A hybrid stochastic-deterministic model calibration method with application to subsurface CO2 storage in geological formations
Final Report Abstract
One of the main outcomes of this project is a new method for solving Bayesian inverse problems. It is based on Gaussian process emulators and employs a sequential sampling strategy (=sequential design of computer experiments). The method works best on inverse problems with a low to moderate number of parameters (10 or less). It is specifically designed for problems with computationally expensive model functions in the sense that it tries to solve the inverse problem with as few model evaluations as possible. Thanks to the sequential sampling strategy, our new method proves to be more efficient, considered from point of view of the required iterations/model evaluations, than methods based on space-filling sampling strategies. This has been confirmed in a number of numerical experiments. As part of this project, our method has then been extended by two features that make it even more powerful. First, it implements a novel way of identifying Gaussian process hyperparameters and is therefore especially user-friendly. Second, if a fast approximation of the model function is available, then our method can take this into account and work as a multi-level method. The multi-level variant of the method is typically faster than the corresponding single-level variant. Furthermore, our method has been adapted to solve two other, related problem types: Bayesian model selection and Bayesian optimization. The methods for Bayesian inverse problems and for Bayesian model selection are available in a python package we called bali (Bayesian likelihood estimation). It is written as a toolbox such that it can be applied to new problems easily. The other outcome is the development of another new hybrid method combining the PCE based stochastic method and the indirect deterministic method, as it was planned originally in the proposal. The method could be applied successfully to the model problem for identifying the two parameters, the porosity and the permeability. From the results obtained, we can say that the new method uses advantages of both the methods and the resulting method is more efficient and stable from both the original methods.
Publications
- Sequential Design of Computer Experiments for the Solution of Bayesian Inverse Problems, SIAM/ASA Journal on Uncertainty Quantification, 5 (2017), pp. 640–664
M. Sinsbeck and W. Nowak
(See online at https://doi.org/10.1137/15M1047659) - Exploratory-phase-free estimation of GP hyperparameters in sequential design methods - at the example of Bayesian inverse problems, Frontiers in Artificial Intelligence, 13 (2020), 1–16
M. Sinsbeck and W. Nowak
(See online at https://doi.org/10.3389/frai.2020.00052) - Sequential design of computer experiments for the computation of Bayesian model evidence, SIAM/ASA Journal on Uncertainty Quantification, 9(1) (2020), pp.260–279
M. Sinsbeck, E. Cooke, and W. Nowak
(See online at https://doi.org/10.1137/20M1320432)
