A stochastic simplex approximate gradient (StoSAG) for optimization under uncertainty

A stochastic simplex approximate gradient (StoSAG) for optimization under uncertainty

Fonseca, R.M. (TU Delft Reservoir Engineering)
Chen, B (University of Tulsa)
Jansen, J.D. (TU Delft Civil Engineering & Geosciences; TU Delft Geoscience and Engineering)
Reynolds, Albert C. (University of Tulsa)

Civil Engineering & Geosciences

Geoscience and Engineering

2016

We consider a technique to estimate an approximate gradient using an ensemble of randomly chosen control vectors, known as Ensemble Optimization (EnOpt) in the oil and gas reservoir simulation community. In particular, we address how to obtain accurate approximate gradients when the underlying numerical mod- els contain uncertain parameters because of geological uncertainties. In that case, ‘robust optimization’ is performed by optimizing the expected value of the objective function over an ensemble of geological mod- els. In earlier publications, based on the pioneering work of Chen et al. (2009), it has been suggested that a straightforward one-to-one combination of random control vectors and random geological models is capa- ble of generating sufficiently accurate approximate gradients. However, this form of EnOpt does not always yield satisfactory results. In a recent article, Fonseca et al. (2015) formulate a modified EnOpt algorithm, referred to here as a Stochastic Simplex Approximate Gradient (StoSAG; in earlier publications referred to as ‘modified robust EnOpt’) and show, via computational experiments, that StoSAG generally yields significantly better gradient approximations than the standard EnOpt algorithm. Here, we provide theoreti- cal arguments to show why StoSAG is superior to EnOpt

Approximate gradient
Stochastic gradient
Ensemble optimization
Robust optimization
StoSAG

http://resolver.tudelft.nl/uuid:a446a27d-f51f-4b66-9014-2d2d8039b0d5

https://doi.org/10.1002/nme.5342

0029-5981

International Journal for Numerical Methods in Engineering, 109 (13), 1756-1776

Institutional Repository

journal article

© 2016 R.M. Fonseca, B Chen, J.D. Jansen, Albert C. Reynolds