Related papers: Iterative Methods for Scalable Uncertainty Quantif…

Using the dynamics of information propagation on a network as our illustrative example, we present and discuss a systematic approach to quantifying heterogeneity and its propagation that borrows established tools from Uncertainty…

Resilience characterizes a system's ability to retain its original function when perturbations happen. In the past years our attention mainly focused on small-scale resilience, yet our understanding of resilience in large-scale network…

Statistical learning algorithms provide a generally-applicable framework to sidestep time-consuming experiments, or accurate physics-based modeling, but they introduce a further source of error on top of the intrinsic limitations of the…

Resilience is a system's ability to maintain its function when perturbations and errors occur. Whilst we understand low-dimensional networked systems' behavior well, our understanding of systems consisting of a large number of components is…

Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the…

Robustness analysis is very important in biology and neuroscience, to unravel behavioural patterns of systems that are conserved despite large parametric uncertainties. To make studies of probabilistic robustness more efficient and scalable…

This paper considers robust stability analysis of a large network of interconnected uncertain systems. To avoid analyzing the entire network as a single large, lumped system, we model the network interconnections with integral quadratic…

Uncertainty quantification in automated image analysis is highly desired in many applications. Typically, machine learning models in classification or segmentation are only developed to provide binary answers; however, quantifying the…

Growing uncertainty from renewable energy integration and distributed energy resources motivate the need for advanced tools to quantify the effect of uncertainty and assess the risks it poses to secure system operation. Polynomial chaos…

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…

Predictive uncertainty estimation remains a challenging problem precluding the use of deep neural networks as subsystems within safety-critical applications. Aleatoric uncertainty is a component of predictive uncertainty that cannot be…

Control and estimation on large-scale social networks often necessitate the availability of models for the interactions amongst the agents. However characterizing accurate models of social interactions pose new challenges due to inherent…

Uncertainty quantification for full-waveform inversion provides a probabilistic characterization of the ill-conditioning of the problem, comprising the sensitivity of the solution with respect to the starting model and data noise. This…

In the presence of modeling errors, the mainstream Bayesian methods seldom give a realistic account of uncertainties as they commonly underestimate the inherent variability of parameters. This problem is not due to any misconception in the…

Existing methods for estimating uncertainty in deep learning tend to require multiple forward passes, making them unsuitable for applications where computational resources are limited. To solve this, we perform probabilistic reasoning over…

Classical problems in computational physics such as data-driven forecasting and signal reconstruction from sparse sensors have recently seen an explosion in deep neural network (DNN) based algorithmic approaches. However, most DNN models do…

For many applications it is critical to know the uncertainty of a neural network's predictions. While a variety of neural network parameter estimation methods have been proposed for uncertainty estimation, they have not been rigorously…

Compressive sensing has become a powerful addition to uncertainty quantification when only limited data is available. In this paper we provide a general framework to enhance the sparsity of the representation of uncertainty in the form of…

In modern engineering, physical processes are modelled and analysed using advanced computer simulations, such as finite element models. Furthermore, concepts of reliability analysis and robust design are becoming popular, hence, making…

A particularly challenging problem in AI safety is providing guarantees on the behavior of high-dimensional autonomous systems. Verification approaches centered around reachability analysis fail to scale, and purely statistical approaches…