Jordi Bolibar - Universal Differential Equations for glacier ice flow modelling using ODINN.jl

Inversion methods play an important role in glacier models, both to calibrate and estimate parameters of interest (e.g. rheology coefficients or basal sliding). However, inversions are usually made for each glacier individually, without using any global information, i.e. without deriving general laws governing the spatiotemporal variability of those parameters. The reason behind this limitation is twofold: the statistical challenge of making constrained inferences with multiple glaciers, and the computational limitation of processing massive glacier datasets. Machine learning powered with differential programming is a tool that can address both limitations. We introduce a statistical framework for functional inversion of physical processes governing global-scale glacier changes. We apply this framework to invert a prescribed function describing the spatial variability of ice rheology. Instead of estimating a single parameter per glacier, we learn the parameters of a regressor (i.e. a neural network) that encode information of a proxy related to each glacier (i.e. long-term air temperature) to the parameter of interest. The inversion is done by embedding a neural network inside the Shallow Ice Approximation PDE - resulting in a Universal Differential Equation - with the goal of minimizing the error on the simulated ice surface velocities. This framework is built inside ODINN.jl, an open-source package in the Julia programming language for global glacier evolution modelling using Universal Differential Equations. ODINN exploits Julia’s automatic differentiation capabilities, as well as a seamless communication with Python libraries, such as the Open Global Glacier Model (OGGM) or xarray.