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Monte Carlo integration becomes prohibitively expensive when each sample requires a high-fidelity model evaluation. Multi-fidelity uncertainty quantification methods mitigate this by combining estimators from high- and low-fidelity models,…

Neural Ordinary Differential Equations (Neural ODEs) represent a significant breakthrough in deep learning, promising to bridge the gap between machine learning and the rich theoretical frameworks developed in various mathematical fields…

Bayesian estimation approaches, which are capable of combining the information of experimental data from different likelihood functions to achieve high precisions, have been widely used in phase estimation via introducing a controllable…

This document describes standard approaches for filtering and estimation for quadrotors, created for the Udacity Flying Cars course. We assume previous knowledge of probability and some knowledge of linear algebra. We do not assume previous…

Bayesian calibration of black-box computer models offers an established framework to obtain a posterior distribution over model parameters. Traditional Bayesian calibration involves the emulation of the computer model and an additive model…

Slow fluctuations of Overhauser fields are an important source for decoherence in spin qubits hosted in III-V semiconductor quantum dots. Focusing on the effect of the field gradient on double-dot singlet-triplet qubits, we present two…

In this work, a novel approach to Bayesian model calibration routines is developed which reinterprets the traditional definition of model discrepancy as defined by Kennedy and O'Hagan (KOH). The novelty lies in the integration of…

Accurate predictions and uncertainty quantification (UQ) are essential for decision-making in risk-sensitive fields such as system safety modeling. Deep ensembles (DEs) are efficient and scalable methods for UQ in Deep Neural Networks…

Bayesian statistics has gained popularity in psychological research due to its intuitive uncertainty quantification and convenient information-updating rules. In many applications, however, prior distributions are introduced merely as…

When incorporating deep neural networks into robotic systems, a major challenge is the lack of uncertainty measures associated with their output predictions. Methods for uncertainty estimation in the output of deep object detectors (DNNs)…

Traditional methods for system discovery frequently struggle with efficient data usage and uncertainty quantification. Identifying the governing equations of complex dynamical systems from data presents a significant challenge in scientific…

Neural surrogate solvers of partial differential equations (PDEs) promise dramatic speedups over numerical methods, especially in scenarios requiring many solves. However, current accuracy-based evaluations do not fully consider two central…

In the context of computer models, calibration is the process of estimating unknown simulator parameters from observational data. Calibration is variously referred to as model fitting, parameter estimation/inference, an inverse problem, and…

Modern deterministic retrieval pipelines prioritize achieving state-of-the-art performance but often lack interpretability in decision-making. These models face challenges in assessing uncertainty, leading to overconfident predictions. To…

The tilted-wave interferometer is a promising technique for the development of a reference measurement system for the highly accurate form measurement of aspheres and freeform surfaces. The technique combines interferometric measurements,…

This article considers estimation of constant and time-varying coefficients in nonlinear ordinary differential equation (ODE) models where analytic closed-form solutions are not available. The numerical solution-based nonlinear least…

We present an efficient quantum algorithm to simulate nonlinear differential equations with polynomial vector fields of arbitrary degree on quantum platforms. Models of physical systems that are governed by ordinary differential equations…

This paper focuses on inverse problems to identify parameters by incorporating information from measurements. These generally ill-posed problems are formulated here in a probabilistic setting based on Bayes's theorem because it leads to a…

Often the regression function appearing in fields like economics, engineering, biomedical sciences obeys a system of higher order ordinary differential equations (ODEs). The equations are usually not analytically solvable. We are interested…

While deep neural networks have become the go-to approach in computer vision, the vast majority of these models fail to properly capture the uncertainty inherent in their predictions. Estimating this predictive uncertainty can be crucial,…