A non-Gaussian Bayesian filter for sequential data assimilation with non-intrusive polynomial chaos expansion

Avasarala, S and Subramani, D (2021) A non-Gaussian Bayesian filter for sequential data assimilation with non-intrusive polynomial chaos expansion. In: International Journal for Numerical Methods in Engineering .

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Abstract

Non-Gaussian data assimilation is vital for several applications with nonlinear dynamical systems, including geosciences, socio-economics, infectious disease modeling, and autonomous navigation. Widespread adoption of non-Gaussian data assimilation requires easy-to-implement schemes. We develop, implement, and apply an efficient nonlinear non-Gaussian data assimilation scheme using non-intrusive stochastic collocation-based polynomial chaos expansion (PCE) and Gaussian mixture model (GMM) priors fit to the state's uncertainty. First, we represent the uncertainty in a dynamical system using PCE and propagate it using the stochastic collocation method until an assimilation time. Then, we convert the polynomial basis prior to its equivalent Karhunen�Loeve (KL) form, fit a GMM in the subspace and perform a Bayesian filtering step. Thereafter, the posterior polynomial basis is recovered from the posterior GMM in the KL form, and uncertainty propagation is continued using the stochastic collocation method. The derivation and new equations required for the above conversions are presented. We apply the new scheme to an illustrative population growth dynamics application and a complex fluid flow problem for demonstrating its capabilities. In both cases, our filter accurately captures the non-Gaussian statistics compared to the polynomial chaos-ensemble Kalman filter and the polynomial chaos-error subspace statistical estimation filter. © 2021 John Wiley & Sons, Ltd.

Item Type:	Journal Article
Publication:	International Journal for Numerical Methods in Engineering
Publisher:	John Wiley and Sons Ltd
Additional Information:	The copyright for this article belongs to John Wiley and Sons Ltd
Keywords:	Dynamical systems; Flow of fluids; Gaussian noise (electronic); Kalman filters; Nonlinear dynamical systems; Polynomials; Population statistics; Probability density function; Stochastic models; Stochastic systems; Uncertainty analysis, Chaos expansions; Data assimilation; Fluid-dynamics; Gaussian Mixture Model; Non-Gaussian data; Non-intrusive; Polynomial chaos; Population growth models; Uncertainty; Uncertainty quantifications, Gaussian distribution
Department/Centre:	Division of Interdisciplinary Sciences > Computational and Data Sciences
Date Deposited:	29 Nov 2021 08:32
Last Modified:	29 Nov 2021 08:32
URI:	http://eprints.iisc.ac.in/id/eprint/70312

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