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Abstract. 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 two-dimensional 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 ∼ 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 in ice creep and basal sliding for ice flow, and new hybrid surface mass balance models.
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icepack: a new glacier flow modeling package in Python, version 1.0
Abstract. We introduce a new software package called “icepack” for modeling the flow of glaciers and ice sheets.The icepack package is built on the finite element modeling library Firedrake, which uses the Unified Form Language (UFL), a domain-specific language embedded into Python for describing weak forms of partial differential equations.The diagnostic models in icepack are formulated through action principles that are specified in UFL.The components of each action functional can be substituted for different forms of the user's choosing, which makes it easy to experiment with the model physics.The action functional itself can be used to define a solver convergence criterion that is independent of the mesh and requires little tuning on the part of the user. Theicepack package includes the 2D shallow ice and shallow stream models.We have also defined a 3D hybrid model based on spectral semi-discretization of the Blatter–Pattyn equations.Finally, icepack includes a Gauss–Newton solver for inverse problems that runs substantially faster than the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method often used in the glaciological literature.The overall design philosophy of icepack is to be as usable as possible for a wide a swath of the glaciological community, including both experts and novices in computational science.
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- Award ID(s):
- 1835321
- PAR ID:
- 10309973
- Date Published:
- Journal Name:
- Geoscientific Model Development
- Volume:
- 14
- Issue:
- 7
- ISSN:
- 1991-9603
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.5194/gmd-14-4593-2021
