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A mechanistic dynamic emulator. (English) Zbl 1274.60128

Summary: In applied sciences, we often deal with deterministic simulation models that are too slow for simulation-intensive tasks such as calibration or real-time control. In this paper, an emulator for a generic dynamic model, given by a system of ordinary nonlinear differential equations, is developed. The nonlinear differential equations are linearized and Gaussian white noise is added to account for the nonlinearities. The resulting linear stochastic system is conditioned on a set of solutions of the nonlinear equations that have been calculated prior to the emulation. A path-integral approach is used to derive the Gaussian distribution of the emulated solution. The solution reveals that most of the computational burden can be shifted to the conditioning phase of the emulator and the complexity of the actual emulation step only scales like \(\mathcal O(Nn)\) in multiplications of matrices of the dimension of the state space. Here, \(N\) is the number of time-points at which the solution is to be emulated and \(n\) is the number of solutions the emulator is conditioned on.
The applicability of the algorithm is demonstrated with the hydrological model logSPM.

MSC:

60G35 Signal detection and filtering (aspects of stochastic processes)
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References:

[1] Kennedy, M. C.; O’Hagan, A., Bayesian calibration of computer models, J. Roy. Statist. Soc. B, 63, 3, 425-464 (2001) · Zbl 1007.62021
[2] Conti, S.; O’Hagan, A., Bayesian emulation of complex multi-output and dynamic computer models, J. Statist Plann. Inference, 140, 640-651 (2010) · Zbl 1177.62033
[3] Bhattacharya, S., A simulation approach to Bayesian emulation of complex dynamic computer models, Bayesian Anal., 2, 783-816 (2007) · Zbl 1331.65019
[4] Conti, S.; Gosling, J. P.; Oakley, J.; O’Hagan, A., Gaussian process emulation of dynamic computer codes, Biometrika, 96, 3, 663-676 (2009) · Zbl 1437.62015
[5] Liu, F.; West, M., A dynamic modelling strategy for Bayesian computer model emulation, J. Bayesian Anal., 4, 2, 393-412 (2009) · Zbl 1330.65034
[6] Bayarri, M. J.; Berger, J. O.; Cafeo, J.; Garcia-Donato, G.; Liu, F.; Palomo, J.; Parthasarathy, R. J.; Paulo, R.; Sacks, J.; Walsh, D., Computer model validation with functional output, Ann. Statist., 35, 5, 1874-1906 (2007) · Zbl 1144.62368
[7] Reichert, P.; White, G.; Bayarri, M. J.; Pitman, E. B., Mechanism-based emulation of dynamic simulation models: concept and application in hydrology, J. Comput. Stat. Data Anal., 55, 1638-1655 (2011) · Zbl 1328.62034
[8] Kleinert, H., Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets (2009), World Scientific Publishing: World Scientific Publishing Singapore · Zbl 1169.81001
[9] Kuczera, G.; Kavetski, D.; Franks, S.; Thyer, M., Towards a Bayesian total error analysis of conceptual rainfall-runoff models: characterising model error using storm-dependent parameters, J. Hydrology, 331, 1-2, 161-177 (2006)
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