Multi-index sequential monte carlo methods for partially observed stochastic partial differential equations
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Computer, Electrical and Mathematical Science and Engineering Division, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Saudi Arabia
KAUST Grant NumberCRG4 grant ref: 2584
Preprint Posting Date2018-05-01
Embargo End Date2022-04-21
Permanent link to this recordhttp://hdl.handle.net/10754/661011
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AbstractIn this paper we consider sequential joint state and static parameter estimation given discrete time observations associated to a partially observed stochastic partial differential equation. It is assumed that one can only estimate the hidden state using a discretization of the model. In this context, it is known that the multi-index Monte Carlo (MIMC) method can be used to improve over direct Monte Carlo from the most precise discretizaton. However, in the context of interest, it cannot be directly applied, but rather must be used within another method such as sequential Monte Carlo (SMC). We show how one can use the MIMC method by renormalizing the standard identity and approximating the resulting identity using the SMC2 method, which is an exact method that can be used in this context. We prove that our approach can reduce the cost to obtain a given mean square error, relative to just using SMC2 on the most precise discretization. We demonstrate this with some numerical examples.
CitationJasra, A., Law, K. J. H., & Xu, Y. (2021). MULTI-INDEX SEQUENTIAL MONTE CARLO METHODS FOR PARTIALLY OBSERVED STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS. International Journal for Uncertainty Quantification, 11(3), 1–25. doi:10.1615/int.j.uncertaintyquantification.2020033219
SponsorsWe would like to thank Abdul-Lateef Haji-Ali for useful discussions relating to the material in this paper. A.J. was supported by a KAUST CRG4 grant ref: 2584 and KAUST baseline funding. K.J.H.L. and A.J. were supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research (ASCR), under field work proposal number ERKJ333. K.J.H.L. was additionally supported by The Alan Turing Institute under the EPSRC grant EP/N510129/1. He was also funded in part by Oak Ridge National Laboratory Directed Research and Development Seed funding.