Related papers: Machine learning with data assimilation and uncert…

Data assimilation (DA) methods combine model predictions with observational data to improve state estimation in dynamical systems, inspiring their increasingly prominent role in geophysical and climate applications. Classical DA methods…

The goals of this chapter are twofold. First, we wish to introduce molecular dynamics (MD) and uncertainty quantification (UQ) in a common setting in order to demonstrate how the latter can increase confidence in the former. In some cases,…

There has been a recent surge in development of accurate machine learning (ML) weather prediction models, but evaluation of these models has mainly been focused on medium-range forecasts, not their performance in cycling data assimilation…

Molecular dynamics simulation is now a widespread approach for understanding complex systems on the atomistic scale. It finds applications from physics and chemistry to engineering, life and medical science. In the last decade, the approach…

Accurate uncertainty quantification (UQ) in Large Language Models (LLMs) is critical for trustworthy deployment. While real-world language is inherently ambiguous, reflecting aleatoric uncertainty, existing UQ methods are typically…

Data assimilation (DA) integrates observations with model forecasts to produce optimized atmospheric states, whose physical consistency is critical for stable weather forecasting and reliable climate research. Traditional Bayesian DA…

This study investigates uncertainty quantification (UQ) using quantum-classical hybrid machine learning (ML) models for applications in complex and dynamic fields, such as attaining resiliency in supply chain digital twins and financial…

This paper provides a comparative study of modern uncertainty quantification (UQ) methods. To greatly enhance real-time performance, both differential algebra (DA) and a directional differential algebra (DDA) approach are employed. This can…

This work integrates ensemble-based data assimilation (DA) with the energy-aware hybrid modeling approach, applied to a three-layer quasi-geostrophic (QG) model of the Gulf Stream flow. Building on prior DA success in the QG channel regime,…

Quantifying uncertainties for machine learning (ML) models is a foundational challenge in modern data analysis. This challenge is compounded by at least two key aspects of the field: (a) inconsistent terminology surrounding uncertainty and…

Much attention has been paid to dynamical simulation and quantum machine learning (QML) independently as applications for quantum advantage, while the possibility of using QML to enhance dynamical simulations has not been thoroughly…

Data assimilation (DA) in the geophysical sciences remains the cornerstone of robust forecasts from numerical models. Indeed, DA plays a crucial role in the quality of numerical weather prediction, and is a crucial building block that has…

Data assimilation (DA) integrates observational data with numerical models to improve the prediction of complex physical systems. However, traditional DA methods often struggle with nonlinear dynamics and multi-scale variability,…

We apply two data assimilation (DA) methods, a smoother and a filter, and a model-free machine learning (ML) shallow network to forecast two weakly turbulent systems. We analyse the effect of the spatial sparsity of observations on accuracy…

Deep neural networks (DNNs) have achieved tremendous success in computer vision, natural language processing, and scientific and engineering domains. However, DNNs can make unexpected, incorrect, yet overconfident predictions, leading to…

Turbulent flows are of central importance across applications in science and engineering problems. For design and analysis, scientists and engineers use Computational Fluid Dynamics (CFD) simulations using turbulence models. Turbulent…

Uncertainty quantification (UQ) is an important component of molecular property prediction, particularly for drug discovery applications where model predictions direct experimental design and where unanticipated imprecision wastes valuable…

Data assimilation (DA) aims at optimally merging observational data and model outputs to create a coherent statistical and dynamical picture of the system under investigation. Indeed, DA aims at minimizing the effect of observational and…

Turbulent flows play an important role in many scientific and technological design problems. Both Sub-Grid Scale (SGS) models in Large Eddy Simulations (LES) and Reynolds Averaged Navier Stokes (RANS) based modeling will require turbulence…

The practice of uncertainty quantification (UQ) validation, notably in machine learning for the physico-chemical sciences, rests on several graphical methods (scattering plots, calibration curves, reliability diagrams and confidence curves)…