contrib-qsi

This repository proposes an implementation of the QSI-SUR criterion described in the article:

Romain Ait Abdelmalek-Lomenech (†), Julien Bect (†), Vincent Chabridon (§) and Emmanuel Vazquez (†)
Bayesian sequential design of computer experiments for quantile set inversion (arXiv:2211.01008)

(†) Université Paris-Saclay, CNRS, CentraleSupélec, Laboratoire des signaux et systèmes, Gif-sur-Yvette, France.
(§) EDF R&D, Chatou, France.

It also includes the implementation of some other Bayesian set inversion methods.

For the experiments of the article, please refer to https://github.com/stk-kriging/qsi-paper-experiments.

Requirements

Utilization of the functions of this repository requiers Matlab (R2014a or newer) and the toolbox STK (v2.8.1)[https://github.com/stk-kriging/stk/tree/2.8.1]. The corresponding version of STK is automatically download when launching startup.m.

How to use this repository

In what follows, the following convention are used:

• it designates a unique (integer) numerical identifier.
• data_dir is the path to a data storage folder, containing the subdirectory doe_init, grid, results/design, results/param, results/deviations, results/time and results\graphs.

The data_dir directory is used to save, temporarily or definitely, all the data generated and used for the construction of sequential designs using the provided strategies. By default, data_dir = path_to_this_repo/data.

Some examples scripts can be found in the folder examples, and in the repository dedicated to the experiments displayed in the article.

Describing a QSI problem

Each test function (and associated QSI problem) is described by several files:

• function.m or function.py, the associated function either coded in matlab or python.
• function_s_trnsf.m, the inverse mapping associated to the probability distribution on the uncertain inputs.
• function_struct.m, describing the problem (threshold, critical region, input spaces...)
• function_config.m, a configuration file for the different matlab-implemented strategies (number of steps, size of the integration grid, number of candidates points...).

Several test functions, used in the original article, are already provided in the folder test_functions . For a full description of the different parameters, please refer to test_functions/example_struct.m and test_functions/example_config.m.

Constructing a Bayesian sequential design

Given a well described problem, the first step is to generate one (or several) initial designs by using generate_doe_init(@funct_struct, @funct_config, it, file_dir). These initial designs are stored in data_dir/doe_init.

A sequential design can then be generated, using a chosen strategy, by executing strategy(@funct_struct, @funct_config, it, data_dir). The available strategies are QSI-SUR (QSI_SUR.m), Joint-SUR (joint_SUR.m), Ranjan (Ranjan.m), max. misclassification (misclassification.m) and random sampling (random.m).

The generated designs, estimated covariance type and parameters are stored in data_dir/results/design and data_dir/results/param.

Using the sequential designs

The generated designs can be used, independantly, for different prediction and uncertainty quantification task in combination with the STK toolbox.

It is possible to extract, step by step, the proportion of misclassified points regarding the provided QSI problem, by executing extract_deviation(@funct_struct, @funct_config, method, it, data_dir), where method is the identifier of the considered strategy (see misc/extract_deviation.m for more details). The results are stored in data_dir/results/deviations.

About computational cost.

SUR methods tend to be computationaly costly. In particular, the QSI-SUR criterion relies heavily on conditial Gaussian sample paths. It is possible to adapt to a given computational budget by several means, in particular:

• By using parallel computing (see parpool).
• By tuning the methods parameters provided in the funct_config.m file.
• By, in the case of repeated experiments, using only a small number of runs of the differents strategies.

Acknowledgements

This work has been funded by the French National Research Agency (ANR), in the context of the project SAMOURAI (ANR-20-CE46-0013).

Copyright & license

Copyright 2024 CentraleSupélec

These computer programs are free software: you can redistribute them and/or modify them under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the license, or (at your option) any later version.

They are distributed in the hope that they will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the license for more details.

You should have received a copy of the license along with the software (see COPYING.md). If not, see http://www.gnu.org/licenses/.