[Rbravo555]

📝 Description

Adds RBF-enhanced ROMs, an alternative to the ANN-enhanced ones in which the superior reduced coordinates are obtained from the inferior ones with radial basis functions instead of a neural network.

The decoder is the same as for the ANN-enhanced ROMs, x = x_ref + Phi_inf q_inf + Phi_sup q_sup(q_inf), so the RBF-enhanced ROMs reuse the ANN-enhanced builders and solvers ("galerkin_rbf" and "lspg_rbf" projection strategies) with an RBF decoder (RomRBFUtility, Gaussian and inverse multiquadric kernels). They are selected with "type_of_decoder": "rbf_enhanced" in the RomManager:

"type_of_decoder": "rbf_enhanced",
"ROM": {
    ...
    "rbf_enhanced_settings": {
        "modes": [5, 50],
        "rbf_solver": "svd",        // or "ridge"
        "training": {"retrain_if_exists": false}
    }
}

The RBF centers are the inferior reduced coordinates of the training snapshots, and the kernel and its epsilon are chosen with the validation cases (mu_validation in Fit). The trained models are stored in the database (saved_rbf_models, new RBF table).

As for the ANN-enhanced ROMs (#14834, #14842):

• coupled solvers get one basis and one RBF per solver (coupled_solvers with their own nodal_unknowns)
• RomManager.ExportRbfEnhancedRom exports the trained model to a folder that runs without the RomManager and its database (RightBasisMatrix.npy, [<sub_solver>_]SingularValues.npy, [<sub_solver>_]rbf_weights.npy, [<sub_solver>_]rbf_centers.npy and the "rbf_enhanced_settings" with the kernel and epsilon in the RomParameters.json)

The export of the ROM parameters is now shared by the ANN and RBF exports.

The test databases include the new (empty) RBF table, so running the tests does not modify them.

🆕 Changelog

• Added RBF-enhanced ROMs ("type_of_decoder": "rbf_enhanced", Galerkin and LSPG), reusing the ANN-enhanced builders and solvers with an RBF decoder
• Added RBF-enhanced ROMs for coupled solvers, with one basis and one RBF per solver
• Added RomManager.ExportRbfEnhancedRom to run the RBF-enhanced ROM without the RomManager
• Added C++ and Python tests (fluid Galerkin and LSPG, export, coupled fluid-thermal)

[NicolasSR]

Good that it resuses the solvers for the ANN to keep the code more tidy. Code makes sense to me and passes the tests (same case as for ANN). Approved.