Tutorials

In these tutorials, how to perform inverse problem analyses using ODAT-SE is explained by examples taken from minimization of analytical functions. In ODAT-SE, the algorithms for solving the inverse problem can be selected from the following algorithms:

• minsearch

  Nealder-Mead method.

• mapper_mpi

  Entire search over a grid for a given parameter.

• random_search

  Random search.

• bayes

  Bayesian optimization.

• exchange

  Sampling by the replica exchange Monte Carlo method.

• pamc

  Sampling by the population annealing Monte Carlo method.

In the following sections, the procedures to run these algorithms are provided. In addition, the usage of [runner.limitation] to apply limitations to the search region will be described. At the end of the section, a description of how to implement a direct problem solver is provided, as well as some tutorials describing some applications.

• Minimization of an analytical function
• Optimization by Nelder-Mead method
• Grid search
• Random search
• Optimization by Bayesian Optimization
• Optimization by replica exchange Monte Carlo
• Optimization by population annealing
• Replica Exchange Monte Carlo search with limitation
• Adding a direct problem solver
• Example: Linear regression and noise estimation
• Example: Gaussian process regression for function modeling