nnopinf.operators.PsdLagrangianOperator#

class nnopinf.operators.PsdLagrangianOperator(acts_on, depends_on, n_hidden_layers, n_neurons_per_layer, activation=<built-in method tanh of type object>, siren_omega_0=30.0, siren_first_layer=False, fourier_features=False, fourier_variables=None, fourier_num_frequencies=2, fourier_base=2.0, fourier_scale=1.0, fourier_frequencies=None, positive=True, name='PsdLagrangianOperator')[source]#

Bases: Module

\(f: x \mapsto \nabla_x \mathcal{L}(x)\) where \(\mathcal{L}(x) = x^T A(x) x\) and \(A(x)\) is an SPD operator.

Constructs a Lagrangian operator whose internal scalar network is formed by an SPD operator acting on the state and then left-multiplied by the state.

Parameters:

  • acts_on (nnopinf.Variable) – The state the operator acts on, i.e., the \(x\).

  • depends_on (tuple of nnopinf.Variable) – The variables the operator depends on.

  • n_hidden_layers (int) – Number of hidden layers in the SPD network.

  • n_neurons_per_layer (int) – Number of neurons in each hidden layer.

  • activation (PyTorch activation function (e.g., torch.nn.functional.relu)) – Activation function used at each layer.

  • siren_omega_0 (float) – Frequency scale for SIREN activations.

  • siren_first_layer (bool) – If True, use a SIREN-style first layer even for non-sine activations.

  • fourier_features (bool) – If True, augment inputs with Fourier features.

  • fourier_variables (iterable of str, optional) – Variable names to augment with Fourier features. Defaults to all inputs.

  • fourier_num_frequencies (int) – Number of frequencies per variable when using Fourier features.

  • fourier_base (float) – Base for geometric progression of Fourier frequencies.

  • fourier_scale (float) – Scaling applied to Fourier frequencies.

  • fourier_frequencies (array-like, optional) – Explicit list of Fourier frequencies. Overrides fourier_num_frequencies.

  • positive (bool) – If operator is SPD or NPD.

  • name (string) – Operator name. Used when saving to file.

forward(inputs, return_jacobian=False)[source]#

Forward pass of operator

Parameters:

  • inputs (dict(str, np.array)) – Dictionary of input data in the form of arrays referenced by the variable name, i.e., inputs[‘x’] = np.ones(3)

  • return_jacobian (bool, optional) – If True, return the (approximate) Jacobian in addition to the output.

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