Mads methods
# **MADS** Methods
* [Model analyses](#model-analyses)
* [Decision support](#decision-support)
* [Contaminant transport simulators](#contaminant-transport-simulators)
* [Test functions](#test-functions)
### Model analyses
**MADS** includes a wide range of techniques for model-based analyses that can perform local and global exploration of model parameter space:
* Optimization techniques for Parameter Estimation (**PE**), Model Inversion, Model Calibration, and Decision Support (**DS**)
* Several different implementations of the local Levenberg-Marquardt (**LM**) optimization technique: [GSL](http://www.gnu.org/s/gsl/), [IMSL](http://www.roguewave.com/products/imsl-numerical-libraries.aspx), [LevMar](http://www.ics.forth.gr/~lourakis/levmar/).
The Levenberg-Marquardt (**LM**) optimization technique can be performed using [acceleration and delayed gratification approaches](http://link.aps.org/doi/10.1103/PhysRevE.83.036701).
In **LM**, the inversion of Jacobian (sensitivity) matrix can be performed using a wide range of techniques: BK (Bunch and Kaufman), LU, QR, QRLS, Cholesky, and SVD (singular value) decompositions using LAPACK and SVDPACK libraries.
**SVD decomposition** allows for highly-parameterized inversion where the number of model parameters is substantially greater than the number of model constraints (calibration targets or model observations); a similar approach is called [SVD-assist](http://www.pesthomepage.org/Highly-parameterized_inversion.php) in [PEST](http://www.pesthomepage.org).
* Multi-Start Levenberg-Marquardt (**MSLM**) optimization technique
* Global Particle Swarm Optimization ([PSO](http://clerc.maurice.free.fr/pso/))
* Global Adaptive Particle Swarm Optimization [TRIBES](http://www.particleswarm.info/Tribes_2006_Cooren.pdf)
* Global Optimization technique coupling Particle Swarm and Levenberg-Marquardt optimization technique [SQUADS](papers/squads_v04.pdf)
* Sensitivity Analysis (**SA**) techniques
* Global Monte-Carlo based analysis
* Local eigen analysis of Jacobian matrix of model parameters
* [Sobol's global sensitivity indices](http://www.mlmatrix.com/uploadfile/200712418203522.pdf)
* Agent-based Global Uncertainty and Sensitivity [ABAGUS](papers/Harp & Vesselinov ABAGUS 2011.pdf) analysis
* Sampling (design of experiment) techniques (based on random or user provided seed):
* Pseudo random sampling
* Latin-Hypercube sampling techniques: random, center, edge
* [Improved Distributed Hypercube Sampling](http://people.sc.fsu.edu/~jburkardt/datasets/ihs/ihs.html) (**IDLHS**; aka **IHS**)
* Uncertainty Quantification (**UQ**) techniques
* Global Monte-Carlo based analysis
* Local analysis based on Jacobian matrix of model parameters
* Agent-based Global Uncertainty and Sensitivity [ABAGUS](papers/Harp & Vesselinov ABAGUS 2011.pdf) analysis
### Decision support
**MADS** includes methods for Model-based Decision Support (**DS**)
* Bayesian analysis utilizing [DREAM](http://www.biometris.wur.nl/UK/Staff/Cajo+ter+Braak/Software+and+Data/DE-MC+and+DREAM+software+page/)
* non-Bayesian analysis utilizing [minimax](http://www.sciencedirect.com/science/article/pii/S0004370206000245), [info-gap](papers/Harp & Vesselinov infogap source 2011.pdf) and [GLUE](http://www.sciencedirect.com/science/article/pii/S0022169401004218)
* Global Optimization technique coupling Particle Swarm and Levenberg-Marquardt optimization techniques [SQUADS](papers/squads_v04.pdf)
* Agent-based Global Uncertainty and Sensitivity [ABAGUS](papers/Harp & Vesselinov ABAGUS 2011.pdf) analysis
### Contaminant transport simulators
**MADS** includes several analytical simulators for representation of 3D contaminant transport in aquifers. The analytical simulation is based on the solutions developed by [Wexler (1992)](http://pubs.usgs.gov/twri/twri3-b7/) and [Park & Zhan (2001)](http://www.sciencedirect.com/science/article/pii/S016977220100136X). The solutions are solved using [GSL](http://www.gnu.org/s/gsl/) subroutines. Alternative solutions are available for contaminant sources with different geometry:
* point source
* plane source (along the top of the aquifer)
* 3D box (straight parallelepiped) source
### Test functions
**MADS** includes a series of test functions that can be applied for efficient testing of model-analysis and decision support techniques. These test functions are commonly used in the practice. The list of all the test functions built-in in **MADS** are listed in the [manual](mads-manual.md)