H44B-01
An automated construction of error models for uncertainty quantification and model calibration

Thursday, 17 December 2015: 16:00
3014 (Moscone West)
Laureline Josset, University of Lausanne, Lausanne, Switzerland and Ivan Lunati, University of Lausanne, Institute of Earth Sciences, Lausanne, Switzerland
Abstract:
To reduce the computational cost of stochastic predictions, it is common practice to rely on approximate flow solvers (or «proxy»), which provide an inexact, but computationally inexpensive response [1,2]. Error models can be constructed to correct the proxy response: based on a learning set of realizations for which both exact and proxy simulations are performed, a transformation is sought to map proxy into exact responses. Once the error model is constructed a prediction of the exact response is obtained at the cost of a proxy simulation for any new realization.
Despite its effectiveness [2,3], the methodology relies on several user-defined parameters, which impact the accuracy of the predictions. To achieve a fully automated construction, we propose a novel methodology based on an iterative scheme: we first initialize the error model with a small training set of realizations; then, at each iteration, we add a new realization both to improve the model and to evaluate its performance.

More specifically, at each iteration we use the responses predicted by the updated model to identify the realizations that need to be considered to compute the quantity of interest. Another user-defined parameter is the number of dimensions of the response spaces between which the mapping is sought. To identify the space dimensions that optimally balance mapping accuracy and risk of overfitting, we follow a Leave-One-Out Cross Validation. Also, the definition of a stopping criterion is central to an automated construction. We use a stability measure based on bootstrap techniques to stop the iterative procedure when the iterative model has converged.

The methodology is illustrated with two test cases in which an inverse problem has to be solved and assess the performance of the method. We show that an iterative scheme is crucial to increase the applicability of the approach.

[1] Josset, L., and I. Lunati, Local and global error models for improving uncertainty quantification, Math.ematical Geosciences, 2013
[2] Josset, L., D. Ginsbourger, and I. Lunati, Functional Error Modeling for uncertainty quantification in hydrogeology, Water Resources Research, 2015
[3] Josset, L., V. Demyanov, A.H. Elsheikhb, and I. Lunati, Accelerating Monte Carlo Markov chains with proxy and error models, Computer & Geosciences, 2015 (In press)
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