In this repository, we show the dimension independence of the infinite-dimensional MCMC algorithms, including pCN and pCNL, for the steady-state Darcy flow problem. The implementation recovers the figures in Subsection 3.4 of the paper "无限维贝叶斯反演理论与算法"(Infinite-dimensional Bayesian inverse theories and algorithms) written in Chinese. The general references of these algorithms:
- S. L. Cotter, G. O. Roberts, A. M. Stuart and D. White, MCMC Methods for Functions: Modifying Old Algorithms to Make Them Faster, Statistical Science, 2013
- M. Dashti, A. M. Stuart, The Bayesian Approch to Inverse Problems, Hankbook of Uncertainty Quantification, 2017 The discretized methods are illustrated in the following paper:
- T. Bui-Thanh, O. Ghattas, J. Martin, G. Stadler, A computational framework for infinite-dimensional Bayesian inverse problems part I: The linearized case, with application to global seismic inversion, SIAM J. Sci. Comput., 2013
You need to run the programs in the following order:
- DarcyFlow/generate_data.py
- DarcyFlow/MCMC/VanillaMCMC_dim_compare.py
- DarcyFlow/MCMC/pCN_dim_independence.py
- DarcyFlow/MCMC/pCN_dim_wrong_prior.py
- DarcyFlow/MCMC/pCNL_dim_independence.py
- DarcyFlow/MCMC/draw.py
The figure will be stored in the folder DarcyFlow/MCMC/results/
To run the program, you need to install FEniCSx(Version 0.7) https://fenicsproject.org/, numpy, scipy, and matplotlib.