Inferring flow law of ice shelves using physics-informed neural networks

Ice shelves are thin films of gravity current floating above sea water. While the nonlinear rheology (e.g. flow law) of ice is measurable with laboratory experiments. The well-known lab-measurement-based model of ice rheology, Glen's law, has been applied to ice sheet models for decades. Yet this flow law doesn't capture processes occurring at much larger time scales such as decades and over long distances such as thousands of kilometers. Here we use physics-informed neural networks to infer ice rheology from the real data of ice velocity, thickness, and surface height. Neural network has been proved as a universal function approximator. Leveraging this property with automatic differentiation and gradient descent optimization, physics-informed neural networks (PINNs) was developed to include physical equations into loss function as an additional constraint to train the neural network to approximate the solution of the equations, as well as be able to infer unknown physical quantities in the equation from given data sets. We demonstrate PINNs' ability to infer the flow law of ice with an idealized example, and explore its robustness against noisy and sparse datasets. Our finding can be extended to identify the flow law of observational data.