Dimension and model reduction approaches for linear Bayesian inverse problems with rank-deficient prior covariances
This MATLAB repository contains code for the numerical results of the following paper:
- König, J., Qian E., Freitag, M. A. "Dimension and model reduction approaches for linear Bayesian inverse problems with rank-deficient prior covariances."
The work in [1] proposes balanced truncation (BT) of a new prior-driven LTI system for model reduction in linear Bayesian inference, particularly suitable for a rank-deficient prior covariance. Numerical examples compare the performance with BT-based Bayesian model reduction from [2] and the optimal dimension reduction from [3], both rewritten for a rank-deficient prior. This work uses code from [2] (to be found at https://github.com/elizqian/balancing-bayesian-inference).
To run this code, you need the MATLAB Control System Toolbox.
To generate the plots from the paper for an incompatible prior (on the left side in Figures 1-3), run the ISS_LR_incompat.m script.
To generate the plots from the paper for a compatible prior (on the right side in Figures 1-3), run the ISS_LR_compat.m script.
- Qian, E., Tabeart, J. M., Beattie, C., Gugercin, S., Jiang, J., Kramer, P. R., and Narayan, A. "Model reduction for linear dynamical systems via balancing for Bayesian inference." Journal of Scientific Computing 91.29 (2022).
- Spantini, A., Solonen, A., Cui, T., Martin, J., Tenorio, L., and Marzouk, Y. "Optimal low-rank approximations of Bayesian linear inverse problems." SIAM Journal on Scientific Computing 37. 6 (2015): A2451-A2487.
Please feel free to contact Josie König with any questions about this repository or the associated paper.