For a detailed description of the model and the application of Universal Differential Equations to glacier ice flow modelling, take a look at our recent publication at Geoscientific Model Development.

Global glacier model using Universal Differential Equations to model and discover processes of climate-glacier interactions.

ODINN.jl uses neural networks and differential equations in order to combine mechanistic models describing glacier physical processes (e.g. ice creep, basal sliding, surface mass balance) with machine learning. Neural networks are used to learn parts of the equations, which then can be interpreted in a mathematical form (e.g. using SINDy) in order to update the original equation from the process. ODINN uses the Open Global Glacier Model (OGGM, Maussion et al., 2019) as a basic framework to retrieve all the topographical and climate data for the initial state of the simulations. This is done calling Python from Julia using PyCall. Then, all the simulations and processing are performed in Julia, benefitting from its high performance and the SciML ecosystem.

Overview of ODINN.jl’s workflow to perform functional inversions of glacier physical processes using Universal Differential Equations. The parameters ($θ$) of a function determining a given physical process ($D_θ$), expressed by a neural network $NN_θ$, are optimized in order to minimize a loss function. In this example, the physical to be inferred law was constrained only by climate data, but any other proxies of interest can be used to design it. The climate data, and therefore the glacier mass balance, are downscaled (i.e. it depends on $S$), with $S$ being updated by the solver, thus dynamically updating the state of the simulation for a given timestep.

In order to install ODINN in a given environment, just do in the REPL:

julia> ] # enter Pkg mode
(@v1.9) pkg> activate MyEnvironment # or activate whatever path for the Julia environment
(MyEnvironment) pkg> add ODINN

ODINN depends on some Python packages, mainly OGGM and xarray. In order to install the necessary Python dependencies in an easy manner, we are providing a Python environment (oggm_env) in environment.yml. To install and activate the environment, we recommend using micromamba:

micromamba create -f environment.yml
micromamba activate oggm_env

In order to call OGGM in Python from Julia, we use PyCall.jl. PyCall hooks on the Python installation and uses Python in a totally seamless way from Julia.

The path to this conda environment needs to be specified in the ENV["PYTHON"] variable in Julia, for PyCall to find it. This configuration is very easy to implement, it just requires providing the Python path to PyCall and building it:

julia # start Julia session

julia> ENV["PYTHON"] = read(`which python`, String)[1:end-1] # trim backspace
julia> import Pkg; Pkg.build("PyCall")
julia> exit()

# Now you can run your code using ODINN in a new Julia session; e.g.:
using ODINN

So now you can start working with ODINN with PyCall correctly configured. These configuration step only needs to be done the first time, so from now on ODINN should be able to correctly find your Python libraries. If you ever want to change your conda environment, you would just need to repeat the steps above. The next step is to start a new Julia session and import ODINN (or just run your script which uses ODINN, e.g. toy_model.jl). If you want to run ODINN using multiprocessing you can enable it using the following command in Julia:

processes = 16
ODINN.enable_multiprocessing(processes)

From this point, it is possible to use ODINN with multiprocessing and to run Python from Julia running the different commands available in the PyCall documentation. In order to get a better idea on how this works, we recommend checking the toy model example toy_model.jl.

ODINN works as a back-end of OGGM, utilizing all its tools to retrieve RGI data, topographical data, climate data and other datasets from the OGGM shop. We use these data to specify the initial state of the simulations, and to retrieve the climate data to force the model. Everything related to the mass balance and ice flow dynamics models is written 100% in Julia. This allows us to run tests with this toy model for any glacier on Earth. In order to choose a glacier, you just need to specify the RGI ID, which you can find here.

A stable API is still being designed, which will be available in the next release. If you plan to start using the model, please contact us, although we recommend to wait until next release for a smoother experience.

If you want to cite this work, please use this BibTex citation from our latest preprint:

@article{bolibar_sapienza_universal_2023,
	title = {Universal differential equations for glacier ice flow modelling},
	author = {Bolibar, J. and Sapienza, F. and Maussion, F. and Lguensat, R. and Wouters, B. and P\'erez, F.},
	journal = {Geoscientific Model Development},
	volume = {16},
	year = {2023},
	number = {22},
	pages = {6671--6687},
	url = {https://gmd.copernicus.org/articles/16/6671/2023/},
	doi = {10.5194/gmd-16-6671-2023}
}