Table 3 Model parameters and the optimized Gaussian process model
From: Modeling nanofluid viscosity: comparing models and optimizing feature selection—a novel approach
Preset | Hyperparameters | Selected features | Feature ranking algorithm | Optimizer options |
|---|---|---|---|---|
Custom Gaussian process regression | Signal standard deviation: 0.20121; Optimize numeric parameters: Yes | 07/19 TC, DP, VF, NPcp, NPde, BFd, BFcp | Novel Feature selection algorithms (NFSA) | Optimizer: Bayesian optimization; Acquisition function: Expected improvement per second plus; Iterations: 30; Training time limit: false |
Custom Gaussian process regression | Signal standard deviation: 0.20121; Optimize numeric parameters: Yes | 19/19 | None | Optimizer: Bayesian optimization; Acquisition function: Expected improvement per second plus; Iterations: 30; Training time limit: false |
Custom Gaussian process regression | Signal standard deviation: 0.20121; Optimize numeric parameters: Yes | 19/19 | FTest | Optimizer: Bayesian optimization; Acquisition function: Expected improvement per second plus; Iterations: 30; Training time limit: false |
Custom Gaussian process regression | Signal standard deviation: 0.20121; Optimize numeric parameters: Yes | 19/19 | MRMR | Optimizer: Bayesian optimization; Acquisition function: Expected improvement per second plus; Iterations: 30; Training time limit: false |
Exponential GPR | Basis function: Constant; Kernel function: Exponential; Use isotropic kernel: Yes; Kernel scale: Automatic; Signal standard deviation: Automatic; Sigma: Automatic; Standardize data: Yes; Optimize numeric parameters: Yes | 19/19 | None | Not applicable |
Rational quadratic GPR | Basis function: Constant; Kernel function: Rational Quadratic; Use isotropic kernel: Yes; Kernel scale: Automatic; Signal standard deviation: Automatic; Sigma: Automatic; Standardize data: Yes; Optimize numeric parameters: Yes | 19/19 | None | Not applicable |
Matern 5/2 GPR | Basis function: Constant; Kernel function: Matern 5/2; Use isotropic kernel: Yes; Kernel scale: Automatic; Signal standard deviation: Automatic; Sigma: Automatic; Standardize data: Yes; Optimize numeric parameters: Yes | 19/19 | None | Not applicable |
Medium neural network | Number of fully connected layers: 1; First layer size: 25; Activation: ReLU; Iteration limit: 1000; Regularization strength (Lambda): 0; Standardize data: Yes | 19/19 | None | Not applicable |
Bilayered neural network | Number of fully connected layers: 2; First layer size: 10; Second layer size: 10; Activation: ReLU; Iteration limit: 1000; Regularization strength (Lambda): 0; Standardize data: Yes | 19/19 | None | Not applicable |
Trilayered Neural Network | Number of fully connected layers: 3; First layer size: 10; Second layer size: 10; Third layer size: 10; Activation: ReLU; Iteration limit: 1000; Regularization strength (Lambda): 0; Standardize data: Yes | 19/19 | None | Not applicable |
Squared exponential GPR | Basis function: Constant; Kernel function: Squared Exponential; Use isotropic kernel: Yes; Kernel scale: Automatic; Signal standard deviation: Automatic; Sigma: Automatic; Standardize data: Yes; Optimize numeric parameters: Yes | 19/19 | None | Not applicable |
Wide neural network | Number of fully connected layers: 1; First layer size: 100; Activation: ReLU; Iteration limit: 1000; Regularization strength (Lambda): 0; Standardize data: Yes | 19/19 | None | Not applicable |
Narrow neural network | Number of fully connected layers: 1; First layer size: 10; Activation: ReLU; Iteration limit: 1000; Regularization strength (Lambda): 0; Standardize data: Yes | 19/19 | None | Not applicable |
Interactions linear | Terms: Interactions; Robust option: Off | 19/19 | None | Not applicable |
Stepwise linear | Initial terms: Linear; Upper bound on terms: Interactions; Maximum number of steps: 1000 | 19/19 | None | Not applicable |
Medium Gaussian SVM | Kernel function: Gaussian; Kernel scale: 4.4; Box constraint: Automatic; Epsilon: Auto; Standardize data: Yes | 19/19 | None | Not applicable |
Fine tree | Minimum leaf size: 4; Surrogate decision splits: Off | 19/19 | None | Not applicable |
Quadratic SVM | Kernel function: Quadratic; Kernel scale: Automatic; Box constraint: Automatic; Epsilon: Auto; Standardize data: Yes | 19/19 | None | Not applicable |
Linear | Terms: Linear; Robust option: Off | 19/19 | None | Not applicable |
Robust linear | Terms: Linear; Robust option: On | 19/19 | None | Not applicable |
Linear SVM | Kernel function: Linear; Kernel scale: Automatic; Box constraint: Automatic; Epsilon: Auto; Standardize data: Yes | 19/19 | None | Not applicable |
Fine Gaussian SVM | Kernel function: Gaussian; Kernel scale: 1.1; Box constraint: Automatic; Epsilon: Auto; Standardize data: Yes | 19/19 | None | Not applicable |
Cubic SVM | Kernel function: Cubic; Kernel scale: Automatic; Box constraint: Automatic; Epsilon: Auto; Standardize data: Yes | 19/19 | None | Not applicable |
Custom Gaussian process regression | Signal standard deviation: 0.20121; Optimize numeric parameters: Yes | 08/19 NPde, NPk, TC, NPri, NPa, VF, DP, NPcp | ReliefF | Optimizer: Bayesian optimization; Acquisition function: Expected improvement per second plus; Iterations: 30; Training time limit: false |
Boosted trees | Minimum leaf size: 8; Number of learners: 30; Learning rate: 0.1; Number of predictors to sample: Select All | 19/19 | None | Not applicable |
Custom Gaussian process regression | Signal standard deviation: 0.20121; Optimize numeric parameters: Yes | 15/19 NPk, BFd, DP, BFa, BFv, NPa, BFkv, BFcp, NPd, BFbp, BFst, BFde, BFk, NPri, NPcp | MRMR | Optimizer: Bayesian optimization; Acquisition function: Expected improvement per second plus; Iterations: 30; Training time limit: false |
Coarse Gaussian SVM | Kernel function: Gaussian; Kernel scale: 17; Box constraint: Automatic; Epsilon: Auto; Standardize data: Yes | 19/19 | None | Not applicable |
Bagged trees | Minimum leaf size: 8; Number of learners: 30; Number of predictors to sample: Select All | 19/19 | None | Not applicable |
SVM kernel | Learner: SVM; Number of expansion dimensions: Auto; Regularization strength (Lambda): Auto; Kernel scale: Auto; Epsilon: Auto; Iteration limit: 1000 | 19/19 | None | Not applicable |
Least squares regression kernel | Learner: Least Squares Kernel; Number of expansion dimensions: Auto; Regularization strength (Lambda): Auto; Kernel scale: Auto; Iteration limit: 1000 | 19/19 | None | Not applicable |
Medium tree | Minimum leaf size: 12; Surrogate decision splits: Off | 19/19 | None | Not applicable |
Coarse tree | Minimum leaf size: 36; Surrogate decision splits: Off | 19/19 | None | Not applicable |