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

Dropout Regularization, serving to reduce variance, is nearly ubiquitous in Deep Learning models. We explore the relationship between the dropout rate and model complexity by training 2,000 neural networks configured with random…

In recent years Deep Neural Networks (DNNs) have been rapidly developed in various applications, together with increasingly complex architectures. The performance gain of these DNNs generally comes with high computational costs and large…

Uncertainty quantification is critical for ensuring robustness in high-stakes machine learning applications. We introduce HybridFlow, a modular hybrid architecture that unifies the modeling of aleatoric and epistemic uncertainty by…

The world is moving towards clean and renewable energy sources, such as wind energy, in an attempt to reduce greenhouse gas emissions that contribute to global warming. To enhance the analysis and storage of wind data, we introduce a deep…

Ice sheet simulations suffer from vast parametric uncertainties, such as the basal sliding boundary condition or geothermal heat flux. Quantifying the resulting uncertainties in predictions is of utmost importance to support judicious…

This paper presents a novel methodology for fast simulation and analysis of transient heat transfer. The proposed methodology is suitable for real-time applications owing to (i) establishing the solution method from the viewpoint of…

A promising approach to improve climate-model simulations is to replace traditional subgrid parameterizations based on simplified physical models by machine learning algorithms that are data-driven. However, neural networks (NNs) often lead…

Estimating and disentangling epistemic uncertainty, uncertainty that is reducible with more training data, and aleatoric uncertainty, uncertainty that is inherent to the task at hand, is critically important when applying machine learning…

In recent years, there has been significant progress in the development of fully data-driven global numerical weather prediction models. These machine learning weather prediction models have their strength, notably accuracy and low…

Multiscale problems are widely observed across diverse domains in physics and engineering. Translating these problems into numerical simulations and solving them using numerical schemes, e.g. the finite element method, is costly due to the…

The Greenland ice sheet is melting at an accelerated rate due to processes that are not fully understood and hard to measure. The distribution of surface meltwater can help understand these processes and is observable through remote…

The accurate estimation of the state of complex uncertain physical systems requires reconciling theoretical models, with inherent imperfections, with noisy experimental data. In this work, we propose an effective hybrid approach that…

Learning spatio-temporal patterns of polar ice layers is crucial for monitoring the change in ice sheet balance and evaluating ice dynamic processes. While a few researchers focus on learning ice layer patterns from echogram images captured…

Dynamic neural networks are a recent technique that promises a remedy for the increasing size of modern deep learning models by dynamically adapting their computational cost to the difficulty of the inputs. In this way, the model can adjust…

When modeling scientific and industrial problems, geometries are typically modeled by explicit boundary representations obtained from computer-aided design software. Unfitted (also known as embedded or immersed) finite element methods offer…

Any experiment with climate models relies on a potentially large set of spatio-temporal boundary conditions. These can represent both the initial state of the system and/or forcings driving the model output throughout the experiment. Whilst…

Artificial intelligence and deep learning are currently reshaping numerical simulation frameworks by introducing new modeling capabilities. These frameworks are extensively investigated in the context of model correction and…

The finite element method (FEM) is a well-established numerical method for solving partial differential equations (PDEs). However, its mesh-based nature gives rise to substantial computational costs, especially for complex multiscale…

Multi-model ensembles provide a pragmatic approach to the representation of model uncertainty in climate prediction. However, such representations are inherently ad hoc, and, as shown, probability distributions of climate variables based on…

The application of neural network models to scientific machine learning tasks has proliferated in recent years. In particular, neural network models have proved to be adept at modeling processes with spatial-temporal complexity.…