MADS Examples

MADS is distributed with a series of example files that can be used to test and verify MADS performance. The following executions can be performed after the code has been successfully installed.

• Optimization: Parameter Estimation (PE), Calibration, Inversion
• Uncertainty Quantification (UQ)
• Sensitivity analysis (SA)

Optimization: Parameter Estimation (PE), Calibration, Inversion

 

No input files are needed for this MADS execution. In this case, a01 is a problem root name for MADS output files. MADS solves optimization problem based on 2-dimensional Rosenbrock test function (2 parameters, 2 observations) using random initial guesses for model parameters. The analysis is performed using the Squads optimization technique.

 

MADS solves optimization problem based on 2-dimensional Rosenbrock test function (2 parameters, 2 observations) using a single set of random initial guesses for model parameters. The analysis is performed using the Levenberg-Marquardt (LM) optimization technique (LM is the default optimization technique).

 

MADS solves optimization problem based on 2-dimensional Rosenbrock test function (10 parameters, 10 observations) using 1000 different random initial guesses for model parameters. The analysis is performed using the Levenberg-Marquardt (LM) optimization technique. The optimization is terminated if the estimated model parameters are with absolute error less than 0.1 from their true values (in this case at the global minimum, all the model parameters are equal to 1)

 

MADS solves optimization problem based on 10-dimensional Rosenbrock test function (10 parameters, 10 observations) using 10 different random initial guesses for model parameters. The analysis is performed using the Multi-Start Levenberg-Marquardt (MSLM) optimization technique with up to 1000 retries. The optimization is terminated if the estimated model parameters are with absolute error less than 0.1 from their true values (at the global minimum, all the model parameters are equal to 1)

 

MADS control file s01.mads is located in directory example/contamination. MADS solves a source identification optimization problem using the Levenberg-Marquardt (LM) optimization technique.

 

MADS control file s02.mads is located in directory example/contamination. MADS solves a source identification optimization problem using the Levenberg-Marquardt (LM) optimization technique.

 

MADS solves a source identification optimization problem using the Levenberg-Marquardt (LM) optimization technique. The analysis is performed using a single set of random initial guesses for model parameters.

 

MADS solves a source identification optimization problem using the Levenberg-Marquardt (LM) optimization technique. The analysis is performed using random initial guesses for model parameters based on a user-defined seed. The analysis is terminated when model predictions are within predefined calibration ranges defined in the MADS control file s01.mads (keyword 'obsrange').

 

MADS solves a source identification optimization problem using the Squads optimization technique. Eigen analysis of the obtained final solution os performed after the optimization has been terminated (keyword 'eigen').

 

MADS solves a source identification optimization problem using the PSO optimization technique.

 

MADS identifies aquifer parameters based on pumping test data using the Levenberg-Marquardt optimization technique. All the files associated with this problem are located in directory example/wells. The analysis is performed in parallel using 2 processors.
For this example, the code WELLS is needed, and it can be obtained at wells.lanl.gov

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Uncertainty Quantification (UQ)

MADS performs uncertainty quantification (UQ) using Monte Carlo analysis based on 100 forward runs with random model parameters. Random model parameters are generated using Improved Distributed Hypercube Sampling (IDHS) (default technique when number of realizations is less than 500). MADS control file s02.mads is located in directory example/contamination.

 

MADS performs global uncertainty and sensitivity analysis using ABAGUS.

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Sensitivity analysis (SA)

MADS performs global sensitivity analysis (SA) of model parameters. The analysis is uses Sobol's technique.

 

MADS performs local sensitivity analysis (SA) for the current model parameters (as provided in the MADS control file s02.mads). The analysis is based on local Jacobian matrix.

 

MADS performs global optimization using the Squads optimization technique. After the optimization is complete, MADS performs local sensitivity analysis for the optimized model parameters. The analysis is based on a local Jacobian matrix.

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