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Uncertainty quantification (UQ) is important to machine learning (ML) force fields to assess the level of confidence during prediction, as ML models are not inherently physical and can therefore yield catastrophically incorrect predictions.…

We introduce a novel Multi-Order Monte Carlo approach for uncertainty quantification in the context of multiscale time-dependent partial differential equations. The new framework leverages Implicit-Explicit Runge-Kutta time integrators to…

Quantitative magnetic resonance imaging (qMRI) requires multi-phase acqui-sition, often relying on reduced data sampling and reconstruction algorithms to accelerate scans, which inherently poses an ill-posed inverse problem. While many…

We analyse and implement a quasi-Monte Carlo (QMC) finite element method (FEM) for the forward problem of uncertainty quantification (UQ) for the Helmholtz equation with random coefficients, both in the second-order and zero-order terms of…

Neural operators (NOs) provide fast, resolution-invariant surrogates for mapping input fields to PDE solution fields, but their predictions can exhibit significant epistemic uncertainty due to finite data, imperfect optimization, and…

Cancer research is increasingly driven by the integration of diverse data modalities, spanning from genomics and proteomics to imaging and clinical factors. However, extracting actionable insights from these vast and heterogeneous datasets…

This paper focuses on the problem of quantifying the effects of model-structure uncertainty in the context of time-evolving dynamical systems. This is motivated by multi-model uncertainty in computer physics simulations: developers often…

Efficient uncertainty quantification algorithms are key to understand the propagation of uncertainty -- from uncertain input parameters to uncertain output quantities -- in high resolution mathematical models of brain physiology. Advanced…

Diffusion Monte Carlo (DMC) simulations for fermions are becoming the standard to provide high quality reference data in systems that are too large to be investigated via quantum chemical approaches. DMC with the fixed-node approximation…

This paper presents a nonlinear reduced-order modeling (ROM) framework that leverages deep learning and manifold learning to predict compressible flow fields with complex nonlinear features, including shock waves. The proposed DeepManifold…

We introduce methodologies for highly scalable quantum Monte Carlo simulations of electron-phonon models, and report benchmark results for the Holstein model on the square lattice. The determinant quantum Monte Carlo (DQMC) method is a…

Operator learning is a rapidly growing field that aims to approximate nonlinear operators related to partial differential equations (PDEs) using neural operators. These rely on discretization of input and output functions and are, usually,…

Uncertainty quantification (UQ) plays a pivotal role in scientific machine learning, especially when surrogate models are used to approximate complex systems. Although multilayer perceptions (MLPs) are commonly employed as surrogates, they…

Uncertainty quantification (UQ) plays a pivotal role in reduction of uncertainties during both optimization and decision making processes. It can be applied to solve a variety of real-world applications in science and engineering. Bayesian…

Multifidelity uncertainty quantification (MF UQ) sampling approaches have been shown to significantly reduce the variance of statistical estimators while preserving the bias of the highest-fidelity model, provided that the low-fidelity…

The subsurface flow is usually subject to uncertain porous media structures. In most cases, however, we only have partial knowledge about the porous media properties. A common approach is to model the uncertain parameters of porous media as…

Uncertainty quantification (UQ) is a crucial but challenging task in many high-dimensional regression or learning problems to increase the confidence of a given predictor. We develop a new data-driven approach for UQ in regression that…

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…

For computational efficiency, surrogate models have been used to emulate mathematical simulators for physical or biological processes. High-speed simulation is crucial for conducting uncertainty quantification (UQ) when the simulation is…

Uncertainty Quantification through Markov Chain Monte Carlo (MCMC) can be prohibitively expensive for target probability densities with expensive likelihood functions, for instance when the evaluation it involves solving a Partial…