Features ataglance

Bayesian inversion

UQLink: universal connection to thirdparty software

Support vector machines for classification and regression

Advanced probabilistic modeling (copulas)

Seamless connection with MATLABbased models

(Sparse) polynomial chaos expansions

Advanced Kriging (Gaussian process modeling)

Polynomial ChaosKriging (PCKriging)

Canonical lowrank tensor approximations

Local and global sensitivity analysis

Reliability analysis (rare event estimation)

UQLib: an opensource numerical library of UQLab
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UQLink allows the seamless connection of thirdparty software to UQLab using universal "wrapping" of external codes through templates and a markup system.

Based on automated text input file generation

Available for all platforms (Windows, Linux, macOS)

Examples with simple C/C++ code and commercial finite element software
UQLink allows the seamless connection of thirdparty software to UQLab using universal "wrapping" of external codes through templates and a markup system.

Based on automated text input file generation

Available for all platforms (Windows, Linux, macOS)

Examples with simple C/C++ code and commercial finite element software
Support vector machines (SVM) come from machine learning and allow one to build predictive models from data. In the context of uncertainty quantification, SVM for regression (SVR) can be used as surrogate models of complex simulators using designs of computer experiments. SVM for classification (SVC) can be used in the context of reliability analysis.

L1SVR and L2SVR formulation for regression

Softmargin classification

Anisotropic and userdefined kernels

Leaveoneout error and span approximations

Multiple optimization algorithms (grid search, BFGS, crossentropy, CMAES, etc.)
In many uncertainty quantification problems, the sources of uncertainty are represented by complex probabilistic models (random vectors). UQLab offers a powerful and extendible set of tools to represent and sample from complex multivariate distributions.

Extensive library of marginal distributions

Modelling dependence with Gaussian copula

Advanced sampling strategies (spacefilling), including MonteCarlo sampling, optimized latin hypercube sampling (LHS), lowdiscrepancy series (Sobol' and Halton sequences)

Sampling enrichment (nested LHS)

Support for customdefined and bounded marginals

Isoprobabilistic transform facilities
Uncertainty quantification aims at predicting the impact of input parameters uncertainty onto the predictions of a computational model. UQLab offers a simple infrastructure to handle analytical models and MATLABbased computational models (solvers).

Builtin support for functions defined as strings, function handles and mfiles

Intuitive integration of more complex codes
Polynomial Chaos Expansions (PCE) are a metamodeling tool that enables the fast construction of surrogate models, which can be efficiently used for moment and sensitivity analysis.

Full and sparse polynomial chaos expansions

Advanced truncation strategies (hyperbolic norms, max interaction, custom basis specification)

Quadrature/sparse Gaussian quadrature (based on Smolyak grids)

Ordinary least squares, Least Angle Regression (LARS) and Orthogonal Matching Pursuit regression algorithms

Degreeadaptive sparse polynomial chaos expansions

Polynomials orthogonal to arbitrary distributions (via Stieltjes construction)
Gaussian process modeling is a flexible and robust technique to build fast surrogate models based on small experimental designs.

Simple, ordinary and universal Kriging

Highly customizable trend and correlation functions

Maximumlikelihood and crossvalidationbased hyperparameter estimation

Gradientbased, global and hybrid optimization methods
Polynomial ChaosKriging (PCK) associates the global approximation behaviour of polynomial chaos expansions and the local accuracy of Kriging to provide a highly accurate surrogate model at low computational costs.

Support for sequential and optimal construction of PCKriging

Full control on both levels of approximation: polynomial chaos expansions and Kriging directly use the corresponding dedicated UQLab modules

Support for sparse, adaptive and arbitrary polynomial chaos expansions

Gradientbased, global and hybrid optimization methods for Kriging
Canonical lowrank approximations (LRA) are a powerful alternative to polynomial chaos expansions that are particularly effective in high dimension.

Lowrank basis construction based on orthonormal polynomials

Adaptive identification of maximum rank and polynomial degree via crossvalidation

Alternate leastsquare calculation of basis elements and coefficients

Polynomials orthogonal to arbitrary distributions (via Stieltjes construction)
The sensitivity analysis module contains screening and global sensitivity analysis methods, which quantitatively measure the importance of each input parameter.

Screening methods (Morris' elementary effects, Cotter indices)

Linear measures: perturbation method (Taylor series expansion), standard regression coefficients, input/output correlation and their rankbased versions

Sobol' indices computed by Monte Carlo simulation or analytically (from polynomialchaos expansions and lowrank tensor approximations)
When the performance of a system is affected by uncertainties on its characteristics or its environment, reliability can be assessed by computing probabilities of failure.

FORM/SORM approximation methods

Sampling methods (Monte Carlo, importance sampling, subset simulation)

Krigingbased adaptive methods (AKMCS, APCKMCS)
UQLink allows the seamless connection of thirdparty software to UQLab using universal "wrapping" of external codes through templates and a markup system.

Differentiation (gradient)

Optimization (grid search, cross entropy, covariance matrix adaptation  evolution strategy, etc.)

Kernel (stationary and nonstationary)

Input/output processing (subsampling)