Related papers: Physics-Guided Machine Learning for Uncertainty Qu…

Humans possess a finely tuned sense of uncertainty that helps anticipate potential errors, vital for adaptive behavior and survival. However, the underlying neural mechanisms remain unclear. This study applies moment neural networks (MNNs)…

Data-driven methods based on machine learning have the potential to accelerate computational analysis of atomic structures. In this context, reliable uncertainty estimates are important for assessing confidence in predictions and enabling…

Data-driven turbulence modelling approaches are gaining increasing interest from the CFD community. However, the introduction of a machine learning (ML) model introduces a new source of uncertainty, the ML model itself. Quantification of…

Accurate representations of unknown and sub-grid physical processes through parameterizations (or closure) in numerical simulations with quantified uncertainty are critical for resolving the coarse-grained partial differential equations…

Machine-learning (ML) interatomic potentials (IPs) trained on first-principles datasets are becoming increasingly popular since they promise to treat larger system sizes and longer time scales, compared to the {\em ab initio} techniques…

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…

Deep neural networks has been increasingly applied in fault diagnostics, where it uses historical data to capture systems behavior, bypassing the need for high-fidelity physical models. However, despite their competence in prediction tasks,…

Nonlinear initial value turbulence simulations often exhibit large temporal variations in their dynamics. Quantifying the temporal uncertainty of turbulence simulation outputs is an important component of validating the simulation results…

Ensembling is now recognized as an effective approach for increasing the predictive performance and calibration of deep networks. We introduce a new approach, Parameter Ensembling by Perturbation (PEP), that constructs an ensemble of…

Modelling uncertainty in Machine Learning models is essential for achieving safe and reliable predictions. Most research on uncertainty focuses on output uncertainty (predictions), but minimal attention is paid to uncertainty at inputs. We…

Quantum machine learning (QML) is making rapid progress, and QML-based models hold the promise of quantum advantages such as potentially higher expressivity and generalizability than their classical counterparts. Here, we present work on…

Data-driven methods are widely used to develop physical models, but there still exist limitations that affect their performance, generalizability and robustness. By combining gene expression programming (GEP) with artificial neural network…

Physics-Informed Neural Networks (PINNs) frequently encounter difficulties in accurately resolving shock waves within high-speed compressible flows, a failure largely attributed to the "gradient pathology" arising from extreme stiffness at…

This paper puts forward a framework to accelerate Electromagnetic Transient (EMT) simulations by replacing individual components with trained Physics-Informed Neural Networks (PINNs). EMT simulations are considered the cornerstone of…

Quantifying the uncertainty of supervised learning models plays an important role in making more reliable predictions. Epistemic uncertainty, which usually is due to insufficient knowledge about the model, can be reduced by collecting more…

An uncertainty quantification framework is developed for Eulerian-Lagrangian models of particle-laden flows, where the fluid is modeled through a system of partial differential equations in the Eulerian frame and inertial particles are…

Increasingly high-stakes decisions are made using neural networks in order to make predictions. Specifically, meteorologists and hedge funds apply these techniques to time series data. When it comes to prediction, there are certain…

Reynolds Averaged Navier Stokes (RANS) modelling is notorious for introducing the model-form uncertainty due to the Boussinesq turbulent viscosity hypothesis. Recently, the eigenspace perturbation method (EPM) has been developed to estimate…

Most machine learning techniques are based upon statistical learning theory, often simplified for the sake of computing speed. This paper is focused on the uncertainty aspect of mathematical modeling in machine learning. Regression analysis…

Computational chemistry has come a long way over the course of several decades, enabling subatomic level calculations particularly with the development of Density Functional Theory (DFT). Recently, machine-learned potentials (MLP) have…