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.

中文翻译：

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使用基于物理的神经网络对沿冰川床滑动力学的数据驱动推理：南极洲拉特福德冰流的案例研究

海平面上升的可靠预测取决于对快速流动的冰川如何沿着它们的床滑动的准确表示。滑动力学通常被参数化为一个本构关系（或“滑动定律”），其正确形式仍然不确定。在这里，我们提出了一种新的基于深度学习的框架，用于从与时间相关的冰速和海拔观测中学习冰川床阻力的时间演变。我们使用前馈神经网络，根据冰流的控制方程，从数据中推断时空变化的基础阻力和相关的不确定性。我们在 1D 和 2D 冰流模拟输出上测试了框架，并证明了在不同水平的观测和建模不确定性下底层基础力学的恢复。