Abstract
The paper proposes an approach aimed at detecting optimal model parameter combinations to achieve the most representative description of uncertainty in the model performance. A classification problem is posed to find the regions of good fitting models according to the values of a cost function. Support Vector Machine (SVM) classification in the parameter space is applied to decide if a forward model simulation is to be computed for a particular generated model. SVM is particularly designed to tackle classification problems in high-dimensional space in a non-parametric and non-linear way. SVM decision boundaries determine the regions that are subject to the largest uncertainty in the cost function classification, and, therefore, provide guidelines for further iterative exploration of the model space. The proposed approach is illustrated by a synthetic example of fluid flow through porous media, which features highly variable response due to the parameter values’ combination.
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Carter JN, Ballester PJ, Tavassoli Z, King PR (2004) Our calibrated model has no predictive value: an example from the petroleum industry. Proceedings of the Fourth International Conference on Sensitivity Analysis
Christie M, Demyanov V, Erbas D (2006) Uncertainty quantification for porous media flows. J Comput Phys 217:143–158
Demyanov V (2007) Neural network guided sampling for uncertainty quantification of production forecasts. Presentation at UFORDS, Scarborough
Demyanov V, Wood SN, Kedwards TJ (2006) Improving ecological impact assessment by statistical data synthesis using process based models. J Royal Stat Soc, Appl Stat (Ser C) 55(1, Part 1):41–62
Erbaş D (2006) Sampling strategies for uncertainty quantification in oil recovery prediction. Thesis for the Degree of Doctor of Philosophy, Heriot-Watt University, August 2006
Hastie T, Tibshirani R, Friedman J (2001) The elements of statistical learning. Springer, New York
Haykin S (1999) Neural networks: a comprehensive foundation. Pearson Higher Education, New Delhi
Kanevski M, Pozdnoukhov A, Timonin V (2009) Machine learning algorithms for geoSpatial data. 369, EPFL Press, Switzerland, p 300
Platt J (1999) Probabilistic outputs for support vector machines and comparison to regularized likelihood methods. In: Smola AJ, Bartlett P, Scholkopf B, Schuurmans (eds) Advances in large margin classifiers. MIT Press, Cambridge, MA
Pozdnoukhov A, Kanevski M (2007). Interactive monitoring network optimization using support vector machines. In Spatial Statistics and GIS conference (Stat-GIS 2007), Klagenfurt
Sambridge M (1999) Geophysical inversion with a neighbourhood algorithm – I. Searching a parameter space. Geophys J Int 138:479–494
Scholkopf B, Smola AJ (2002) Learning with kernels. MIT press, Cambridge, MA
Subbey S, Christie MA, Sambridge M (2002) Uncertainty reduction in reservoir modelling. In: Chen Z, Ewing RE (eds) Fluid flow and transport in porous media: mathematical and numerical treatment. American Mathematical Society Contemporary Mathematics Monograph, Providence, Rhode Island, pp 457–467
Tavassoli Z, Carter JN, King PR (2004) Errors in history matching, SPE Journal, September 2004, pp 352–361
Vapnik V (1995) The nature of statistical learning theory. Springer, New York
Acknowledgements
Funding of this work was provided by UK Engineering and Physical Sciences Research Council (GR/T24838/01) and by the industrial sponsors of the Heriot-Watt Uncertainty Project.
The authors acknowledge Swiss National Science Foundation funding “GeoKernels: kernel-based methods for geo and environmental sciences” project N∘200021 − 113944.
The authors would like to thank J. Carter of Imperial College for providing the model and the data for the IC Fault case study.
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Demyanov, V., Pozdnoukhov, A., Christie, M., Kanevski, M. (2010). Detection of Optimal Models in Parameter Space with Support Vector Machines. In: Atkinson, P., Lloyd, C. (eds) geoENV VII – Geostatistics for Environmental Applications. Quantitative Geology and Geostatistics, vol 16. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2322-3_30
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DOI: https://doi.org/10.1007/978-90-481-2322-3_30
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