Training

The training is done in three sequential steps:

1. Training of the auto-encoder to find a low-dimensional subspace (latent space of dimension d) of the inputs that accounts for the variation of the outputs.

2. Clustering in the latent space using Newman's clustering algorithm to separate regions with different dynamics.

3. Training RBF networks on each Newman cluster in a two-stage framework:

   1. n_rbf centers \(\mathbf{X}^c\) are computed using the K_Means algorithm.

   2. The optimal weights are obtained by solving the corresponding RBF linear system.

• Encoder
• Newman’s clustering algorithm
• K-Means
• Kernel functions
  • Exponential Kernel
  • Spline Kernel

RONAALP.Ronaalp.train(self, x_train, z_train, x_test, z_test)

Train the model to find a reduced-order representation of the high-dimensional mapping between x_train and z_train in a latent space of dimension d with n_clusters distinct clusters .

Parameters

x_trainndarray, shape (m,D,)

Array of points where function values are known. m is the number of sampling points and D is the number of input dimensions.

z_trainndarray, shape (m,P,)

Array of function values at x_train. P is the number of output dimensions.

x_testndarray, shape (_,D,)

Similar as x_train but for testing.

z_testndarray, shape (_,P,)

Similar as z_train but for testing.