Features ataglance

Random fields

Stochastic spectral embedding

Highperformance computing (HPC) dispatcher

Reliabilitybased design optimization

Bayesian inference for model calibration and inverse problems

UQLib: an opensource library of UQLab

Local and global sensitivity analysis

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

Reliability analysis (rare event estimation)
Random fields
NEW!
Many uncertainty quantification problems feature random variables that vary in space and time. Such variables are known as random fields. UQLab offers an intuitive way to define random fields, discretize them and sample trajectories

Gaussian and nonGaussian translation random fields

Conditional random fields

Expansion optimal linear estimation (EOLE)

KarhunenLoève expansion (PCAbased discrete approach and Nyström method)
Stochastic spectral embedding
NEW!
Stochastic spectral embedding is a novel metamodelling technique that gradually refines a global spectral expansion into a sequence of local expansions on increasingly smaller domains.
The UQLab SSE module provides the original (and so far unique) implementation of the method, both in its static and adaptive flavours.

Construct PCEbased SSE with only a few lines of code

Complete control over the embedded sparse PCE expansions

Support for all experimental sampling strategies included in UQLab

Adaptive experimental design refinement where the model complexity demands it

Efficient sparse tree representation and options for expansion flattening

Advanced visualization options in 1D and 2D
Highperformance computing (HPC) dispatcher
The highperformance computing (HPC) dispatcher module allows one to connect UQLab to common distributed computing resources (e.g., HPC clusters), providing a convenient interface to set up, submit, and retrieve remote computations directly from within UQLab running on their PC.

Conveniently dispatch computations from within UQLab to distributed computing resources

Monitor and retrieve the results of dispatched computations directly from the command line

Support for dispatched evaluations of all UQLab models (including thirdparty software
through UQLink) 
Support for dispatched evaluations of generic MATLAB functions (e.g., for parametric studies)

Support for parallel computations without MATLAB or UQLab on the remote machine

Outofthebox support for various job schedulers (including SLURM, LSF, etc.);
support for custom schedulers via userdefined settings
Reliabilitybased design optimization
The reliabilitybased design optimization (RBDO) module offers a set of stateoftheart algorithms to solve various types of optimization problems under probabilistic constraints. They include:

Reliability index approach (RIA)

Performance measure approach (PMA)

Single loop approach (SLA)

Sequential optimization and reliability assessment (SORA)
On top of these wellknown algorithms, the modular design of the RBDO module allows the user to set up customized solution schemes by combining all of the reliability, surrogate modeling, and optimization techniques available in UQLab.
Bayesian inference for model calibration and inverse problems
Bayesian inference is a powerful tool for probabilistic model calibration and inverse problems. UQLab offers a flexible and intuitive way to setup and solve Bayesian inverse problems.

Intuitive definition of prior knowledge, forward model and data

Stateoftheart Markov Chain Monte Carlo (MCMC) algorithms

Customizable discrepancy between model and measurements

Support for userspecified custom likelihood

Support for multiple forward models and multiple discrepancy models (joint inversion)

Fully integrated with UQLab (e.g. surrogate models, complex priors, etc.)
UQLib
UQLib is a collection of generalpurpose opensource MATLAB libraries that are useful in the context of uncertainty quantification. These functions are currently used across the scientific modules of UQLab, but they are designed for generic use.

Optimization (e.g., crossentropy optimization, covariance matrix adaptationevolution strategy and its constrained variant)

Differentiation (e.g., gradient computation)

Kernel (stationary and nonstationary kernel functions)

Input/output processing (e.g., subsampling)
Sensitivity analysis
The sensitivity analysis module contains samplebased, linearization, and global sensitivity analysis methods, that quantitatively measure the importance of each input parameter.

Samplebased methods (input/output correlation and standard regression coefficients,
with their rankbased versions) 
Linearization (perturbation) method

Screening methods (Morris' elementary effects, Cotter indices)

Momentindependent global method (Borgonovo indices)

Sobol' indices computed by Monte Carlo simulation or analytically
(from polynomial chaos expansions and lowrank tensor approximations) 
Generalization of Sobol' indices for dependent input parameters
(Kucherenko and ANCOVA indices)
UQLink
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
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.)
Advanced probabilistic modeling tools
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, infer, and sample from complex multivariate distributions.

Extensive library of marginal distributions

Modeling dependence with Gaussian and Vine copulas

Statistical Inference of marginals and copulas from data

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
Easy plugin of MATLABbased models
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
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)

Regression algorithms: Ordinary least squares (OLS), Least Angle Regression (LARS), Orthogonal Matching Pursuit (OMP), Subspace Pursuit (SP), and Bayesian Compressive Sensing (BCS)

Degreeadaptive and qnormadaptive polynomial chaos expansions

Polynomials orthogonal to arbitrary distributions (via Stieltjes construction)
Kriging (Gaussian process modeling)
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

Interpolation (noisefree response) and regression (noisy response) modes
Polynomial ChaosKriging (PCKriging)
Polynomial ChaosKriging associates the global approximation behavior 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 tensor polynomial approximations
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)
Reliability analysis (rare event estimation)
When the performance of a system is affected by uncertainties on its characteristics and/or its environment, reliability can be assessed by computing probabilities of failure.
UQLab offers stateoftheart reliability algorithms and a powerful modular framework
for active learning reliability.

FORM/SORM approximation methods

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

Modular framework to build custom active learning solution schemes

Krigingbased adaptive methods (AKMCS, APCKMCS)