A Machine Learning Approach to Mass-Conserving Ice Thickness Interpolation

The subglacial topography of the Earth's ice sheets is a critical input to models of the evolution of ice sheets and sea level rise. Direct measurements of ice thickness, however, are sparse, necessitating techniques for interpolating these measurements. One class of interpolation methods enforces physical constraints to transform the problem into an inversion. A challenge with these approaches is that multiple unknown parameters must be solved for simultaneously. We introduce a new numerical approach to solving for mass conservation-constrained ice thickness maps. This technique, based on a physics-informed neural network, allows for the flexible incorporation of a range of soft constraints. In the future, this could enable simultaneous estimation of ice velocity, bed topography, and sliding parameters.