Uncertainty Quantification with Support Vector Regression Prediction Models

Vasily Demyanov1, Alexei Pozdnoukhov2, Mikhail Kanevski3, Mike Christie1

1. Institute of Petroleum Engineering, Heriot-Watt University, Edinburgh, UK
2. National Centre for Geocomputation, National University of Ireland, Maynooth, Ireland
3. Institute of Geomatics and Risk Analysis, University of Lausanne, Switzerland
1. { vasily.demyanov, mike.christie }@pet.hw.ac.uk
2. alexei.pozdnoukhov@nuim.ie
3. Mikhail.Kanevski@unil.ch

Abstract: Uncertainty quantification of petroleum reservoir models is one of the present challenges, which is usually approached with a wide range of geostatistical tools linked with statistical optimisation or/and inference algorithms. The paper considers a data driven approach in modelling uncertainty in spatial predictions. Proposed semi-supervised Support Vector Regression (SVR) model has demonstrated its capability to represent realistic features and describe stochastic variability and non-uniqueness of spatial properties. It is able to capture and preserve key spatial dependencies such as connectivity, which is often difficult to achieve with two-point geostatistical models. Semi-supervised SVR is designed to integrate various kinds of conditioning data and learn dependences from them. A stochastic semi-supervised SVR model is integrated into a Bayesian framework to quantify uncertainty with multiple models fitted to dynamic observations. The developed approach is illustrated with a reservoir case study. The resulting probabilistic production forecasts are described by uncertainty envelopes.

Keywords: uncertainty; prediction; petroleum; machine learning; support vectors; data integration

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