Márk Somogyvári | Searcharxiv

arXiv2026

Transdimensional Data Assimilation for dynamic model selection problems

In this paper we combine the non-linear filtering capabilities of particle filters with the transdimensional inference of the reversible-jump Markov chain Monte Carlo method for a data assimilation methodology over dynamic problems with variable dimensionality. By using transdimensional MCMC steps for the rejuvenation of the particle filter, the algorithm could change the number of state space parameters on the fly and can be applied for transdimensional data assimilation purposes. Classic inversion methodologies use pre-defined models, and only changes the individual parameter values during interpretation. This is often not feasible when the optimal model parametrization is not known a priori or when the model resolution needs to change with time. The proposed transdimensional particle filter algorithm, combines the advantages of particle filters and the transdimensional MCMC methods, and provides an easily implementable data assimilation algorithm that could tackle such problems. The methodology could also improve the computational efficiency of particle filters as it could inherently optimize the model complexity in a data-driven way. We demonstrate the capabilities of the enhanced algorithm on two simple model examples.

physics.geo-ph↗

arXiv2019

Convergence Tests for Transdimensional Markov Chains in Geoscience Imaging

Classic inversion methods adjust a model with a predefined number of parameters to the observed data. With transdimensional inversion algorithms such as the reversible-jump Markov Chain Monte Carlo (rjMCMC), it is possible to vary this number during the inversion and to interpret the observations in a more flexible way. Geoscience imaging applications use this behaviour to automatically adjust model resolution to the inhomogeneities of the investigated system, while keeping the model parameters on an optimal level. The rjMCMC algorithm produces an ensemble as result, a set of model realizations which together represent the posterior probability distribution of the investigated problem. The realizations are evolved via sequential updates from a randomly chosen initial solution, and converge toward the target posterior distribution of the inverse problem. Up to a point in the chain, the realizations may be strongly biased by the initial model, and have to be discarded from the final ensemble. With convergence assessment techniques, this point in the chain can be identified. Transdimensional MCMC methods produce ensembles which are not suitable for classic convergence assessment techniques because of the changes in parameter numbers. To overcome this hurdle, three solutions are introduced to convert model realizations to a common dimensionality while maintaining the statistical characteristics of the ensemble. A scalar, a vector and a matrix representation for models is presented, inferred from tomographic subsurface investigations, and three classic convergence assessment techniques are applied on them. It is shown that appropriately chosen scalar conversions of the models could retain similar statistical ensemble properties as geologic projections created by rasterization.

physics.geo-ph↗