Constraints

This module contains concrete implementations of the constraint component.

GradParams

__init__(self, n_params, n_eqs) special

Constrains the neural network by optimizing over the coefficients together with the network. Coefficient vectors are randomly initialized from a standard Gaussian.

Parameters:

Name	Type	Description	Default
n_params	int	number of features in feature matrix.	required
n_eqs	int	number of outputs / equations to be discovered.	required

Source code in deepymod/model/constraint.py

def __init__(self, n_params: int, n_eqs: int) -> None:
    """Constrains the neural network by optimizing over the coefficients together with the network.
       Coefficient vectors are randomly initialized from a standard Gaussian.

    Args:
        n_params (int): number of features in feature matrix.
        n_eqs (int): number of outputs / equations to be discovered.
    """
    super().__init__()
    self.coeff_vectors = torch.nn.ParameterList([torch.nn.Parameter(torch.randn(n_params, 1)) for _ in torch.arange(n_eqs)])

calculate_coeffs(self, sparse_thetas, time_derivs)

Returns the coefficients of the constraint, since we're optimizing them by gradient descent.

Parameters:

Name	Type	Description	Default
sparse_thetas	List[torch.Tensor]	List containing the sparse feature tensors of size (n_samples, n_active_features).	required
time_derivs	List[torch.Tensor]	List containing the time derivatives of size (n_samples, n_outputs).	required

Returns:

Type	Description
(TensorList)	Calculated coefficients of size (n_features, n_outputs).

Source code in deepymod/model/constraint.py

def calculate_coeffs(self, sparse_thetas: TensorList, time_derivs: TensorList):
    """Returns the coefficients of the constraint, since we're optimizing them by
       gradient descent.

    Args:
        sparse_thetas (TensorList): List containing the sparse feature tensors of size (n_samples, n_active_features).
        time_derivs (TensorList): List containing the time derivatives of size (n_samples, n_outputs).

    Returns:
        (TensorList): Calculated coefficients of size (n_features, n_outputs).
    """
    return self.coeff_vectors

LeastSquares

__init__(self) special

Least Squares Constraint solved by QR decomposition

Source code in deepymod/model/constraint.py

def __init__(self) -> None:
    """ Least Squares Constraint solved by QR decomposition"""
    super().__init__()

calculate_coeffs(self, sparse_thetas, time_derivs)

Calculates the coefficients of the constraint using the QR decomposition for every pair of sparse feature matrix and time derivative.

Parameters:

Name	Type	Description	Default
sparse_thetas	List[torch.Tensor]	List containing the sparse feature tensors of size (n_samples, n_active_features).	required
time_derivs	List[torch.Tensor]	List containing the time derivatives of size (n_samples, n_outputs).	required

Returns:

Type	Description
List[torch.Tensor]	(TensorList): Calculated coefficients of size (n_features, n_outputs).

Source code in deepymod/model/constraint.py

def calculate_coeffs(self, sparse_thetas: TensorList, time_derivs: TensorList) -> TensorList:
    """Calculates the coefficients of the constraint using the QR decomposition for every pair
    of sparse feature matrix and time derivative.

    Args:
        sparse_thetas (TensorList): List containing the sparse feature tensors of size (n_samples, n_active_features).
        time_derivs (TensorList): List containing the time derivatives of size (n_samples, n_outputs).

    Returns:
        (TensorList): Calculated coefficients of size (n_features, n_outputs).
    """
    opt_coeff = []
    for theta, dt in zip(sparse_thetas, time_derivs):
        Q, R = torch.qr(theta)  # solution of lst. sq. by QR decomp.
        opt_coeff.append(torch.inverse(R) @ Q.T @ dt)

    # Putting them in the right spot
    coeff_vectors = [torch.zeros((mask.shape[0], 1)).to(coeff_vector.device).masked_scatter_(mask[:, None], coeff_vector)
                     for mask, coeff_vector
                     in zip(self.sparsity_masks, opt_coeff)]
    return coeff_vectors