Related papers: A Hybrid Deep Neural Operator/Finite Element Metho…
Predicting nutrient transport and salinity distribution is crucial for mitigating climate-related threats to agromaritime systems. Traditional PDE-based models can capture the physics of nutrient dispersion, salinity and water quality.…
Ice sheet models are routinely used to quantify and project an ice sheet's contribution to sea level rise. In order for an ice sheet model to generate realistic projections, its parameters must first be calibrated using observational data;…
The increasingly populated cities of the 21st Century face the challenge of being sustainable and resilient spaces for their inhabitants. However, climate change, among other problems, makes these objectives difficult to achieve. The Urban…
Accurate simulations of the oceans are crucial in understanding the Earth system. Despite their efficiency, simulations at lower resolutions must rely on various uncertain parameterizations to account for unresolved processes. However,…
Quantifying uncertainty in weather forecasts is critical, especially for predicting extreme weather events. This is typically accomplished with ensemble prediction systems, which consist of many perturbed numerical weather simulations, or…
Obtaining accurate estimates of uncertainty in climate scenarios often requires generating large ensembles of high-resolution climate simulations, a computationally expensive and memory intensive process. To address this challenge, we train…
Recently, the use of neural networks to accelerate the solving of partial differential equations (PDEs) has gained significant traction in both academia and industry. However, employing neural networks as standalone surrogate models raises…
Numerical simulations of seismic wave propagation in heterogeneous 3D media are central to investigating subsurface structures and understanding earthquake processes, yet are computationally expensive for large problems. This is…
In the present work, we investigate the computational efficiency afforded by higher-order finite-element discretization of the saddle-point formulation of orbital-free density functional theory. We first investigate the robustness of viable…
Although considerable effort has been dedicated to improving the solution to the hyperspectral unmixing problem, non-idealities such as complex radiation scattering and endmember variability negatively impact the performance of most…
We consider non-spherical rigid body particles in an incompressible fluid in the regime where the particles are too large to assume that they are simply transported with the fluid without back-coupling and where the particles are also too…
Arctic warming threatens over 100 billion in permafrost-dependent infrastructure across Northern territories, yet existing risk assessment frameworks lack spatiotemporal validation, uncertainty quantification, and operational…
We introduce a new method for speeding up the inference of deep neural networks. It is somewhat inspired by the reduced-order modeling techniques for dynamical systems.The cornerstone of the proposed method is the maximum volume algorithm.…
Weather forecasting is usually solved through numerical weather prediction (NWP), which can sometimes lead to unsatisfactory performance due to inappropriate setting of the initial states. In this paper, we design a data-driven method…
This work presents a matrix-free finite element solver for finite-strain elasticity adopting an $hp$-multigrid preconditioner. Compared to classical algorithms relying on a global sparse matrix, matrix-free solution strategies significantly…
We analyze a hybrid method that enriches coarse grid finite element solutions with fine scale fluctuations obtained from a neural network. The idea stems from the Deep Neural Network Multigrid Solver (DNN-MG), (Margenberg et al., J Comput…
A hybrid framework integrating the Virtual Element Method (VEM) with deep learning is presented as an initial step toward developing efficient and flexible numerical models for one-dimensional Euler-Bernoulli beams. The primary aim is to…
Despite tremendous progress in developing deep-learning-based weather forecasting systems, their design space, including the impact of different design choices, is yet to be well understood. This paper aims to fill this knowledge gap by…
Mathematical modeling is an essential step, for example, to analyze the transient behavior of a dynamical process and to perform engineering studies such as optimization and control. With the help of first-principles and expert knowledge, a…
Climate models (CM) are used to evaluate the impact of climate change on the risk of floods and strong precipitation events. However, these numerical simulators have difficulties representing precipitation events accurately, mainly due to…