• For data analysis, OpenTURNS provides various statistical tools to manage a sample, to estimate the parameters of a probabilistic model, to quantify dependence, to estimate the parameters of a stochastic process and to visualize the data.
  • For quantization, OpenTURNS allows to define the random vector as input to the calculation code. This random vector can be modeled by the association of marginal laws and copulas. This mechanism allows complex manipulations of multivariate probability laws. When a sample of observations is available, the library provides statistical processing functions, including parametric and non-parametric adjustment tests (histogram or kernel smoothing). The estimation of the parameters of a distribution can be carried out on a sample and the library allows to obtain the distribution of the parameters.
  • stochastic processes can be defined, by their covariance model, by their spectral decomposition or by Karhunen-Loève decomposition.
  • for propagation, OpenTURNS proposes analytical calculation methods as soon as possible for the determination of the probability law of the variable of interest, based on the manipulation of characteristic functions. The library provides several simulation methods for estimating the central tendency or the probability of exceeding a threshold, thanks to different types of experimental designs as well as iterative algorithms allowing to minimize the number of code calls. For reliability, the library provides FORM and SORM methods generalized to elliptic copulas.
  • for prioritization, OpenTURNS evaluates importance and sensitivity factors adapted to the selected propagation methods, in particular the Sobol’ indices. The library allows to estimate the sensitivity indices by sampling or by iterative algorithms.
  • for calibration, OpenTURNS allows to estimate the parameters of a model allowing to reconcile the observations and the predictions of the model. The calibration can be done by least squares or by Bayesian methods. The Bayesian calibration can be conducted in full generality by MCMC or in a simpler framework with a Gaussian a priori. In all cases, the distribution of the calibration parameters is determined by exact or approximate methods.
  • For expensive models, OpenTURNS can create metamodels. The library allows to create metamodels and response surfaces, and in particular simple regression models, chaos polynomials and regression models by Gaussian processes or kriging.
  • Any computational code, Python function or symbolic function can be studied, thanks to the different connection mechanisms available to define a function. When the code can be evaluated by file exchange, the library facilitates the connection to drive the calculation code. When it is possible, the calculation can be parallelized in a local or distributed way.