A hybrid deep neural operator/finite element method for ice-sheet modeling

• Published in: Journal of computational physics Vol. 492; p. 112428
• Main Authors: He, QiZhi, Perego, Mauro, Howard, Amanda A., Karniadakis, George Em, Stinis, Panos
• Format: Journal Article
• Language: English
• Published: United States Elsevier Inc 01.11.2023; Elsevier
• Subjects: artificial intelligence; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Deep learning surrogate; Finite element; Hybrid model; Ice-sheet dynamics; Neural operator; Neural operator; Hybrid model; Deep learning surrogate; Ice-sheet dynamics; Finite element
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2023.112428

One of the most challenging and consequential problems in climate modeling is to provide probabilistic projections of sea level rise. A large part of the uncertainty of sea level projections is due to uncertainty in ice sheet dynamics. At the moment, accurate quantification of the uncertainty is hindered by the cost of ice sheet computational models. In this work, we develop a hybrid approach to approximate existing ice sheet computational models at a fraction of their cost. Our approach consists of replacing the finite element model for the momentum equations for the ice velocity, the most expensive part of an ice sheet model, with a Deep Operator Network, while retaining a classic finite element discretization for the evolution of the ice thickness. We show that the resulting hybrid model is very accurate and it is an order of magnitude faster than the traditional finite element model. Further, a distinctive feature of the proposed model compared to other neural network approaches, is that it can handle high-dimensional parameter spaces (parameter fields) such as the basal friction at the bed of the glacier, and can therefore be used for generating samples for uncertainty quantification. We study the impact of hyper-parameters, number of unknowns and correlation length of the parameter distribution on the training and accuracy of the Deep Operator Network on a synthetic ice sheet model. We then target the evolution of the Humboldt glacier in Greenland and show that our hybrid model can provide accurate statistics of the glacier mass loss and can be effectively used to accelerate the quantification of uncertainty. •We develop a hybrid Deep Operator Network/Finite Element model for ice-sheet dynamics.•Our hybrid model can handle high-dimensional parameter spaces.•We demonstrate the hybrid approach on realistic simulations of a Greenland glacier.•The hybrid model is efficient in producing accurate statistics of glacier mass loss.