Kernel embedded nonlinear observational mappings in the variational mapping particle filter

Pulido, M., Van Leeuwen, P. J. and Posselt, D. J. (2019) Kernel embedded nonlinear observational mappings in the variational mapping particle filter. In: ICCS 2019, 12-14 Jun 2019, Faro, Portugal, pp. 141-155. doi: 10.1007/978-3-030-22747-0_11

Abstract/Summary

Recently, some works have suggested methods to combine variational probabilistic inference withMonte Carlo sampling. One promis- ing approach is via local optimal transport. In this approach, a gradient steepest descent method based on local optimal transport principles is formulated to transform deterministically point samples from an interme- diate density to a posterior density. The local mappings that transform the intermediate densities are embedded in a reproducing kernel Hilbert space (RKHS). This variational mapping method requires the evaluation of the log-posterior density gradient and therefore the adjoint of the ob- servational operator. In this work, we evaluate nonlinear observational mappings in the variational mapping method using two approximations that avoid the adjoint, an ensemble based approximation in which the gradient is approximated by the particle covariances in the state and observational spaces the so-called ensemble space and an RKHS approx- imation in which the observational mapping is embedded in an RKHS and the gradient is derived there. The approximations are evaluated for highly nonlinear observational operators and in a low-dimensional chaotic dynamical system. The RKHS approximation is shown to be highly successful and superior to the ensemble approximation.

Item Type	Conference or Workshop Item (Paper)
URI	https://reading-clone.eprints-hosting.org/id/eprint/86234
Identification Number/DOI	10.1007/978-3-030-22747-0_11
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > National Centre for Earth Observation (NCEO) Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
Publisher	Springer
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