Calibrate Emulate Sample (CES)

Tools for Ensemble Kalman Inversion (EKI), Ensemble Kalman Sampler (EKS) and Gaussian Process Emulation (using Gpflow) for Uncertainty Quantification in inverse problems.

⚠️ Note: Outdated examples can be found as jupyter notebooks.⚠️

To import the module into a python script or project, type

import sys
sys.path.append(<your path/ces/>)

# to load test cases 
from ces.utils import *

# to load the calibration code (EKS)
from ces.calibrate import *

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Overview:

• enka contains the ensemble Kalman algorithms.
• utils contains the additional tools for running the examples. Like test functions, and PDEs constrained functions. The goal is to solve inverse problems through an approximate Bayesian method.

The provided code can be used for the following:

• MCMC through Metropolis Hastings.
• Accelerated MCMC using GPs as surrogate models.

Dependencies:

• tqdm
• numpy
• gpflow
• scipy
• pandas

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References:

• Garbuno-Inigo, A., Nüsken, N., & Reich, S. (2020). Affine invariant interacting Langevin dynamics for Bayesian inference. SIAM Journal on Applied Dynamical Systems, 19(3), 1633-1658.

• Garbuno-Inigo, A., Hoffmann, F., Li, W., & Stuart, A. M. (2020). Interacting Langevin diffusions: Gradient structure and ensemble Kalman sampler. SIAM Journal on Applied Dynamical Systems, 19(1), 412-441.

• Iglesias, M. A., Law, K. J., & Stuart, A. M. (2013). Ensemble Kalman methods for inverse problems. Inverse Problems, 29(4), 045001.