Functional Inversion of Glacier Rheology from Ice Velocities using ODINN.jl

Abstract

Inversion methods play an important
role in glacier models, both to calibrate and estimate parameters of
interest (e.g. Glen's coefficients). 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 Glen’s coefficient (A). Instead
of estimating a single parameter per glacier, we learn the parameters of
a regressor (i.e. a neural network) that encodes information 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. We previously had shown that this hybrid model
training is possible thanks to the use of differential programming,
enabling differentiation of a PDE, a numerical solver and a neural
network simultaneously. In this work we upscale this approach to include
larger datasets and with the goal of learning real empirical laws from
observations.
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 the latest generation of ice surface
velocities and geodetic mass balance remote sensing products, as well as
many preprocessing tools from the Open Global Glacier Model (OGGM).