Spatiotemporal-inverse-problem

Bayesian spatiotemporal modeling for inverse problems (B-STIP)

https://arxiv.org/abs/2204.10929

software preparation

• FEniCS Go to this webpage for installation.

• hIPPYlib Go to this webpage for installation.

• It is recommended to use Conda to install FEniCS and pip to install hIPPYlib. Create a FEniCS environment. Load FEniCS environment in terminal session and include hIPPYlib in PYTHONPATH for that session. Alternatively, install hIPPYlib directly in the FEniCS environment.

package structure

• adv-diff contains files for advection-diffusion inverse problem (requires FEniCS and hIPPYlib).

  • run_advdiff_geoinfMC.py to collect samples using geometric infinite-dimensional MCMC algorithms (pCN, inf-MALA and inf-HMC).
  • plot_mcmc_estimates_comparelik.py to plot MCMC estimates (mean and standard deviation) for different likelihood models.
  • get_mcmc_rem_comparelik.py to generate table comparing relative errors of posterior mean between different likelihood models.
  • get_prederr_comparelik.py to generate table comparing prediction errors of forward outputs between different likelihood models.
  • plot_predictions_comparelik.py to plot forward prediction at selective locations and compare the truth covering rate of credible bands.

• chaotic dynamical inverse problems contain 3 chaotic dynamics Lorenz(63), Rossler and Chen each having:

  • run_XXX_EnK.py to collect ensembles using ensemble Kalman (EnK) methods (EKI and EKS).
  • run_XXX_EnK_spinavgs.py to run EnK algorithms by varying spin-up length t<sub>0</sub> and observation window size T.
  • get_enk_rem_comparelik.py to generate table comparing relative errors of posterior mean between different likelihood models.
  • plot_enk_rem_comparelik.py to plot relative errors of mean by EnK between different likelihood models.
  • plot_enk_rem_spinavgs.py to plot relative errors of mean for different spin-up lengths and window sizes between different likelihood models.
  • plot_predictions_comparelik.py to plot forward predictions.
  • prep_traindata.py to extract training data for NN emulator from EnK outputs.
  • run_XXX_einfGMC.py to run MCMC algorithms based on NN emulators.
  • plot_postdist.py to plot marginal and pairwise posterior densities based on emulative MCMC samples.

• optimizer contains ensemble Kalman algorithms as optimization (EKI) or approximate sampling (EKS) methods.

  • EnK.py: Ensemble Kalman algorithms

• sampler contains different MCMC algorithms

  • geoinfMC.py: infinite-dimensional Geometric Monte Carlo.
  • geoinfMC_dolfin.py: infinite-dimensional Geometric Monte Carlo (working with dolfin in FEniCS).

• util contains utility functions supplementary to dolfin package in FEniCS.

  • stgp: spatiotemporal Gaussian process models.

• nn contains neural network definitions:

  • dnn: densely connected neural network.
  • dnn_rnn: DNN-RNN (recurrent neural network) type of network.

• Simple likelihood method refers to either static model (adv-diff) or time-averaged approach (chaotic dynamics).