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Class ParamKoopman

It represents a mapping \(K: \mathrm{span}(\Psi) \times U \rightarrow \mathrm{span}(\Psi)\), which is a finite-dimensional approximation of the parametric Koopman operator.

Attributes

  • _network (torch.nn.Module): The neural network that approximates the parametric Koopman operator. Given the parameters u, returns the generated Koopman operator matrix.
  • _size (int): The size of the Koopman operator matrix.

Methods

  • __init__(self, size_K, network)
  • __call__(self, para, x): Applies the parametric Koopman operator on (x, para), which should satisfy \(x \in \mathbb{R}^{N \times N_{\psi}}\), \(\text{para} \in \mathbb{R}^{N \times N_u}\).
  • parameters(self): Returns the parameters of the neural network.
  • predict(self, para, x0, dictionary, dim_nontrain, traj_len): Predicts the trajectory of the system given the initial state x0, the dictionary dictionary, and the parameters para.
    • para (tensor): The parameters of the system.
    • x0 (tensor): The initial state of the system.
    • dictionary (Dictionary): The dictionary used to represent the state of the system.
    • dim_nontrain (int): The dimension of the non-trainable part of the state.
    • traj_len (int): The length of the trajectory to predict.