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1. A Graph Neural Network Emulator of a Finite Element Ice Flow Model

   Downs, Jacob; Brinkerhoff, Douglas; Johnson, Jesse (December 2023, AGU23 Online Program)

   Tedesco, Marco; Lai, Ching_Yao; Brinkerhoff, Douglas; Stearns, Leigh (Ed.)

   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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2. Computationally Efficient Emulation of Spheroidal Elastic Deformation Sources Using Machine Learning Models: A Gaussian‐Process‐Based Approach

   https://doi.org/10.1029/2024JH000161  

   Anderson, Kyle R; Gu, Mengyang (September 2024, Journal of Geophysical Research: Machine Learning and Computation)

   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. 

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3. Using Machine Learning to Predict Urban Canopy Flows for Land Surface Modeling

   https://doi.org/10.1029/2022GL102313  

   Lu, Yanle; Zhou, Xu‐Hui; Xiao, Heng; Li, Qi (January 2023, Geophysical Research Letters)

   Abstract Developing urban land surface models for modeling cities at high resolutions needs to better account for the city‐specific multi‐scale land surface heterogeneities at a reasonable computational cost. We propose using an encoder‐decoder convolutional neural network to develop a computationally efficient model for predicting the mean velocity field directly from urban geometries. The network is trained using the geometry‐resolving large eddy simulation results. Systematic testing on urban structures with increasing deviations from the training geometries shows the prediction error plateaus at 15%, compared to errors sharply increasing up to 35% in the null models. This is explained by the trained model successfully capturing the effects of pressure drag, especially for tall buildings. The prediction error of the aerodynamic drag coefficient is reduced by 32% compared with the default parameterization implemented in mesoscale modeling. This study highlights the potential of combining computational fluid dynamics modeling and machine learning to develop city‐specific parameterizations. 

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4. Deep Learning Forecasts Caldera Collapse Events at Kı̄lauea Volcano

   https://doi.org/10.1029/2024JB029471  

   McBrearty, Ian W; Segall, Paul (August 2024, Journal of Geophysical Research: Solid Earth)

   Abstract During the 3 month long eruption of Kı̄lauea volcano, Hawaii in 2018, the pre‐existing summit caldera collapsed in over 60 quasi‐periodic failure events. The last 40 of these events, which generated Mw > 5 very long period (VLP) earthquakes, had inter‐event times between 0.8 and 2.2 days. These failure events offer a unique data set for testing methods for predicting earthquake recurrence based on locally recorded GPS, tilt, and seismicity data. In this work, we train a deep learning graph neural network (GNN) to predict the time‐to‐failure of the caldera collapse events using only a fraction of the data recorded at the start of each cycle. We find that the GNN generalizes to unseen data and can predict the time‐to‐failure to within a few hours using only 0.5 days of data, substantially improving upon a null model based only on inter‐event statistics. Predictions improve with increasing input data length, and are most accurate when using high‐SNR tilt‐meter data. Applying the trained GNN to synthetic data with different magma‐chamber pressure decay times predicts failure at a nearly constant stress threshold, revealing that the GNN is sensing the underling physics of caldera collapse. These findings demonstrate the predictability of caldera collapse sequences under well monitored conditions, and highlight the potential of machine learning methods for forecasting real world catastrophic events with limited training data. 

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5. Reliable emulation of complex functionals by active learning with error control

   https://doi.org/10.1063/5.0121805  

   Fang, Xinyi; Gu, Mengyang; Wu, Jianzhong (December 2022, The Journal of Chemical Physics)

   A statistical emulator can be used as a surrogate of complex physics-based calculations to drastically reduce the computational cost. Its successful implementation hinges on an accurate representation of the nonlinear response surface with a high-dimensional input space. Conventional “space-filling” designs, including random sampling and Latin hypercube sampling, become inefficient as the dimensionality of the input variables increases, and the predictive accuracy of the emulator can degrade substantially for a test input distant from the training input set. To address this fundamental challenge, we develop a reliable emulator for predicting complex functionals by active learning with error control (ALEC). The algorithm is applicable to infinite-dimensional mapping with high-fidelity predictions and a controlled predictive error. The computational efficiency has been demonstrated by emulating the classical density functional theory (cDFT) calculations, a statistical-mechanical method widely used in modeling the equilibrium properties of complex molecular systems. We show that ALEC is much more accurate than conventional emulators based on the Gaussian processes with “space-filling” designs and alternative active learning methods. In addition, it is computationally more efficient than direct cDFT calculations. ALEC can be a reliable building block for emulating expensive functionals owing to its minimal computational cost, controllable predictive error, and fully automatic features. 

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