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Neural networks make accurate predictions but often fail to provide reliable uncertainty estimates, especially under covariate distribution shifts between training and testing. To address this problem, we propose a Bayesian framework for…

Graphical modelling techniques based on sparse selection have been applied to infer complex networks in many fields, including biology and medicine, engineering, finance, and social sciences. One structural feature of some of the networks…

Practical structural engineering problems often exhibit a significant degree of uncertainty in the material properties being used, the dimensions of the modeled structures, etc. In this paper, we consider a cantilever beam and a beam…

Machine learning classifiers are probabilistic in nature, and thus inevitably involve uncertainty. Predicting the probability of a specific input to be correct is called uncertainty (or confidence) estimation and is crucial for risk…

This paper presents a machine learning framework for Bayesian systems identification from noisy, sparse and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in differentiable…

Predicting microporosity and permeability in clastic reservoirs is a challenge in reservoir quality assessment, especially in formations where direct measurements are difficult or expensive. These reservoir properties are fundamental in…

Models under location uncertainty are derived assuming that a component of the velocity is uncorrelated in time. The material derivative is accordingly modified to include an advection correction, inhomogeneous and anisotropic diffusion…

Electronic health records (EHR) are characterized as non-stationary, heterogeneous, noisy, and sparse data; therefore, it is challenging to learn the regularities or patterns inherent within them. In particular, sparseness caused mostly by…

Linear programming is widely used for decision-making in science, engineering, and operations research, yet in many modern applications the coefficients entering the constraints and objective are not known exactly and must be learned from…

We present an information-based uncertainty quantification method for general Markov Random Fields. Markov Random Fields (MRF) are structured, probabilistic graphical models over undirected graphs, and provide a fundamental unifying…

Spectral clustering is a popular unsupervised learning technique which is able to partition unlabelled data into disjoint clusters of distinct shapes. However, the data under consideration are often experimental data, implying that the data…

In this paper, we present an approach for designing correct-by-design controllers for cyber-physical systems composed of multiple dynamically interconnected uncertain systems. We consider networked discrete-time uncertain nonlinear systems…

We continue our study [Domain Uncertainty Quantification in Computational Electromagnetics, JUQ (2020), 8:301--341] of the numerical approximation of time-harmonic electromagnetic fields for the Maxwell lossy cavity problem for uncertain…

Sparse model identification enables nonlinear dynamical system discovery from data. However, the control of false discoveries for sparse model identification is challenging, especially in the low-data and high-noise limit. In this paper, we…

Economists often rely on estimates of linear fixed effects models produced by other teams of researchers. Assessing the uncertainty in these estimates can be challenging. I propose a form of sample splitting for networks that partitions the…

Multilevel techniques are efficient approaches for solving the large linear systems that arise from discretized partial differential equations and other problems. While geometric multigrid requires detailed knowledge about the underlying…

Due to the steadily increasing relevance of machine learning for practical applications, many of which are coming with safety requirements, the notion of uncertainty has received increasing attention in machine learning research in the last…

Optimization under uncertainty deals with the problem of optimizing stochastic cost functions given some partial information on their inputs. These problems are extremely difficult to solve and yet pervade all areas of technological and…

This paper studies the sparse identification problem of unknown sparse parameter vectors in stochastic dynamic systems. Firstly, a novel sparse identification algorithm is proposed, which can generate sparse estimates based on least squares…

Neural networks (NNs) are currently changing the computational paradigm on how to combine data with mathematical laws in physics and engineering in a profound way, tackling challenging inverse and ill-posed problems not solvable with…