Universal differential equations for glacier ice flow modelling
<p>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...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Copernicus Publications
2023-11-01
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| Series: | Geoscientific Model Development |
| Online Access: | https://gmd.copernicus.org/articles/16/6671/2023/gmd-16-6671-2023.pdf |
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| author | J. Bolibar J. Bolibar F. Sapienza F. Maussion F. Maussion R. Lguensat B. Wouters B. Wouters F. Pérez |
| author_facet | J. Bolibar J. Bolibar F. Sapienza F. Maussion F. Maussion R. Lguensat B. Wouters B. Wouters F. Pérez |
| author_sort | J. Bolibar |
| collection | DOAJ |
| description | <p>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 <code>ODINN.jl</code>, 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 <span class="inline-formula">∼</span> 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.</p> |
| first_indexed | 2024-03-11T10:15:58Z |
| format | Article |
| id | doaj.art-9fda70f7cf2f4e539881f6cc40570f27 |
| institution | Directory Open Access Journal |
| issn | 1991-959X 1991-9603 |
| language | English |
| last_indexed | 2024-03-11T10:15:58Z |
| publishDate | 2023-11-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Geoscientific Model Development |
| spelling | doaj.art-9fda70f7cf2f4e539881f6cc40570f272023-11-16T09:44:36ZengCopernicus PublicationsGeoscientific Model Development1991-959X1991-96032023-11-01166671668710.5194/gmd-16-6671-2023Universal differential equations for glacier ice flow modellingJ. Bolibar0J. Bolibar1F. Sapienza2F. Maussion3F. Maussion4R. Lguensat5B. Wouters6B. Wouters7F. Pérez8Institute for Marine and Atmospheric research Utrecht, Utrecht University, Utrecht, the NetherlandsFaculty of Civil Engineering and Geosciences, Technische Universiteit Delft, Delft, the NetherlandsDepartment of Statistics, University of California, Berkeley, CA, USADepartment of Atmospheric and Cryospheric Sciences, Universität Innsbruck, Innsbruck, AustriaBristol Glaciology Centre, School of Geographical Sciences, University of Bristol, Bristol, UKInstitut Pierre-Simon Laplace, IRD, Sorbonne Université, Paris, FranceInstitute for Marine and Atmospheric research Utrecht, Utrecht University, Utrecht, the NetherlandsFaculty of Civil Engineering and Geosciences, Technische Universiteit Delft, Delft, the NetherlandsDepartment of Statistics, University of California, Berkeley, CA, USA<p>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 <code>ODINN.jl</code>, 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 <span class="inline-formula">∼</span> 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.</p>https://gmd.copernicus.org/articles/16/6671/2023/gmd-16-6671-2023.pdf |
| spellingShingle | J. Bolibar J. Bolibar F. Sapienza F. Maussion F. Maussion R. Lguensat B. Wouters B. Wouters F. Pérez Universal differential equations for glacier ice flow modelling Geoscientific Model Development |
| title | Universal differential equations for glacier ice flow modelling |
| title_full | Universal differential equations for glacier ice flow modelling |
| title_fullStr | Universal differential equations for glacier ice flow modelling |
| title_full_unstemmed | Universal differential equations for glacier ice flow modelling |
| title_short | Universal differential equations for glacier ice flow modelling |
| title_sort | universal differential equations for glacier ice flow modelling |
| url | https://gmd.copernicus.org/articles/16/6671/2023/gmd-16-6671-2023.pdf |
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