Geostatistical Inversion
Author madsjulia
2 Stars
Updated Last
1 Year Ago
Started In
December 2016


Coverage Status

This package provides methods for inverse analysis using parameter fields that are represented using geostatistical (stochastic) methods. Currently, two geostatistical methods are implemented. One is the Principal Component Geostatistical Approach (PCGA) proposed by Kitanidis & Lee. The other utilizes a Randomized Geostatistical Approach (RGA) that builds on PCGA.

Randomized Geostatistical Approach (RGA) references:

Two versions of PCGA are implemented in this package

  • pcgadirect, which uses full matrices and direct solvers during iterations
  • pcgalsqr, which uses low rank representations of the matrices combined with iterative solvers during iterations

The RGA method, rga, can use either of these approaches using the keyword argument. That is, by doing rga(...; pcgafunc=GeostatInversion.pcgadirect) or rga(...; pcgafunc=GeostatInversion.pcgalsqr).

GeostatInversion is a module of MADS.


import GeostatInversion

Ns = map(x->round(Int, 25 * x), 1 + rand(N))
k0 = randn()
dk = rand()
beta = -2 - rand()
k = GeostatInversion.FFTRF.powerlaw_structuredgrid(Ns, k0, dk, beta)


MADS (Model Analysis & Decision Support) is an integrated open-source high-performance computational (HPC) framework in Julia. MADS can execute a wide range of data- and model-based analyses:

  • Sensitivity Analysis
  • Parameter Estimation
  • Model Inversion and Calibration
  • Uncertainty Quantification
  • Model Selection and Model Averaging
  • Model Reduction and Surrogate Modeling
  • Machine Learning and Blind Source Separation
  • Decision Analysis and Support

MADS has been tested to perform HPC simulations on a wide-range multi-processor clusters and parallel environments (Moab, Slurm, etc.). MADS utilizes adaptive rules and techniques which allows the analyses to be performed with a minimum user input. The code provides a series of alternative algorithms to execute each type of data- and model-based analyses.


All the available MADS modules and functions are described at



Installation behind a firewall

Julia uses git for the package management. To install Julia packages behind a firewall, add the following lines in the .gitconfig file in your home directory:

[url "https://"]
        insteadOf = git://

or execute:

git config --global url."https://".insteadOf git://

Set proxies:

export ftp_proxy=http://proxyout.<your_site>:8080
export rsync_proxy=http://proxyout.<your_site>:8080
export http_proxy=http://proxyout.<your_site>:8080
export https_proxy=http://proxyout.<your_site>:8080
export no_proxy=.<your_site>

For example, if you are doing this at LANL, you will need to execute the following lines in your bash command-line environment:

export ftp_proxy=
export rsync_proxy=
export http_proxy=
export https_proxy=

MADS examples

In Julia REPL, do the following commands:

import Mads

To explore getting-started instructions, execute:

There are various examples located in the examples directory of the Mads repository.

For example, execute

include(Mads.madsdir * "/../examples/contamination/contamination.jl")

to perform various example analyses related to groundwater contaminant transport, or execute

include(Mads.madsdir * "/../examples/bigdt/bigdt.jl")

to perform Bayesian Information Gap Decision Theory (BIG-DT) analysis.



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