UQpy architecture

Distributions

The UML diagram below explains the class hierarchy of the distributions module. In case of distributions a series of abstract base classes are defined. Distribution is the basis, with classes such as Distribution1D and DistributionND abstract base classes refining this hierarchy according to the distribution dimensionality. The 1D case if further refined with DistributionContinuous1D and DistributionDiscrete1D to take into account different types of random variables. Finally, the Copula abstract base class serves as the common interface for all copula implementations. Note that all the above are abstract classes and cannot be directly instantiated.

Sampling

The sampling module contains multiple methods and the UML diagrams below are focused to one method at a time to reduce the complexity of the graphs. Before starting with hierarchy of each different method, we should mention that the classes MonteCarloSampling, SimplexSampling and ImportanceSampling are independent object and do not extend any baseclass.

Starting with the Markov Chain Monte Carlo algorithms, the diagram below makes obvious the dependency between the different implementations. the MCMC abstract base class includes the common functionality between the methods, while the specific algorithms only override the abstract methods of that base class.

The case of stratified sampling is more elaborate, as it includes a family of algorithms. The abstract base class StratifiedSampling serves as the interface between the concrete implementations LatinHypercubeSampling, TrueStratifiedSampling and RefinedStratifiedSampling. In the case of LatinHypercubeSampling the Strategy Design Pattern was used to extract the Latin Hypercube criteria from the sampling. Here the Criterion base class provides the interface that the specific criteria need to override. In a similar manner, the geometric stratification in the case of TrueStratifiedSampling is extracted under the Strata abstract base class. Last but not least, in the case of RefinedStratifiedSampling the different strata refinement strategies are extracted using the Refinement baseclass as their common interface.

UML diagram of Stratified sampling class hierarchy.

In the case of AdaptiveKriging sampling methods, again the different learning functions are extracted into separate classes under the common LearningFunction class.

UML diagram of Adaptive Kriging Hierarchy.

Transformations

The transformations module is one of the most simple in UQpy with three independent classes available, namely Nataf, Correlate and Decorrelate.

Stochastic Processes

The stochastic process module is has again simple structure with five independent classes available.

UML diagram of Stochastic Process module.

Run Model

In case of the RunModel module, the final algorithm to run is constructed by object composition of two different inputs. Initially, the type of the model to run, with PythonModel and ThirdPartyModel being the two available options, while the execution part is delegated to either the SerialExecution or ParallelExecution alternatives.

Inference

Compared to v3, the inference module has undergone a major refactoring towards v4. The initial InferenceModel class that contained all cases of computing the posterior log-likelihood is now split into three independent cases. Given the inference models, backward uncertainty propagation can be performed be choosing between MLE, BayesParameterEstimation to infer the parameter distributions of a model, or InformationModelSelection and BayesModelSelection to select the model that best describes the available data. In the case of InformationModelSelection the selection criteria have been extracted into separate classes under the InformationCriterion baseclass. Similarly, the evidence methods of BayesModelSelection are also parameters that implement the abstract base class EvidenceMethod.

Reliability

The reliability module maintained the same class hierarachy as in v3, with SubsetSimulation being an independent class and FORM and SORM methods providing concrete implementations to the TaylorSeries abstract base class.

Surrogates

Another module that has extensively restructured in v4 is the surrogates. Apart from the SROM method which was retained as an independent algorithm, the previous Kriging functionality was removed. It is now replaced with GaussianProcessRegression. The functionality of the Gaussian is constructed using object composition, and the specific implementation of Regression and Kernel abstract base classes. An additional functionality of constrained surrogates is added by implementing the ConstraintsGPR abstract class. The functionality of PolynomialChaosExpansion was rewritten from scratch to address some performance issues of v3. The Strategy Design pattern was used here as well, with three abstract base classes Polynomials, PolynomialBasis ans Regression serving as the interface for the concrete classes.

Sensitivity

The sensitivity module has significantly benefited from the enhanced of modularity of the code introduced in v4. Apart from the existing independent MorrisSensitivity method, the PceSensitivity was added as an independent class. Finally, based on the common Sensitivity abstract base class, a series of new algorithms were introduced such as SobolSensitivity, GeneralizedSobolSensitivity, ChatterjeeSensitivity and CramerVonMisesSensitivity.

Dimension Reduction

The final but one of the most import modules in UQpy is dimension reduction. The SnapshotPOD and DirectPOD methods were retained under the POD abstract base class. HigherOrderSVD method was introduced as independent class, while special attention was given to Grassmann Manifolds. The abstract base class GrassmannProjection serves as an interface for different methods to project data on the Grassmann Manifold, with GrassmannOperations and GrassmannInterpolation support all related operations.