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\author[Mur\'e et al.]{
J. Mur\'e \inst{1} \and
J. Pelamatti \inst{1} \and
M. Baudin \inst{1} \and
J. Pelamatti \inst{1} \and \\
J. Schueller \inst{2} \and
A. Marion \inst{2}
}
Expand Down Expand Up @@ -302,16 +303,9 @@ \section{OpenTURNS Overview}

\small
\begin{itemize}
\item Compatibility with most popular python packages
\begin{itemize}
\scriptsize
\item Numpy
\item Scipy
\item Matplotlib
\item scikit-learn
\end{itemize}
\item C++ and Python interface
\vspace{10pt}
\item Parallel computational with shared memory (TBB)
\item Parallel computations with shared memory (TBB)
\vspace{10pt}
\item Optimized linear algebra with LAPACK and BLAS
\vspace{10pt}
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\small
\begin{itemize}
\item We want a surrogate $\hat{h}$ of a model $h$ that maps a time series to a vector:
\item We want a \href{http://openturns.github.io/openturns/1.22/auto_reliability_sensitivity/reliability_processes/plot_field_fca_sobol.html}{surrogate} $\hat{h}$ of a model $h$ that maps a time series to a vector:
\begin{equation*}
h: \mathcal{F}([0, 1], \mathbb{R}^d) \rightarrow \mathbb{R}^p
\end{equation*}
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\end{itemize}

\begin{lstlisting}
timegrid = ot.RegularGrid(start, step, N)
collection = ... # collection of numpy arrays with shape (N, d)
import openturns as ot
timegrid = ot.RegularGrid(start, step, NT) # NT is the number of time steps
collection = ... # collection of N numpy arrays with shape (NT, d)
x = ot.ProcessSample(timegrid, collection) # functional input data
y = ... # numpy array of shape (N, p)
\end{lstlisting}

\begin{itemize}
\item Step 1: for each dimension of the input data, perform PCA.
\item Step 2: build a polynomial chaos mappling the PCA coefficients to the outputs
\item Step 2: build a polynomial chaos mapping the PCA coefficients to the outputs
\item The \texttt{FieldToPointFunctionalChaosAlgorithm} experimental class does both steps at once:
\end{itemize}

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\small
\centering

\begin{block}{Mapping categories to a latent space with Gaussian correlation kernel}
\medskip
\begin{block}{Mapping categories to a latent space with Gaussian correlation kernel\footnote{Zhang, Y., Tao, S., Chen, W., and Apley, D. W. (2020)}}
\centering
\begin{tikzpicture}
\draw[gray!30] (-1.25,-1.25) grid[xstep=1.0, ystep=1.0] (2.25,2.25);
Expand All @@ -559,7 +553,7 @@ \section{OpenTURNS 1.22: Functional surrogate model}
\node[right =2pt of {-6,-0.5}, outer sep=2pt,fill=white] {mouse};
\draw[line width = 1pt, -{Stealth}] (-4,0.5) -- (-2.5,0.5);
\end{tikzpicture}
\vspace{-0.25cm}
\vspace{-0.4cm}

\begin{itemize}
\item First category: automatically mapped to $(0,0,...,0)$: here dog to $(0,0)$.
Expand All @@ -569,7 +563,7 @@ \section{OpenTURNS 1.22: Functional surrogate model}

\begin{lstlisting}
from openturns.experimental import LatentVariableModel
covModel = LatentVariableModel(3, 2) # 3 categories (doc, cat, mouse) in 2D
covModel = LatentVariableModel(3, 2) # 3 categories (dog, cat, mouse) in 2D
activeCoordinates = [1.5, 1.0, 1.5] # [cat_0, mouse_0, mouse_1]
covModel.setLatentVariables(activeCoordinates)
\end{lstlisting}
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\begin{frame}[containsverbatim]
\frametitle{Example: 1 continuous + 1 boolean variable}
\small
Product of a 5/2 Mat\'ern covariance kernel for the continuous variable and a latent variable kernel for the boolean variable:
Product of a 5/2 Mat\'ern covariance kernel for the continuous variable and a \href{http://openturns.github.io/openturns/1.22/auto_meta_modeling/kriging_metamodel/plot_kriging_categorical.html#sphx-glr-auto-meta-modeling-kriging-metamodel-plot-kriging-categorical-py}{latent variable kernel} for the boolean variable:

\begin{lstlisting}
# Standard 5/2 Matern covariance kernel for the continuous variable
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\begin{frame}{Project overview}
\begin{itemize}
\item
Partnership between \'Electricit\'e De France (EDF) and Phimeca since 2015
Partnership between EDF and Phimeca since 2015

\begin{itemize}
\item
Expand Down Expand Up @@ -717,22 +711,20 @@ \section{Persalys Overview}
\protect\hypertarget{persalys-installation}{}
\begin{itemize}

\item
Today the material is provided
\item
Github: sources
\item
For executables you can request the material at
\url{https://persalys.fr/obtenir.php}
You can request executables at
\url{https://persalys.fr/obtenir.php?la=en}
\item
Depending on your OS

\begin{itemize}

\item
Linux -\textgreater{} .AppImage (600 Mo)
\href{https://openturns.github.io/openturns/1.22/usecases/use_case_logistic.html}{Linux} $\rightarrow$ .AppImage (600 Mo)
\item
Windows -\textgreater{} .exe will create a shortcut on your Desktop
Windows $\rightarrow$ .exe will create a shortcut on your Desktop
(program is 1.45 Go)
\end{itemize}
\item Also distributed by Debian-based GNU/Linux distributions (e.g. Debian, Ubuntu...)
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\includegraphics[width=0.59\textwidth]{figure/overviewMetamodel.png}

\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% \section{PERSALYS, the graphical user interface}

% \begin{frame}
% \frametitle{PERSALYS, the graphical user interface of \ot{}}

% \begin{columns}
% \column{0.7\textwidth}

% \begin{itemize}
% \item Provide a graphical interface of
% \ot{} in and out of the SALOME integration platform
% \item Features : probabilistic model,
% distribution fitting, central tendency,
% sensitivity analysis, probability estimate,
% surrogate modeling (polynomial chaos, kriging), screening (Morris),
% optimization, design of experiments
% \item GUI language : English, French

% \item Partners : EDF, Phim\'eca
% \item Licence : LGPL

% \item Schedule : Since summer 2016, two releases per year, currently V12
% \item On the internet (free) : SALOME\_EDF since 2018 on
% \url{www.salome-platform.org}

% \end{itemize}

% \column{0.3\textwidth}

% \begin{center}
% \includegraphics[width=0.95\textwidth]{figures/PERSALYS-LOGO.png}
% \end{center}

% \end{columns}


% \end{frame}


% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% \begin{frame}
% \frametitle{Calibration}

% Given a physical model $h$, observed inputs $\boldsymbol{x}$,
% observed outputs $y$ we can calibrate $\boldsymbol{\theta}$ so that
% $$
% y = h(\boldsymbol{x}, \boldsymbol{\theta}) + \epsilon
% $$
% where $\epsilon$ is a random (Gaussian) variable.

% Calibration outputs:
% \begin{itemize}
% \item the optimal value estimator $\hat{\boldsymbol{\theta}}$,
% \item the distribution of $\hat{\boldsymbol{\theta}}$ and a confidence or credibility
% interval of each marginal,
% \item the distribution of the residuals $\epsilon = y - h(\boldsymbol{x}, \hat{\boldsymbol{\theta}})$.
% \end{itemize}

% We implemented 4 methods\footnote{M. Baudin \& R. Lebrun, Linear algebra of linear and nonlinear Bayesian calibration. UNCECOMP 2021.} :

% \begin{center}
% \begin{tabular}{lll}
% & {\bf Linear} & {\bf Non Linear} \\
% \hline
% No prior & Least squares & Least squares \\
% & linear & non linear \\
% \hline
% Gaussian prior & Linear calib. & 3DVAR \\
% \hline
% \end{tabular}
% \end{center}

% \end{frame}


% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% \begin{frame}
% \frametitle{Calibration}

% In PERSALYS, this requires:
% \begin{itemize}
% \item a physical model $h$ with parameters to calibrate,
% \item a data file containing the observed inputs and outputs.
% \end{itemize}

% \begin{center}
% \includegraphics[width=0.35\textwidth]{figures/calibration_observations_contextMenu.png}
% \end{center}

% \begin{columns}
% \column{0.5\textwidth}

% On output, we present the optimal value of each calibrated parameter,
% along with a 95\% confidence interval.

% \column{0.5\textwidth}

% \begin{center}
% \includegraphics[width=0.9\textwidth]{figures/calibration-ks-zv-zm-optimal_focus.png}
% \end{center}

% \end{columns}
% \end{frame}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% \begin{frame}
% \frametitle{Calibration}

% \begin{center}
% \includegraphics[width=0.86\textwidth]{figures/calibration-Zv-prior-posterior.png}
% \end{center}

% \end{frame}

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% \begin{frame}
% \frametitle{What's next ?}
% \begin{columns}
% \column{0.5\textwidth}

% PERSALYS Roadmap :
% \begin{itemize}
% \item New surrogate models
% \item 2D Fields, 3D Fields
% \item In-Situ fields based on the MELISSA library (with INRIA):
% when we cannot store the whole sample in memory or on the hard drive,
% update the statistics (e.g. the mean, Sobol' indices) sequentially,
% with distributed computing.
% \end{itemize}

% \column{0.5\textwidth}

% \begin{center}
% \includegraphics[height=0.5\textheight]{figures/image034.png}
% \end{center}

% \end{columns}

% \end{frame}

% \note{

% The next features we plan to add to PERSALYS is the management
% of 2D and 3D stochastic fields.

% We also work on the use of the MELISSA software which performs
% in-situ studies.

% This library allows to perform UQ studies in situations
% where we cannot store more than a couple of multidimensional fields
% in memory or on the hard drive.
% }

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}

\begin{center}
Thanks !
\end{center}
\begin{block}{OpenTURNS resources}
\begin{itemize}
\item Website and documentation: \url{www.openturns.org}
\item GitHub: \url{https://github.com/openturns/openturns}
\item Forum: \url{https://openturns.discourse.group}
\end{itemize}
\end{block}

\begin{center}
Questions ?
\end{center}
\begin{block}{Persalys resources}
\begin{itemize}
\item Website and documentation: \url{https://persalys.fr/?la=en}
\item Forum: \url{https://persalys.discourse.group}
\end{itemize}
\end{block}

\begin{columns}
\column{0.5\textwidth}
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