| Summary: | Reliable projections of sea-level rise depend on accurate representations of how fast-flowing glaciers slip along their beds. The mechanics of slip are often parameterized as a constitutive relation (or "sliding law") whose proper form remains uncertain. Here, we present a novel deep learning-based framework for learning the time evolution of drag at glacier beds from time-dependent ice velocity and elevation observations. We use a feedforward neural network, informed by the governing equations of ice flow, to infer spatially and temporally varying basal drag and associated uncertainties from data. We test the framework on 1D and 2D ice flow simulation outputs and demonstrate the recovery of the underlying basal mechanics under various levels of observational and modeling uncertainties. We apply this framework to time-dependent velocity data for Rutford Ice Stream, Antarctica, and present evidence that ocean-tide-driven changes in subglacial water pressure drive changes in ice flow over the tidal cycle. © 2021 The Authors. Journal of Advances in Modeling Earth Systems published by Wiley Periodicals LLC on behalf of American Geophysical Union. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. Issue Online: 10 November 2021; Version of Record online: 10 November 2021; Accepted manuscript online: 23 September 2021; Manuscript accepted: 17 September 2021; Manuscript revised: 15 September 2021; Manuscript received: 12 May 2021. The authors thank three anonymous reviewers for their constructive feedback for improving the quality of this work. Funding for this work was provided by the Earl A Killian III (1978) and Waidy Lee Fund and the NEC Corporation Fund for Research in Computers and Communications. Computing resources were partially funded through a Microsoft AI For Earth computing grant. The authors declare that they have no competing interests. Data ...
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