Features ataglance
Generalized Lambda Models View ➜
Stochastic spectral embedding View ➜
Highperformance computing (HPC) dispatcher View ➜
Reliabilitybased design optimization View ➜
Bayesian inference for model calibration and inverse problems View ➜
UQLib: an opensource library of UQLab View ➜
Local and global sensitivity analysis View ➜
UQLink: universal connection to thirdparty software View ➜
Support vector machines for classification and regression View ➜
Advanced probabilistic modeling (copulas) View ➜
Seamless connection with deterministic and stochastic MATLABbased models View ➜
(Sparse) polynomial chaos expansions View ➜
Advanced Kriging (Gaussian process modeling) View ➜
Polynomial chaosKriging (PCKriging) View ➜
Stochastic Polynomial Chaos Expansions
Stochastic polynomial chaos expansions (SPCE) are a recently introduced surrogate model that can reproduce the nondeterministic behavior of stochastic simulators. With the SPCE module, you can easily train an accurate emulator that can handle multimodal stochastic models, without the need of expensive model replications.

Adaptive sparse construction of the SPCE model

Mean estimation

Multiple integration strategies

Postprocessing of the results
NEW!
Generalized lambda models
Generalized lambda models (GLaM) allow the user to efficiently emulate the behavior of stochastic simulators, thanks to the flexible family of Lambda distributions. With this UQLab module, GLaMs can be easily deployed as all other surrogate models.

Support for both replicationbased and replicationfree training strategies

Multiple lambda parameter estimation methods

Direct evaluation of the (semi)analytical conditional response PDF, CDF and inverse CDF

Postprocessing of the results
NEW!
Random fields
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
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
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

Support for stochastic simulators
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

Fast resampling though UQLab Random Fields module
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)

Adaptive and Bayesian line sampling