Ensemble-marginalized Kalman filter for linear time-dependent PDEs with noisy boundary conditions: Application to heat transfer in building walls.

Ensemble-marginalized Kalman filter for linear time-dependent PDEs with noisy boundary conditions: Application to heat transfer in building walls.

Iglesias, Marco, Zaid Sawlan, Marco Scavino, Raul Tempone, and Christopher Wood. "Ensemble-marginalized Kalman filter for linear time-dependent PDEs with noisy boundary conditions: Application to heat transfer in building walls." Inverse Problems 34, no. 7 (2018): 075008.​
Iglesias, Marco, Zaid Sawlan, Marco Scavino, Raul Tempone, and Christopher Wood.
Ensemble Kalman filter, linear PDEs, heat equation, nuisance boundary parameters marginalization, heat flux measurements, thermal resistance, heat capacity
2018
In this work, we present the ensemble-marginalized Kalman filter (EnMKF), a sequential algorithm analogous to our previously proposed approach (Ruggeri et al 2017 Bayesian Anal. 12 407–33, Iglesias et al 2018 Int. J. Heat Mass Transfer 116 417–31), for estimating the state and parameters of linear parabolic partial differential equations in initial-boundary value problems when the boundary data are noisy. We apply EnMKF to infer the thermal properties of building walls and to estimate the corresponding heat flux from real and synthetic data. Compared with a modified ensemble Kalman filter (EnKF) that is not marginalized, EnMKF reduces the bias error, avoids the collapse of the ensemble without needing to add inflation, and converges to the mean field posterior using 50 %  or less of the ensemble size required by EnKF. According to our results, the marginalization technique in EnMKF is key to performance improvement with smaller ensembles at any fixed time.