Related papers: Functional PCA and Deep Neural Networks-based Baye…

A central challenge in scientific machine learning (ML) is the correct representation of physical systems governed by multi-regime behaviours. In these scenarios, standard data analysis techniques often fail to capture the nature of the…

Assessing the quality of aleatoric uncertainty estimates from uncertainty quantification (UQ) deep learning methods is important in scientific contexts, where uncertainty is physically meaningful and important to characterize and interpret…

This work proposes a data-driven surrogate modeling framework for cost-effectively inferring the torque of a permanent magnet synchronous machine under geometric design variations. The framework is separated into a reduced-order modeling…

Computational models of the human head are promising tools for estimating the impact-induced response of brain, and thus play an important role in the prediction of traumatic brain injury. Modern biofidelic head model simulations are…

High-dimensional tensor data often exhibit strong temporal correlations that appear as low-dimensional structures in the frequency domain. While the low-tubal-rank tensor model effectively captures these spectral features, making it…

Early work established convergence of the principal component estimators of the factors and loadings up to a rotation for large dimensional approximate factor models with weak factors in that the factor loading $\Lambda^{(0)}$ scales…

Uncertainty quantification (UQ) in deep learning regression is of wide interest, as it supports critical applications including sequential decision making and risk-sensitive tasks. In heteroskedastic regression, where the uncertainty of the…

Dielectric response (DR) of insulating materials is key input information for designing electrical insulation systems and defining safe operating conditions of various HV devices. In dielectric materials, different polarization and…

Trajectory prediction models that can infer both finite future trajectories and their associated uncertainties of the target vehicles in an online setting (e.g., real-world application scenarios) is crucial for ensuring the safe and robust…

We present $\Delta$-UQ -- a novel, general-purpose uncertainty estimator using the concept of anchoring in predictive models. Anchoring works by first transforming the input into a tuple consisting of an anchor point drawn from a prior…

Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving PDEs, yet existing uncertainty quantification (UQ) approaches for PINNs generally lack rigorous statistical guarantees. In this work, we bridge this…

We describe a computational framework linking Uncertainty Quantification (UQ) methods for continuum problems depending on random parameters with Equation-Free (EF) methods for performing continuum deterministic numerics by acting directly…

Principal component analysis (PCA) aims at estimating the direction of maximal variability of a high-dimensional dataset. A natural question is: does this task become easier, and estimation more accurate, when we exploit additional…

In this article, we present a novel data assimilation strategy in pore-scale imaging and demonstrate that this makes it possible to robustly address reactive inverse problems incorporating Uncertainty Quantification (UQ). Pore-scale…

A quantum neural network (QNN) is a parameterized mapping efficiently implementable on near-term Noisy Intermediate-Scale Quantum (NISQ) computers. It can be used for supervised learning when combined with classical gradient-based…

Physics-informed neural networks (PINNs) have recently emerged as an alternative way of solving partial differential equations (PDEs) without the need of building elaborate grids, instead, using a straightforward implementation. In…

In principle, deep learning models trained on medical time-series, including wearable photoplethysmography (PPG) sensor data, can provide a means to continuously monitor physiological parameters outside of clinical settings. However, there…

The present paper proposes a Bayesian framework for inverse problems that seamlessly integrates optimization and inversion to enable rapid surrogate modeling, accurate parameter inference, and rigorous uncertainty quantification. Bayesian…

Neural Network (NN) models provide potential to speed up the drug discovery process and reduce its failure rates. The success of NN models require uncertainty quantification (UQ) as drug discovery explores chemical space beyond the training…

Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…