DEEP LEARNING OF PARAMETERIZED EQUATIONS WITH APPLICATIONS TO UNCERTAINTY QUANTIFICATION

Applications | Uncertainty in Deep Learning

In previous chapters we linked stochastic regularisation techniques (SRTs) to approximate inference in Bayesian neural networks (NNs), and studied the resulting model uncertainty for popular SRTs such as dropout. We have yet to give any real-world applications stemming from this link though, leaving it somewhat in the realms of “theoretical work”. But a theory is worth very little if we can’t u...

Uncertainty Quantification for Kinetic Equations

Kinetic equations contain uncertainties in their collision kernels or scattering coefficients, initial or boundary data, forcing terms, geometry, etc. Quantifying the uncertainties in kinetic models have important engineering and industrial applications. In this article we survey recent efforts in the study of kinetic equations with random inputs, including their mathematical properties such as...

Bayesian Deep Learning | Uncertainty in Deep Learning

Uncertainty in Deep Learning

Deep learning has attracted tremendous attention from researchers in various fields of information engineering such as AI, computer vision, and language processing [Kalchbrenner and Blunsom, 2013; Krizhevsky et al., 2012; Mnih et al., 2013], but also from more traditional sciences such as physics, biology, and manufacturing [Anjos et al., 2015; Baldi et al., 2014; Bergmann et al., 2014]. Neural...

Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantification

State-of-the-art computer codes for simulating real physical systems are often characterized by vast number of input parameters. Performing uncertainty quantification (UQ) tasks with Monte Carlo (MC) methods is almost always infeasible because of the need to perform hundreds of thousands or even millions of forward model evaluations in order to obtain convergent statistics. One, thus, tries to ...