Related papers: A Hybrid Deep Neural Operator/Finite Element Metho…

Sea ice at the North Pole is vital to global climate dynamics. However, accurately forecasting sea ice poses a significant challenge due to the intricate interaction among multiple variables. Leveraging the capability to integrate multiple…

Operator learning for complex nonlinear systems is increasingly common in modeling multi-physics and multi-scale systems. However, training such high-dimensional operators requires a large amount of expensive, high-fidelity data, either…

Physical motion models offer interpretable predictions for the motion of vehicles. However, some model parameters, such as those related to aero- and hydrodynamics, are expensive to measure and are often only roughly approximated reducing…

This work proposes a hybrid modeling framework based on recurrent neural networks (RNNs) and the finite element (FE) method to approximate model discrepancies in time dependent, multi-fidelity problems, and use the trained hybrid models to…

In this paper, we propose a novel $hr$-adaptive finite element method, enhanced by neural networks, for parabolic equations. The main challenge of the conventional $h$-adaptive finite element method is interpolating the finite element…

Hybrid modeling combining data-driven techniques and numerical methods is an emerging and promising research direction for efficient climate simulation. However, previous works lack practical platforms, making developing hybrid modeling a…

We present a method that employs physics-informed deep learning techniques for parametrically solving partial differential equations. The focus is on the steady-state heat equations within heterogeneous solids exhibiting significant phase…

We introduce a method that combines neural operators, physics-informed machine learning, and standard numerical methods for solving PDEs. The proposed approach extends each of the aforementioned methods and unifies them within a single…

Producing probabilistic forecasts for large collections of similar and/or dependent time series is a practically relevant and challenging task. Classical time series models fail to capture complex patterns in the data, and multivariate…

This work introduces a hybrid approach that combines the Proper Generalised Decomposition (PGD) with deep learning techniques to provide real-time solutions for parametrised mechanics problems. By relying on a tensor decomposition, the…

In this paper, based on the combination of finite element mesh and neural network, a novel type of neural network element space and corresponding machine learning method are designed for solving partial differential equations. The…

Accurate long-range prediction of geophysical systems is difficult due to strongly nonlinear dynamics, the high computational cost of full-physics simulations, and the error accumulation that arise when one-step autoregressive surrogates…

Modern weather forecast models perform uncertainty quantification using ensemble prediction systems, which collect nonparametric statistics based on multiple perturbed simulations. To provide accurate estimation, dozens of such…

Cloud-related parameterizations remain a leading source of uncertainty in climate projections. Although machine learning holds promise for Earth system models (ESMs), many data-driven parameterizations lack interpretability, physical…

Deep learning models have demonstrated remarkable success in various fields, including seismology. However, one major challenge in deep learning is the presence of mislabeled examples. Additionally, accurately estimating model uncertainty…

Computational modeling of a complex system is limited by the parts of the system with the least information. While detailed models and high-resolution data may be available for parts of a system, abstract relationships are often necessary…

Evidence-based deep learning represents a burgeoning paradigm for uncertainty estimation, offering reliable predictions with negligible extra computational overheads. Existing methods usually adopt Kullback-Leibler divergence to estimate…

Climate-economic modeling under uncertainty presents significant computational challenges that may limit policymakers' ability to address climate change effectively. This paper explores neural network-based approaches for solving…

Numerical ice sheet models compute evolving ice geometry and velocity fields using various stress-balance approximations and boundary conditions. At high spatial resolution, with horizontal mesh/grid resolutions of a few kilometers or…

We present a novel hybrid strategy based on machine learning to improve curvature estimation in the level-set method. The proposed inference system couples enhanced neural networks with standard numerical schemes to compute curvature more…