Related papers: A Hybrid Deep Neural Operator/Finite Element Metho…
We present an efficient hybrid Neural Network-Finite Element Method (NN-FEM) for solving the viscous-plastic (VP) sea-ice model. The VP model is widely used in climate simulations to represent large-scale sea-ice dynamics. However, the…
In this study, we integrate the established obstacle problem formulation from ice sheet modeling with cutting-edge deep learning methodologies to enhance ice thickness predictions, specifically targeting the Greenland ice sheet. By…
Multiscale modeling is an effective approach for investigating multiphysics systems with largely disparate size features, where models with different resolutions or heterogeneous descriptions are coupled together for predicting the system's…
Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…
In numerical modeling of the Earth System, many processes remain unknown or ill represented (let us quote sub-grid processes, the dependence to unknown latent variables or the non-inclusion of complex dynamics in numerical models) but…
Understanding Greenland's subglacial topography is critical for projecting the future mass loss of the ice sheet and its contribution to global sea-level rise. However, the complex and sparse nature of observational data, particularly…
This paper proposes a methodology to estimate stress in the subsurface by a hybrid method combining finite element modeling and neural networks. This methodology exploits the idea of obtaining a multi-frequency solution in the numerical…
The representation of nonlinear sub-grid processes, especially clouds, has been a major source of uncertainty in climate models for decades. Cloud-resolving models better represent many of these processes and can now be run globally but…
Projecting sea-level change in various climate-change scenarios typically involves running forward simulations of the Earth's gravitational, rotational and deformational (GRD) response to ice mass change, which requires high computational…
Coupled multiphysics simulations for high-dimensional, large-scale problems can be prohibitively expensive due to their computational demands. This article presents a novel framework integrating a deep operator network (DeepONet) with the…
We introduce a novel hybrid methodology combining classical finite element methods (FEM) with neural networks to create a well-performing and generalizable surrogate model for forward and inverse problems. The residual from finite element…
Metal forging is used to manufacture dies. We require the best set of input parameters for the process to be efficient. Currently, we predict the best parameters using the finite element method by generating simulations for the different…
Rapid changes in Earth's cryosphere caused by human activity can lead to significant environmental impacts. Computer models provide a useful tool for understanding the behavior and projecting the future of Arctic and Antarctic ice sheets.…
Climate simulations, at all grid resolutions, rely on approximations that encapsulate the forcing due to unresolved processes on resolved variables, known as parameterizations. Parameterizations often lead to inaccuracies in climate models,…
Global warming leads to the increase in frequency and intensity of climate extremes that cause tremendous loss of lives and property. Accurate long-range climate prediction allows more time for preparation and disaster risk management for…
Recently, deep learning has emerged as a promising tool for statistical downscaling, the set of methods for generating high-resolution climate fields from coarse low-resolution variables. Nevertheless, their ability to generalize to climate…
Computer simulations are becoming an essential tool in many scientific fields from molecular dynamics to aeronautics. In glaciology, future predictions of sea level change require input from ice sheet models. Due to uncertainties in the…
Deep learning is a powerful tool to represent subgrid processes in climate models, but many application cases have so far used idealized settings and deterministic approaches. Here, we develop stochastic parameterizations with calibrated…
We describe and analyze a hybrid finite element/neural network method for predicting solutions of partial differential equations. The methodology is designed for obtaining fine scale fluctuations from neural networks in a local manner. The…
A significant fraction (4%-13%) of Antarctic sea ice remains stationary as landfast sea-ice ("fast ice"), typically anchored by grounded icebergs. Current global climate models do not represent fast-ice formation due to iceberg grounding,…