MADS Methods

• Model analyses
• Decision support
• Contaminant transport simulators
• Test functions

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, IMSL, LevMar.
  The Levenberg-Marquardt (LM) optimization technique can be performed using acceleration and delayed gratification approaches.
  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 in PEST.
• Multi-Start Levenberg-Marquardt (MSLM) optimization technique
• Global Particle Swarm Optimization (PSO)
• Global Adaptive Particle Swarm Optimization TRIBES
• Global Optimization technique coupling Particle Swarm and Levenberg-Marquardt optimization technique SQUADS
• Sensitivity Analysis (SA) techniques
• Global Monte-Carlo based analysis
• Local eigen analysis of Jacobian matrix of model parameters
• Sobol's global sensitivity indices
• Agent-based Global Uncertainty and Sensitivity ABAGUS 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 (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 analysis

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MADS includes methods for Model-based Decision Support (DS)

• Bayesian analysis utilizing DREAM
• non-Bayesian analysis utilizing minimax, info-gap and GLUE
• Global Optimization technique coupling Particle Swarm and Levenberg-Marquardt optimization techniques SQUADS
• Agent-based Global Uncertainty and Sensitivity ABAGUS analysis

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) and Park & Zhan (2001). The solutions are solved using 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

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

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