A backward SDE method for uncertainty quantification in deep learning

Forward and Backward Uncertainty Quantification in Optimization

This contribution gathers some of the ingredients presented during the Iranian Operational Research community gathering in Babolsar in 2019.It is a collection of several previous publications on how to set up an uncertainty quantification (UQ) cascade with ingredients of growing computational complexity for both forward and reverse uncertainty propagation.

Forward-backward SDE games and stochastic control under model uncertainty

We study optimal stochastic control problems under model uncertainty. We rewrite such problems as (zero-sum) stochastic differential games of forward-backward stochastic differential equations. We prove general stochastic maximum principles for such games, both in the zero-sum case (finding conditions for saddle points) and for the non-zero sum games (finding conditions for Nash equilibria). We...

Bayesian Deep Learning | Uncertainty in Deep Learning

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 ...

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...