POD-based Interpolation Models Implementation

This module contains concrete implementations of POD-based interpolation models that inherit from PODImodelAbstract. These models combine Proper Orthogonal Decomposition with various machine learning techniques for reduced-order modeling of high-dimensional field data.

The models are categorized into two types:

1. Direct field models (fields*): Learn direct mapping from parameters to field values
2. POD coefficient models (POD*): Learn mapping from parameters to POD coefficients

Available Models

Linear Regression Models:

• fieldsLinear: Direct field prediction using linear regression
• PODLinear: POD coefficient prediction using linear regression
• fieldsRidge: Direct field prediction using Ridge regression
• PODRidge: POD coefficient prediction using Ridge regression

Gaussian Process Regression Models:

• fieldsGPR: Direct field prediction using Gaussian Process Regression
• PODGPR: POD coefficient prediction using Gaussian Process Regression
• fieldsRidgeGPR: Field prediction with Ridge regularization and GPR
• PODRidgeGPR: POD coefficient prediction with Ridge regularization and GPR

Radial Basis Function Models:

• fieldsRBF: Direct field prediction using Radial Basis Function interpolation
• PODRBF: POD coefficient prediction using Radial Basis Function interpolation
• fieldsRidgeRBF: Field prediction with Ridge regularization and RBF
• PODRidgeRBF: POD coefficient prediction with Ridge regularization and RBF

Neural Network Models:

• PODANN: POD coefficient prediction using Artificial Neural Networks

Examples

1. POD with interpolation using GPR model = PODGPR(rank=15, with_scaler_x=True, with_scaler_y=True) model.fit(parameters, field_snapshots) predictions = model.predict(new_parameters)

2. Direct field prediction with RBF model = fieldsRBF(kernel='thin_plate_spline', degree=2) model.fit(parameters, field_snapshots) field_prediction = model.predict(test_parameters)