Observational estimates of Antarctic ice loss have accelerated in recent decades, and worst-case scenarios of modeling studies have suggested potentially catastrophic sea level rise (~2 meters) by the end of the century. However, modeled contributions to global mean sea level from the Antarctic ice-sheet (AIS) in the 21st century are highly uncertain, in part because ice-sheet model parameters are poorly constrained. Individual ice-sheet model runs are also deterministic and not computationally efficient enough to generate the continuous probability distributions required for incorporation into a holistic framework of probabilistic sea-level projections. To address these shortfalls, we statistically emulate an ice-sheet model using Gaussian Process (GP) regression. GP modeling is a non-parametric machine-learning technique which maps inputs (e.g. forcing or model parameters) to target outputs (e.g. sea-level contributions from the Antarctic ice-sheet) and has the inherent and important advantage that emulator uncertainty is explicitly quantified. We construct emulators for the last interglacial period and an RCP8.5 scenario, and separately for the western, eastern, and total AIS. Separate emulation of western and eastern AIS is important because their evolutions and physical responses to climate forcing are distinct. The emulators are trained on 196 ensemble members for each scenario, composed by varying the parameters of maximum rate of ice-cliff wastage and the coefficient of hydrofracturing. We condition the emulators on last interglacial proxy sea-level records and modern GRACE measurements and exclude poor-fitting ensemble members. The resulting emulators are sampled to produce probability distributions that fill intermediate gaps between discrete ice-sheet model outcomes. We invert emulated high and low probability sea-level contributions in 2100 to explore 21st century evolution pathways; results highlight the deep uncertainty of ice-sheet model physics and the importance of using observations to narrow the range of parameters. Our approach is designed to be flexible such that other ice-sheet models or parameter spaces may be substituted and explored with the emulator.
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This content will become publicly available on December 14, 2024
A Graph Neural Network Emulator of a Finite Element Ice Flow Model
Emulators of ice flow models have shown promise for speeding up simulations of glaciers and ice sheets. Existing ice flow emulators have relied primarily on convolutional neural networks (CNN’s), which assume that model inputs and outputs are discretized on a uniform computational grid. However, many existing finite element-based ice sheet models such as the Ice-Sheet and Sea-level System model (ISSM) benefit from their ability to use unstructured computational meshes. Unstructured meshes allow for greater flexibility and computational efficiency in many modeling scenarios.
In this work, we present an emulator of a higher order, finite element ice flow model based on a graph neural network (GNN) architecture. In this architecture, an unstructured finite element mesh is represented as a graph, with inputs and outputs of the ice flow model represented as variables on graph nodes and edges. An advantage of this approach is that the ice flow emulator can interface directly with a standard finite element –based ice sheet model by mapping between the finite element mesh and a graph suitable for the GNN emulator. We test the ability of the GNN to predict velocity fields on complex mountain glacier geometries and show how the emulated velocity can be used to solve for mass continuity using a standard finite element approach.
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- Award ID(s):
- 2107605
- PAR ID:
- 10548835
- Editor(s):
- Tedesco, Marco; Lai, Ching_Yao; Brinkerhoff, Douglas; Stearns, Leigh
- Publisher / Repository:
- AGU23 Online Program
- Date Published:
- Format(s):
- Medium: X
- Institution:
- American Geophysical Union
- Sponsoring Org:
- National Science Foundation
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Summary This work describes a domain embedding technique between two nonmatching meshes used for generating realizations of spatially correlated random fields with applications to large‐scale sampling‐based uncertainty quantification. The goal is to apply the multilevel Monte Carlo (MLMC) method for the quantification of output uncertainties of PDEs with random input coefficients on general and unstructured computational domains. We propose a highly scalable, hierarchical sampling method to generate realizations of a Gaussian random field on a given unstructured mesh by solving a reaction–diffusion PDE with a stochastic right‐hand side. The stochastic PDE is discretized using the mixed finite element method on an embedded domain with a structured mesh, and then, the solution is projected onto the unstructured mesh. This work describes implementation details on how to efficiently transfer data from the structured and unstructured meshes at coarse levels, assuming that this can be done efficiently on the finest level. We investigate the efficiency and parallel scalability of the technique for the scalable generation of Gaussian random fields in three dimensions. An application of the MLMC method is presented for quantifying uncertainties of subsurface flow problems. We demonstrate the scalability of the sampling method with nonmatching mesh embedding, coupled with a parallel forward model problem solver, for large‐scale 3D MLMC simulations with up to 1.9·109unknowns.
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Abstract The Antarctic ice sheet (AIS) will be a dominant contributor to global mean sea level rise in the 21st century but remains a major source of uncertainty. The Ice Sheet Model Intercomparison for CMIP6 (ISMIP6) is an ensemble of continental‐scale models for studying the evolution of the AIS and projecting its future contribution to sea level. Due to their complexity and computational cost, ISMIP6 simulations are sparse and generated infrequently. Emulators are smaller‐scale models that approximate ISMs and enable experimentation and exploration into the drivers of sea level change. We introduce a neural network (NN) emulator to approximate the ISMIP6 ensemble, using a variational Long Short‐Term Memory (LSTM) with Monte Carlo dropout to quantify single‐projection uncertainty. The proposed NN emulator is compared to a Gaussian Process (GP) emulator on four criteria: accuracy of point estimates and predictive distributions of individual model projections, approximation of the ensemble projections, and model training time. The NN predicts more accurately on single projections, with a mean absolute error of 0.46 mm Sea Level Equivalent (SLE) versus 0.73 mm SLE for the GP, and has more accurate uncertainty estimates. The NN emulator also better approximates the ensemble distribution of ISMIP6 model projections, with a Kullback‐Leibler divergence of 18.26 versus 199.14 for GP at the projection year 2100. The NN enables more accurate experimentation with a reduced runtime, offering a new tool for understanding the important role of regional precipitation, ice sheet drainage systems, and interannual and longer timescale dynamics.
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Elastic continuum mechanical models are widely used to compute deformations due to pressure changes in buried cavities, such as magma reservoirs. In general, analytical models are fast but can be inaccurate as they do not correctly satisfy boundary conditions for many geometries, while numerical models are slow and may require specialized expertise and software. To overcome these limitations, we trained supervised machine learning emulators (model surrogates) based on parallel partial Gaussian processes which predict the output of a finite element numerical model with high fidelity but >1,000× greater computational efficiency. The emulators are based on generalized nondimensional forms of governing equations for finite non‐dipping spheroidal cavities in elastic halfspaces. Either cavity volume change or uniform pressure change boundary conditions can be specified, and the models predict both surface displacements and cavity (pore) compressibility. Because of their computational efficiency, using the emulators as numerical model surrogates can greatly accelerate data inversion algorithms such as those employing Bayesian Markov chain Monte Carlo sampling. The emulators also permit a comprehensive evaluation of how displacements and cavity compressibility vary with geometry and material properties, revealing the limitations of analytical models. Our open‐source emulator code can be utilized without finite element software, is suitable for a wide range of cavity geometries and depths, includes an estimate of uncertainties associated with emulation, and can be used to train new emulators for different source geometries.more » « less
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Abstract A fundamental requirement in standard finite element method (FEM) over four‐node quadrilateral meshes is that every element must be convex, else the results can be erroneous. A mesh containing concave element is said to be
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