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Convolutional neural networks (CNN) trained from high-order ice-flow model realisations have proven to be outstanding emulators in terms of fidelity and computational performance. However, the dependence on an ensemble of realisations of an instructor model renders this strategy difficult to generalise to a variety of ice-flow regimes found in the nature. To overcome this issue, we adopt the approach of physics-informed deep learning, which fuses traditional numerical solutions by finite differences/elements and deep-learning approaches. Here, we train a CNN to minimise the energy associated with high-order ice-flow equations within the time iterations of a glacier evolution model. As a result, our emulator is a promising alternative to traditional solvers thanks to its high computational efficiency (especially on GPU), its high fidelity to the original model, its simplified training (without requiring any data), its capability to handle a variety of ice-flow regimes and memorise previous solutions, and its relatively simple implementation. Embedded into the ‘Instructed Glacier Model’ (IGM) framework, the potential of the emulator is illustrated with three applications including a large-scale high-resolution (2400x4000) forward glacier evolution model, an inverse modelling case for data assimilation, and an ice shelf.

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.