of ice flow solutions leading to nearly identical transient thickness evolution. Switching to the GPU often permits additional significant speed-ups, especially when emulating Stokes dynamics or/and modelling at high spatial resolution. IGM is an open-source Python code which deals with two-dimensional (2-D) gridded input and output data. Together with a companion library of trained ice flow emulators, IGM permits user-friendly, highly efficient and mechanically state-of-the-art glacier and icefields simulations.

Inversion of a Stokes glacier flow model emulated by deep learning

“…Following Jouvet and others (2021), our ice flow emulator predicts vertically average and surface horizontal velocity from ice thickness, surface slope and ice flow strength parameter :where input and output are two-dimensional fields, which are defined over the discretized computational domain (or subparts) of size N X × N Y . The above emulator is the one introduced by Jouvet and others (2021) but augmented with the surface velocity in the output variable set as necessary to define a misfit with observations.…”

“…Here, we used the network architecture from Jouvet and others (2021), which was found to be optimal in terms of model fidelity to number of parameters. At training, we minimize the sole L 1 loss function using a stochastic gradient method – the Adam optimizer (Kingma and Ba, 2014) – with a learning rate of 0.0001, a batch size of 64 and 200 epochs (or iterations) to reach convergence.…”

“…On the other hand, the linear dependence in z we imposed is a common feature of mass balance and elevation change of mountain glaciers. However, when observation of the divergence flux is available d obs , we may replace by:Note that the flux divergence is approximated by finite-difference using an upwind first-order scheme similar to the solving of the mass conservation equation in the glacier evolution model (Appendix A, Jouvet and others, 2021).…”

“…The optimization is implemented within the framework of the ‘Instructed Glacier Model’ (IGM, ) (Jouvet and others, 2021), which is a Python open-source code based on the Tensorflow library (), and which can be used for prognostic glacier simulations based on the ice flow emulator (Eqn ). IGM runs both on central and graphics processing units (CPU and GPU).…”

“…The complexity and computational costs of inversion methods for high-order ice flow models (Blatter or Stokes) as well as the lack of observed velocity data hinder their generalization at a large scale and the possibility to optimize several variables simultaneously. In this paper, we take advantage of a new global dataset for surface ice flow speeds (Millan and others, 2022), and present a new method to simultaneously seek ice thickness and basal conditions of valley glaciers by inverting an emulated Stokes ice flow model in form of the convolutional neural network (CNN) proposed by Jouvet and others (2021). Doing so with a CNN emulator instead of a traditional Stokes model has two major advantages (i) automatic differentiation techniques avoid the manual derivation of an adjoint problem and (ii) once trained, CNNs are computationally inexpensive, especially with graphics processing unit (GPU) considerably speeding-up their evaluation.…”