Click the criterion item in the explorer to edit its options in the property window. The name, unit and comment can be changed here. As alternative, the criteria editor can be used for a large number of criteria.
Weight
It is normally set to 1. The weight factor is used for weighting differences between several self-defined criteria in the experiment in the case of a multi-objective optimization. The weight has to be set between [0, 1]. If the value of the weight is set out of the range, it will be set automatically to the nearest range boundary 0 or 1. Depending on the optimization method, 2 cases are available:
Hooke-Jeeves-Method: The weight will be multipled by the value of the corresponding criteria. The total objective function of the optimization will be yield from weighted single criteria. The optimization returns in this case no Pareto-optimal solution set, but only one solution point based on this weighting factors.
Evolutionary Algorithms: The optimization returns here a Pareto-optimal solution set. The weight is used to calculate the optimal solution point from the Pareto-optimal solution set. A mathematical decision making support is used. The weight shows the ideal point of the normalized criteria located between [0, 1].
Cluster
Cluster Method
The used method for clustering: "Non-Cluster", "Userdefined", "Binary Tree", "K-Means" and "HDBSCAN*". "Userdefined" does nothing and it is a manuall clustering method, where user should select data points from DOE-Table or Scatter-Plot and add to new cluster manually.
Cluster Size
The max. number of data point for each cluster.
Cluster Type
The given cluster size can be minimal or maximal for all clusters.
Normed Space
If it is True, all data will be standardized for a normed space. In this case, alternating dimension will be chosen for axis spliting by Binary Tree. If it is False, the widest dimension will be chosen for axis spliting.
Axis Spliting
User can choose the point as Center or Mean Value for the spiting the axis.
Cluster Number
This is the number of all clusters
Neighbor Size
This is the number of neares neighbors
Random Initialization
The random generator for can be initialized by "Time Dependent Seed" or "User Defined Seed". By "Time Dependent Seed", the random seed will be generated by the actual time and thus, the random numbers and its clustering results will be different by re-starting clustering. The last used random seed will be saved in the option "Random Seed". By "User Defined Seed", the seed can be set manually.
Random Seed
This is the seed for initialization of the random number generator.
Include All Parameters
If it is True, all parameters will be include for clustering. If the option is False, a list of all parameters will be shown and user can select any parameter for clustering
Include Criteria
If it is True, user can select a list of criteria as additional parameter for clustering
Include Constraints
If it is True, user can select a list of constraints as additional parameter for clustering
Approximation
The method of approximation can be setup individually. There are 3 possible methods Polynomial, Gaussian Process or Hilbert Space to choose. The defult setting is "Auto-Approximation". In this case, the best approximation method from polynomial or Gaussian process will be chosen automatically for this variable. This setting is not valid for the moment methods, because these methods use first or second order Taylor series for the approximation
Type
There are 2 types of the approximation regression and classification. The regression treats the output as analog, while the classification considers the output as digital, Digital output can be only one of same defined stats or classses.
Include All Parameters
If the option is selected, all stochastic parameters of the experiment will be input parameter for the approximation (metamodel). If it is not selected, user can choose any stochastic parameters as input parameter from all stochastic parameters of the experiment for the approximation.
Gaussian Process
Covariance Function
If the approximation is set to "Gaussian Process", this option will be available. They are different implemented covariance functions for the Gaussian process being selected: "Best Covariance", "Square Exponential", "Exponential", "Gamma-Exponential", "Matern Class 3/2", "Matern Class 5/2", "Rational Quadratic" and "Periodic". The covariance function represents the interpolation between support points in the design space. It is an assumption and a critical factor of the Gaussian process. The option is normally set to "Best Covariance". In this case, the all availble covariances will be calculated to choose the best covariance for this variable.
Low-Rank Approximation
There are 3 options "Full Matrix", "Low-Rank Matrix" and "Hierarchical Matrix". The option "Full Matrix" will use full input data for the Gaussian process. By "Low-Rank Matrix", the low-rank approximation for the Gaussian process will be carried out for reducing number of input data points.
Approximation Rank [%]
This option allows users to input the exact rank of the input matrix by low-rank approximation. This rank is caculated by percentage of the full input matrix size. If the value is 100, the full input matrix will be used for Gaussian process. If the value is 50, the half of the input matrix will be taken. If the both options "Approximation Rank" and "Approximation Error" are given, the used low-rank of the input matrix will be the min. rank of both calculation cases.
Approximation Error [%]
This option allows users to input the exact error of the low-rank approximation. This error is caculated by percentage of the maximal eigenvalue of the input matrix. All eigenvalues of the matrix will be cut off, if they are smaller then this approximation error. If the value is zero, all ranks of the input matrix is used for least square. If the value is 100, only 1 rank is used. If the both options "Approximation Rank" and "Approximation Error" are given, the used low-rank of the input matrix will be the min. rank of both calculation cases.
Gaussian Noise [%]
This option is only visible if the option "Noise Optimization" = False for design of experiment. The value is defined as procentage of the absolute difference |Ymax-Ymin| of the criterion. The Gaussian noise is very important for the meta-model. It decides about the smoothness, accuracy and existence of the meta-model. if the Gaussin noise is big, the model is very smooth, but the accuracy is bad. If the Gaussian noise is smaller, the smoothness of the meta-model is worse, but the auccuracy is better. Depending on the concrete data, if the Gaussian noise is too small, the solution of the Gaussian process cannot be found. All parameters and covariances are zero. If the noise optimzation for design of experiment is on, the optimal Gaussian noise will be found automatically.
Polynom
Polynomial Type
This is the order type of the polynomial regression for the approximation. There are 3 options to choose "Best Order", "Uniform Order" and "Manual Order". If "Uniform Order" is selected, user can set the same polynomial order for all parameters. Otherwise, different polynomial orders can be set for single parameters if "Manual Order" is selected. By "Best Order", the best polynomial order for different parameters will be calculated autmatically.
Polynomial Order
User can set here the order for the uniform polynomial regression.All parameters will have got the same polynomial order.
Low-Rank Approximation
There are 2 available options: "Full Matrix" and "Low-Rank Matrix". By "Low-Rank Matrix", the low-rank approximation will be ued for regularization of the least square method.Other option takes the full matrix for calculation of least square.
Approximation Error [%]
This option allows users to reduce the rank of input matrix at the low-rank approximation. This apprximation error is caculated by percentage of the maximal eigenvalue of the input matrix. All eigenvalues of the matrix will be cut off, if they are smaller then this approximation error. If the value is zero, all ranks of the input matrix is used for least square. If the value is 100, only 1 rank is used.
Hilbert Space
Uniform Space
If the option is selected, all input parameters of the metamodel will have got the same covariance function and the same number of features or same polynomial order. Otherwise, user can define different covariance function and number of features for different input parameters.
Covariance Function
They are covariance functions for the Hilbert Space being selected: "Square Exponential", "Exponential", "Gamma-Exponential", "Matern Class 3/2", "Matern Class 5/2", "Polynomial" and "User-Defined". By "User-Defined", mathematical expressions for the feature can be modeled individually. Also parameters can be defined and used for training this user-defined feature by the option "Parameter". If the operator of integration of this feature will be used in partial differential equation or state variables, user must select the option "Integral", than derivate and input these integral terms self here for the feature. Otherway, the option "Integral" does not need to be selected.
Number of Features
It is the number of the mathematical terms for the input parameter vector (feature vector) of the metamodel.
Order of Features
It is the order of the polynomial feature.
Approximation Error [%]
This option allows users to input the exact error of the low-rank approximation for kernal method. This error is caculated by percentage of the maximal eigenvalue of the input matrix. All eigenvalues of the matrix will be cut off, if they are smaller then this approximation error. If the value is zero, all ranks of the input matrix is used for least square. If the value is 100, only 1 rank is used. If the both options "Approximation Rank" and "Approximation Error" are given, the used low-rank of the input matrix will be the min. rank of both calculation cases.
Gaussian Noise [%]
The value is defined as procentage of the absolute difference |Ymax-Ymin| of the criterion. The Gaussian noise is very important for the meta-model. It decides about the smoothness, accuracy and existence of the meta-model. if the Gaussin noise is big, the model is very smooth, but the accuracy is bad. If the Gaussian noise is smaller, the smoothness of the meta-model is worse, but the auccuracy is better. Depending on the concrete data, if the Gaussian noise is too small, the solution of the Gaussian process cannot be found. All parameters and covariances are zero. If the noise optimzation for design of experiment is on, the optimal Gaussian noise will be found automatically.
Regularization Weight
This is the weight of the regularization term on the training process for nonlinear methods.
Include DOE
If the opption is selected, the DOE data will be used for approximation. Otherwise, the DOE data will be not considered.
Weight
It is the weight for optimization of the training process. if the option "Weight Optimization" in the design of experiment is selected, this value will be used as start value for the optimization process.
Partial Differential Equation
If the opption is selected, user can define a partial differential equation (PDE).
PDE
A dialog will be opend to input the partial differential equation for physics-informed machine learning.
Linear
The option is selected, if the partial differential equation is linear
Sampling Level
The partial differential equation will be sampled to generate the data for training the metamodel. The parameter space will be divided into a grid and each parameter will be sampled in number of Sampling Level.
Adaptive Sampling
The partial differential equation will be sampled adaptive.
Stop Sensitivity [%]
The adaptive sampling will be stopped if the relationship between min. and max. residual of PDE in percent has been reached out
Resampling Points
The number of points with max residual of PDE will be resampled.
Weight
It is the weight for optimization of the training process. if the option "Weight Optimization" in the design of experiment is selected, this value will be used as start value for the optimization process.
User-Defined
If the option is selected, user can define and import the sampling data for PDE.
Geometry Data
If the option User-Defined is selected, the geometry data can be selected as sampling dataa for the PDE.
Boundary Conditions
If the opption is selected, user can define boundary conditions.
Number of Boundaries
This is the number of boundary conditions.
Boundary Function
A dialog will be open to input the mathematical expression for the boundary condition.
Number of fixed Values
This is the number of fiexed values for the boundary conditions.
Fixed Parameter
User can select the input parameter which will be fixed for the boundary condition.
Value
The value for the fixed parameter.
Sampling Level
The boundary conditions will be sampled to generate the data for training the metamodel. The parameter space will be divided into a grid and each parameter will be sampled in number of Sampling Level.
Weight
It is the weight for optimization of the training process. if the option "Weight Optimization" in the design of experiment is selected, this value will be used as start value for the optimization process.
User-Defined
If the option is selected, user can define and import the sampling data for bounbdary conditions.
Geometry Data
If the option User-Defined is selected, the geometry data can be selected as sampling data for the Boundary.
Constraints
If the opption is selected, user can define constraints.
Number of Constraints
This is the number of constraints.
Constraint Function
A dialog will be open to input the mathematical expression for the constraint.
Type
The constraint fuction can be greater than, smaller than or equal the Value.
Value
The value for comparison of the constraint function
Sampling Level
The constraint will be sampled to generate the data for training the metamodel. The parameter space will be divided into a grid and each parameter will be sampled in number of Sampling Level.
Weight
It is the weight for optimization of the training process. if the option "Weight Optimization" in the design of experiment is selected, this value will be used as start value for the optimization process.
User-Defined
If the option is selected, user can define and import the sampling data for constraint.
Geometry Data
If the option User-Defined is selected, the geometry data can be selected as sampling dataa for the constraint.
Parameters
If the opption is selected, user can define parameters which can be used in state variables, partial differential equation, boundary conditions or constraints above. These parameters will be considered as unknown input parameters for the physics model. They will be optimized by the machine learning training process to get optimal values.
Number of Parameters
This is the number of parameters.
Name
The name of the parameter.
Value
The value for the parameter. The value will be start value by optimization.
Fixed
If the option is selected, the parameter will be fixed for training process. Otherwise, the parameter will be optimized getting optimal value.
Lower Boundary
This is the lower boundary for the optimization process.
Upper Boundary
This is the upper boundary for the optimization process.
Global Parameter
If it is selected, the parameter value will be synchronized with the same global parameter in other criteria. The parameter is global in all criteria.