Slides on calibration in OpenTURNS for User's Day 2024

README.rst

@@ -85,6 +85,7 @@ OpenTURNS Presentations
 
  - `Release highlights <https://github.com/openturns/openturns.github.io/blob/master/presentation/master/userday2024relhi.pdf>`_
  - `Automotive Reliability Engineering with OpenTURNS : the Phimeca product for Renault : StaRe (STAtistical REliability) <https://github.com/openturns/openturns.github.io/blob/master/presentation/master/ud2024-stare.pdf>`_
+ - `Overview of calibration <https://github.com/openturns/openturns.github.io/blob/master/presentation/master/calibration2024.pdf>`_
 
 - Uncecomp 2023
 

userday2024/calibration2024/.gitignore

@@ -0,0 +1,2 @@
+calibration2024.run.xml
+calibration2024.bcf

userday2024/calibration2024/calibration2024.bib

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+
+@inproceedings{Baudin2021,
+ title={Linear algebra of linear and nonlinear {Bayesian} calibration},
+ author={Baudin, Michaël and Lebrun, Régis},
+ year={2021},
+ booktitle = {UNCECOMP 2021},
+ pages = {339--353},
+ organization = "4th ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering M. Papadrakakis, V. Papadopoulos, G. Stefanou (eds.) Streamed from Athens, Greece, 28-30 June 2021",
+}
+
+@Book{Bjorck1996,
+ author = {Ake Björck},
+ title = {Numerical Methods for Least Squares Problems},
+ publisher = {Society for Industrial Applied Mathematics},
+ year = {1996},
+}
+
+@INPROCEEDINGS{Hansen00thelcurve,
+ author = {P. C. Hansen},
+ title = {The {L}-Curve and its Use in the Numerical Treatment of Inverse Problems},
+ booktitle = {in Computational Inverse Problems in Electrocardiology, ed. P. Johnston, Advances in Computational Bioengineering},
+ year = {2000},
+ pages = {119--142},
+ publisher = {WIT Press}
+}
+
+@article{trucano2006calibration,
+ title={Calibration, validation, and sensitivity analysis: What's what},
+ author={Trucano, Timothy G and Swiler, Laura Painton and Igusa, Takera and Oberkampf, William L and Pilch, Martin},
+ journal={Reliability Engineering \& System Safety},
+ volume={91},
+ number={10-11},
+ pages={1331--1357},
+ year={2006},
+ publisher={Elsevier}
+}
+
+@techreport{Blanchard2020,
+author = {Jean-Baptiste Blanchard and Guillaume Damblin and Michaël Baudin},
+title = {Introduction aux problèmes de calibration de paramètres.},
+year = {2020}, 
+institution = {I3P, EDF R\&D et CEA}, 
+}
+
+@book{Evensen2009,
+title = {Data Assimilation - The Ensemble {Kalman} Filter},
+author = {Geir Evensen},
+year = {2009},
+publisher = {SIAM}
+}
+
+@book{Tarantola2005,
+ author = "Albert Tarantola",
+ title = "Inverse problem theory",
+ year = "2005",
+ publisher = "SIAM",
+}
+
+@book{Asch2016,
+ title={Data assimilation. Methods, algorithms and applications.},
+ author={Asch, Mark and Bocquet, Marc and Nodet, Maëlle},
+ year={2016},
+ publisher={SIAM}
+}
+
+
+@Inbook{Baudin2016,
+author="Baudin, Micha{\"e}l and Dutfoy, Anne and Iooss, Bertrand and Popelin, Anne-Laure",
+title="{OpenTURNS}: An Industrial Software for Uncertainty Quantification in Simulation. In: Ghanem R., Higdon D., Owhadi H. (eds) Handbook of Uncertainty Quantification.",
+year="2016",
+publisher="Springer International Publishing",
+address="Cham",
+pages="1--38",
+isbn="978-3-319-11259-6",
+doi="10.1007/978-3-319-11259-6_64-1",
+url="https://doi.org/10.1007/978-3-319-11259-6_64-1"
+}
+
+@techreport{BaudinMethodes2020,
+author = {Michaël Baudin and Régis Lebrun},
+title = {Méthodes de calage : algorithmes mathématiques et implémentation dans {OpenTURNS}.},
+year = {2020}, 
+institution = {EDF R\&D}, 
+number={6125-3119-2020-02448-FR}
+}
+
+@techreport{BaudinMethodes2022,
+author = {Michaël Baudin},
+title = {Méthodes de calage : algorithmes mathématiques avancés et implémentation dans {OpenTURNS}.},
+year = {2022}, 
+institution = {EDF R\&D}, 
+number={6125-3119-2022-00175-FR}
+}
+
+@techreport{garbow1980implementation,
+ title={Implementation guide for {MINPACK}-1.},
+ author={Garbow, Burton S. and Hillstrom, Kenneth E. and More, Jorge J.},
+ year={1980},
+ institution={Argonne National Lab., IL (USA)}
+}
+
+@book{kern2016methodes,
+ title={M{\'e}thodes num{\'e}riques pour les problemes inverses},
+ author={Kern, Michel},
+ year={2016},
+ publisher={ISTE Group}
+}
+
+
+@book{lawson1995solving,
+ title={Solving least squares problems},
+ author={Lawson, Charles L. and Hanson, Richard J.},
+ year={1995},
+ publisher={SIAM}
+}
+
+@book{idier2013bayesian,
+ title={Bayesian approach to inverse problems},
+ author={Idier, J{\'e}r{\^o}me},
+ year={2013},
+ publisher={John Wiley \& Sons}
+}
+
+@book{hansen2013least,
+ title={Least squares data fitting with applications},
+ author={Hansen, Per Christian and Pereyra, Victor and Scherer, Godela},
+ year={2013},
+ publisher={JHU Press}
+}

userday2024/calibration2024/calibration2024.tex

@@ -0,0 +1,149 @@
+% Copyright (C) 2024 - Michaël Baudin
+
+\documentclass[9pt]{beamer}
+
+%\setbeameroption{hide notes}
+%\setbeameroption{show notes}
+%\setbeameroption{show only notes}
+
+\input{macros}
+
+\title[Calibration in OpenTURNS]{Overview of calibration features in OpenTURNS}
+
+\author[M. Baudin]{
+Michaël Baudin \inst{1}
+}
+
+\institute[EDF]{
+\inst{1} EDF R\&D. 6, quai Watier, 78401, Chatou Cedex - France, [email protected]
+}
+
+
+\date[]{June 19th 2024, Palaiseau, France}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{document}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\titlepage
+
+\begin{center}
+\includegraphics[height=0.15\textheight]{figures/edf.jpg}
+\end{center}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Introduction}
+
+Calibration is the step B' of the generic methodology\footnote{See\cite{Baudin2016, BaudinMethodes2020}.}.
+
+\begin{figure}
+\begin{center}
+\includegraphics[width=0.7\textwidth]{MethodologieIncertitude-EN.pdf}
+\end{center}
+\caption{The step B' brings the observed predictions from the model
+closer to the observed outputs to calibrate the parameters.}
+\end{figure}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}
+\frametitle{Introduction}
+
+We have:
+\begin{itemize}
+\item a dataset,
+\item a parametric model with unknown parameters.
+\end{itemize}
+
+We search for:
+\begin{itemize}
+\item parameter values,
+\item such that the predictions of the model are as close as possible to the data.
+\end{itemize}
+
+Since the dataset is random, we want the distribution of the parameters.
+
+From there, we can compute confidence intervals of the parameters.
+
+\begin{figure}
+\begin{center}
+\includegraphics[width=0.5\textwidth]{flooding_before_calibration.pdf}
+\end{center}
+\caption{Observations compared to the predictions of a model.}
+\end{figure}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}[fragile]
+\section{Overview}
+\frametitle{Overview}
+
+In OpenTURNS, we have several calibration features:
+\begin{itemize}
+\item \href{https://openturns.github.io/openturns/latest/theory/data_analysis/data_analysis.html#calibration}{theory help pages}
+\item \href{https://openturns.github.io/openturns/latest/user_manual/calibration.html}{API help pages}
+\item \href{https://openturns.github.io/openturns/latest/auto_calibration/index.html}{examples}.
+\end{itemize}
+
+
+There are two types of features :
+\begin{itemize}
+\item linear and non linear least squares, Gaussian linear and non linear calibration : \pyvar{*Calibration} classes. These classes compute the \textbf{posterior distribution of the parameters}.
+\item Monte Carlo Markov Chain (MCMC) algorithms : \pyvar{*MetropolisHastings}, etc. These classes \textbf{generate a sample from the posterior distribution of the parameters}.
+\end{itemize}
+
+The simplest example is \href{https://openturns.github.io/openturns/latest/auto_calibration/least_squares_and_gaussian_calibration/plot_calibration_quickstart.html#sphx-glr-auto-calibration-least-squares-and-gaussian-calibration-plot-calibration-quickstart-py}{Calibrate a parametric model: a quick-start guide to calibration}
+
+Here, we are going to review the \href{https://openturns.github.io/openturns/latest/auto_calibration/least_squares_and_gaussian_calibration/plot_calibration_flooding.html#sphx-glr-auto-calibration-least-squares-and-gaussian-calibration-plot-calibration-flooding-py}{Calibration of the flooding model}
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}[fragile]
+\section{Conclusion}
+\frametitle{Conclusion}
+
+Other tools :
+\begin{itemize}
+\item Calibration methods are also available in \href{https://persalys.fr}{Persalys} : linear and non linear least squares, Gaussian linear and non linear calibration.
+\end{itemize}
+
+Perspectives:
+\begin{itemize}
+\item provide bounds to the optimization algorithms (return truncated normal distribution if necessary);
+\item unify the \pyvar{ParametricFunction} in \pyvar{*Calibration} and \pyvar{*MetropolisHastings} classes (exchange the roles of $x$ and $\theta$);
+\item calibrate parametric functions with field output more easily;
+\item provide algorithms to automatically compute finite difference steps (not specific to calibration);
+\item provide the covariance matrix of the parameters as a diagonal matrix when possible;
+\item scale the parameters to calibrate (not specific to calibration);
+\item implement \pyvar{CalibrationResult.isBayesian()} (see \href{https://github.com/openturns/openturns/issues/2560}{2560});
+\item implement a \pyvar{CalibrationResult} structure for M.-H. classes.
+\end{itemize}
+\end{frame}
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\section{References}
+\begin{frame}[allowframebreaks]
+\frametitle{Références}
+\nocite{*}
+\bibliographystyle{apalike}
+\bibliography{calibration2024}
+\end{frame}
+
+\end{document}