JuliaCon 2023

Modeling Glacier Ice Flow with Universal Differential Equations
07-26, 11:00–11:30 (US/Eastern), Online talks and posters

We introduce ODINN.jl, an open-source package that uses Universal Differential Equations to model and discover physical processes of climate-glacier interactions. We show how ODINN incorporates tools from the SciML ecosystem (differential equation solvers, automatic differentiation) to recover prescribed laws inside the differential equation describing glacier ice flow, paving the way for functional inversions of empirical laws governing glacier physical processes at a global scale.

Global glacier models attempt to simulate different glacier processes, in order to model the evolution and response to climate change of all 200,000 glaciers on Earth. Calibrating the model parameters with noisy and sparse observations coming mostly from satellite data is a very challenging task. Traditionally, this calibration is usually made at a regional or even global level, or sometimes for each glacier individually if enough data is available. However, no global information is used to derive general laws governing the spatiotemporal variability of those parameters. With the increase of remote sensing derived datasets with a global coverage, new opportunities arise to discover empirical laws describing physical processes of climate-glacier interactions. The main reasons why this is technically difficult to achieve are twofold: (1) the computational cost of modelling massive glacier datasets and solving the differential equations that describe their dynamics; and (2) the statistical challenge of making constrained parameter or functional inversions from real satellite observations covering glaciers in widely diverse climates and topographies. Scientific Machine Learning is a modelling framework that can address both limitations.

We introduce ODINN.jl, an open-source model for global glacier modelling making use of tools from the Scientific Machine Learning Julia ecosystem. ODINN uses Universal Differential Equations (UDEs) to learn subparts of a differential equation governing glacier ice flow. The full code is differentiable using Zygote.jl, which allows gradient-based optimization for the parameters of the neural network embedded inside the differential equation. ODINN exploits the latest generation of glacier ice surface velocities and geodetic mass balance remote sensing products, as well as many preprocessing tools from the Open Global Glacier Model (OGGM) in Python. The retrieval and preprocessing of these datasets is done in ODINN using PyCall.jl to run Python code from OGGM.

We showcase the implementation of a 2D Shallow Ice Approximation for glacier ice dynamics (mathematically equivalent to a 2D heat equation with spatio-temporally dependent diffusivity coefficient) and a temperature-index mass balance model per glacier (i.e. the source). We then show how the model successfully infers parameters of ice rheology based on prescribed synthetic laws. This simple example illustrates the first steps of a new global glacier modelling framework in Julia that allows the estimation of global empirical laws for the physical parameters. Furthermore, the lessons learned on implementing UDEs for stiff nonlinear diffusivity PDEs are applicable to other domains, particularly in Earth sciences where the input data consists of gridded remote sensing products. To conclude, we also discuss some of the main challenges and limitations of the current SciML suite in terms of implementing UDEs for 2D physical processes using real observations.

Work in collaboration with Jordi Bolibar, Redouane Lguensat, Bert Wouters and Fernando Pérez.

PhD Student at UC Berkeley interested in Machine Learning and Physics. Previously studied Physics and Mathematics at the University of Buenos Aires.