ODINN

Mountain glaciers, sea ice and ice sheets are the canary in the coal mine of climate change. They play a critical role on the delicate balance of our planet. Understanding the governing laws of ice masses is critical from both scientific and social perspectives. Furthermore, with the advent of new remote sensing datasets with global coverage (~220.000 mountain glaciers), there is a need for desinging models based on geophysical principles but that can learn from observations.

Machine learning offers a new posibility to learn more complex and empirically accurate laws that underlie ice flow. Automated learning approaches are particularly suited to integrate the vast flood of new remote sensing data, creating feedback between models and data that accurately captures the underlying uncertainties in an interpretable manner. This problem requires statistics, physics, numerical modeling and data engineering infrastructure.

Picture taken from the Malchin Peak in Mongolia in the Altai Mountains, right in the border between Mongolia, Russia and China.

In collaboration with Jordi Bolibar, Fernando Pérez, among others, we work in the development of ODINN.jl, an open-source glacier evolution model in the Julia programming language, Glacier dynamics can be modelled with differential equations, although classical approaches are not suitable for assimilating large spatio-temporal datasets, and they are becoming increasingly harder to optimize. ODINN is based in Universal Differential Equations, a novel approach where learning task can be incorporated inside numerical solvers for differential equations. Parts of the equation (e.g. a parameter) can be learnt by a regressor (e.g. a neural network or a set of basis functions), which provides the model with more flexibility. This model is built on top of the Open Global Glacier Model (OGGM) in Python, one of the most popular frameworks for large-scale glacier modelling. Our final goal is to calibrate and validate this glacier evolution model with remote sensing data and climate reanalyses in order to understand past glacier changes and the role played by ice dynamics and mass balance.

Diagram of the workflow in ODINN.

Some of the features of ODINN are

Efficient implementetion of the 2D SIA equation for mountain glaciers
Implemented differential programming toold in the Julia SciML ecosystem that allows to compute gradients in the numerical solver for the 2D SIA equation
Python-Julia integration via PyCall.jl that allow us to run libraries like Xarray and OGGM inside ODINN

Some ongoing work in progress

Writing of review paper about sensitivity methods for differential equations, that is, the differential programming capabilities that enable all the workflow inside ODINN.

Geoscientific models are facing increasing challenges to exploit growing datasets coming from remote sensing. Universal Differential Equations (UDEs), aided by differentiable programming, provide a new scientific modelling paradigm enabling both complex functional inversions to potentially discover new physical laws and data assimilation from heterogeneous and sparse observations. We demonstrate an application of UDEs as a proof of concept to learn the creep component of ice flow, i.e. a nonlinear diffusivity differential equation, of a glacier evolution model. By combining a mechanistic model based on a 2D Shallow Ice Approximation Partial Differential Equation with an embedded neural network, i.e. a UDE, we can learn parts of an equation as nonlinear functions that then can be translated into mathematical expressions. We implemented this modelling framework as ODINN.jl, a package in the Julia programming language, providing high performance, source-to-source automatic differentiation (AD) and seamless integration with tools and global datasets from the Open Global Glacier Model in Python. We demonstrate this concept for 17 different glaciers around the world, for which we successfully recover a prescribed artificial law describing ice creep variability by solving ca 500,000 Ordinary Differential Equations in parallel. Furthermore, we investigate which are the best tools in the scientific machine learning ecosystem in Julia to differentiate and optimize large nonlinear diffusivity UDEs. This study represents a proof of concept for a new modelling framework aiming at discovering empirical laws for large-scale glacier processes, such as the variability of ice creep and basal sliding for ice flow, and new hybrid surface mass balance models.

References

2023