15.1. Task algorithm “EnsembleOfSimulationGenerationTask

This algorithm is reserved for use in the textual user interface (TUI), and therefore not in graphical user interface (GUI).

15.1.1. Description

This algorithm allows to generate a set of physical results, of simulation or observation type, using the H operator for a design of experiment of the \mathbf{x} parametric state space. The result of this algorithm is a homogeneous collection of simulated vectors \mathbf{y} (available using the storable variable “EnsembleOfSimulations”) corresponding directly to the chosen homogeneous collection of state vectors \mathbf{x} (available using the storable variable “EnsembleOfStates”).

The sampling of the states \mathbf{x} can be given explicitly or under form of hypercubes, explicit or sampled according to classic distributions, or using Latin hypercube sampling (LHS) or Sobol sequences. The computations are optimized according to the computer resources available and the options requested by the user. You can refer to the Requirements for describing a state sampling for an illustration of sampling. Beware of the size of the hypercube (and then to the number of computations) that can be reached, it can grow quickly to be quite large. When a state is not observable, a “NaN” value is returned.

To be visible by the user while reducing the risk of storage difficulties, the results of sampling or simulations has to be explicitly asked for using the required variable.

The results obtained with this algorithm can be used to feed an Task algorithm “MeasurementsOptimalPositioningTask”. In a complementary way, and if the goal is to evaluate the calculation-measurement error, an Checking algorithm “SamplingTest” uses the same sampling commands to establish a set of error functional values J from observations \mathbf{y}^o.

15.1.2. Optional and required commands

The general required commands, available in the editing user graphical or textual interface, are the following:

CheckingPoint

Vector. The variable indicates the vector used as the state around which to perform the required check, noted \mathbf{x} and similar to the background \mathbf{x}^b. It is defined as a “Vector” or “VectorSerie” type object. Its availability in output is conditioned by the boolean “Stored” associated with input.

ObservationOperator

Operator. The variable indicates the observation operator, usually noted as H, which transforms the input parameters \mathbf{x} to results \mathbf{y} to be compared to observations \mathbf{y}^o. Its value is defined as a “Function” type object or a “Matrix” type one. In the case of “Function” type, different functional forms can be used, as described in the section Requirements for functions describing an operator. If there is some control U included in the observation, the operator has to be applied to a pair (X,U).

The general optional commands, available in the editing user graphical or textual interface, are indicated in List of commands and keywords for a dedicated task or study oriented case. Moreover, the parameters of the command “AlgorithmParameters” allow to choose the specific options, described hereafter, of the algorithm. See Description of options of an algorithm by “AlgorithmParameters” for the good use of this command.

The options are the following:

SampleAsExplicitHyperCube

List of list of real values. This key describes the calculations points as an hyper-cube, from a given list of explicit sampling of each variable as a list. That is then a list of lists, each of them being potentially of different size. By nature, the points are included in the domain defined by the bounds of the explicit lists for each variable.

Example : {"SampleAsExplicitHyperCube":[[0.,0.25,0.5,0.75,1.], [-2,2,1]]} for a state space of dimension 2.

SampleAsIndependantRandomVariables

List of triplets [Name, Parameters, Number]. This key describes the calculations points as an hyper-cube, for which the points on each axis come from a independent random sampling of the axis variable, under the specification of the distribution, its parameters and the number of points in the sample, as a list ['distribution', [parameters], number] for each axis. The possible distributions are ‘normal’ of parameters (mean,std), ‘lognormal’ of parameters (mean,sigma), ‘uniform’ of parameters (low,high), or ‘weibull’ of parameter (shape). That is then a list of the same size than the one of the state. By nature, the points are included in the unbounded or bounded domain, depending on the characteristics of the distributions chosen for each variable.

Example : {"SampleAsIndependantRandomVariables":[['normal',[0.,1.],3], ['uniform',[-2,2],4]]} for a state space of dimension 2.

SampleAsMinMaxLatinHyperCube

List of triplets of pair values. This key describes the bounded domain in which the calculations points will be placed, from a [min,max] pair for each state component. The lower bounds are included. This list of pairs, identical in number to the size of the state space, is augmented by a pair of integers [dim,nbr] containing the dimension of the state space and the desired number of sample points. Sampling is then automatically constructed using the Latin hypercube method (LHS). By nature, the points are included in the domain defined by the explicit bounds.

Example : {"SampleAsMinMaxLatinHyperCube":[[0.,1.],[-1,3]]+[[2,11]]} for a state space of dimension 2 and 11 sampling points.

SampleAsMinMaxSobolSequence

List of triplets of pair values. This key describes the bounded domain in which the calculations points will be placed, from a [min,max] pair for each state component. The lower bounds are included. This list of pairs, identical in number to the size of the state space, is augmented by a pair of integers [dim,nbr] containing the dimension of the state space and the minimum desired number of sample points (by construction, the number of points generated in the Sobol sequence will be the power of 2 immediately above this minimum number). Sampling is then automatically constructed using the Sobol sequence method. By nature, the points are included in the domain defined by the explicit bounds.

Remark: it is required to have Scipy version 1.7.0 or higher to use this sampling option.

Example : {"SampleAsMinMaxSobolSequence":[[0.,1.],[-1,3]]+[[2,11]]} for a state space of dimension 2 and 11 sampling points (there will be 16 points in practice).

SampleAsMinMaxStepHyperCube

List of triplets of real values. This key describes the calculations points as an hyper-cube, from a given list of implicit sampling of each variable by a triplet [min,max,step]. That is then a list of the same size than the one of the state. The bounds are included. By nature, the points are included in the domain defined by the explicit bounds.

Example : {"SampleAsMinMaxStepHyperCube":[[0.,1.,0.25],[-1,3,1]]} for a state space of dimension 2.

SampleAsnUplet

List of states. This key describes the calculations points as a list of n-uplets, each n-uplet being a state. By nature, points are included in the bounded domain defined as the convex envelope of explicitly designated points.

Example : {"SampleAsnUplet":[[0,1,2,3],[4,3,2,1],[-2,3,-4,5]]} for 3 points in a state space of dimension 4.

SetDebug

Boolean value. This variable leads to the activation, or not, of the debug mode during the function or operator evaluation. The default is “False”, the choices are “True” or “False”.

Example: {"SetDebug":False}

SetSeed

Integer value. This key allow to give an integer in order to fix the seed of the random generator used in the algorithm. By default, the seed is left uninitialized, and so use the default initialization from the computer, which then change at each study. To ensure the reproducibility of results involving random samples, it is strongly advised to initialize the seed. A simple convenient value is for example 123456789. It is recommended to put an integer with more than 6 or 7 digits to properly initialize the random generator.

Example: {"SetSeed":123456789}

StoreSupplementaryCalculations

List of names. This list indicates the names of the supplementary variables, that can be available during or at the end of the algorithm, if they are initially required by the user. Their availability involves, potentially, costly calculations or memory consumptions. The default is then a void list, none of these variables being calculated and stored by default (excepted the unconditional variables). The possible names are in the following list (the detailed description of each named variable is given in the following part of this specific algorithmic documentation, in the sub-section “Information and variables available at the end of the algorithm”): [ “EnsembleOfSimulations”, “EnsembleOfStates”, ].

Example : {"StoreSupplementaryCalculations":["CurrentState", "Residu"]}

15.1.3. Information and variables available at the end of the algorithm

At the output, after executing the algorithm, there are information and variables originating from the calculation. The description of Variables and information available at the output show the way to obtain them by the method named get, of the variable “ADD” of the post-processing in graphical interface, or of the case in textual interface. The input variables, available to the user at the output in order to facilitate the writing of post-processing procedures, are described in the Inventory of potentially available information at the output.

Permanent outputs (non conditional)

The unconditional outputs of the algorithm are the following:

EnsembleOfSimulations

List of vectors or matrix. This key contains an ordered collection of physical or simulated state vectors \mathbf{y} (called “snapshots” in reduced basis terminology), with 1 state per column if it is a matrix, or 1 state per element if it is a list. Caution: the numbering of the support or points, on which or to which a state value is given in each vector, is implicitly that of the natural order of numbering of the state vector, from 0 to the “size minus 1” of this vector.

Example : {"EnsembleOfSimulations":[y1, y2, y3...]}

Set of on-demand outputs (conditional or not)

The whole set of algorithm outputs (conditional or not), sorted by alphabetical order, is the following:

EnsembleOfSimulations

List of vectors or matrix. This key contains an ordered collection of physical or simulated state vectors \mathbf{y} (called “snapshots” in reduced basis terminology), with 1 state per column if it is a matrix, or 1 state per element if it is a list. Caution: the numbering of the support or points, on which or to which a state value is given in each vector, is implicitly that of the natural order of numbering of the state vector, from 0 to the “size minus 1” of this vector.

Example : {"EnsembleOfSimulations":[y1, y2, y3...]}

EnsembleOfStates

List of vectors or matrix. Each element is an ordered collection of physical or parameter state vectors \mathbf{x}, with 1 state per column if it is a matrix, or 1 state per element if it is a list. Caution: the numbering of the support or points, on which or to which a state value is given in each vector, is implicitly that of the natural order of numbering of the state vector, from 0 to the “size minus 1” of this vector.

Example : {"EnsembleOfStates":[x1, x2, x3...]}