aphin.layers package

Submodules

aphin.layers.descriptor_ph_layer module

TensorFlow layers for identification of dynamical systems e.g. LTI systems (LTILayer), port-Hamiltonian systems (PHLayer), … intended for standalone use or the use in the latent space of an autoencoder. All layers approximate the right-hand side of the ODE given states z(t), inputs u(t) and parameters mu and should be trained using reference values of the states, inputs, parameters and the left-hand side of the ODE which is assumed to depend only on the time derivative of the states.

class aphin.layers.descriptor_ph_layer.DescriptorPHLayer(*args, **kwargs)[source]

Bases: PHLayer

Layer for port-Hamiltonian (pH) approximation with a descriptive matrix of the time derivative of the latent variable E * z’(t) = (J - R) * z(t) + B * u(t) with J skew-symmetric, R symmetric positive definite, and E symmetric.

property E

Get the symmetric matrix E.

Returns:: Symmetric matrix E.
Return type:: tf.Tensor

lhs(dz_dt)[source]

Evaluate left-hand side of the system ODE given z’(t) as dz_dt.

For descriptor systems: E * z’(t).

Parameters:: dz_dt (array-like) – Time derivative of the system states z’(t).
Returns:: Left-hand side of the system ODE.
Return type:: tf.Tensor

class aphin.layers.descriptor_ph_layer.DescriptorPHQLayer(*args, **kwargs)[source]

Bases: PHQLayer

Layer for port-Hamiltonian (pH) approximation with a descriptive matrix of the time derivative of the latent variable E * z’(t) = (J - R) * Q * z(t) + B * u(t) with J skew-symmetric, R symmetric positive definite, Q symmetric positive definite, and E symmetric. This is a generalization of DescriptorPHLayer.

property E

Get the symmetric matrix E.

Returns:: Symmetric matrix E.
Return type:: tf.Tensor

lhs(dz_dt)[source]

Evaluate left-hand side of the system ODE given z’(t) as dz_dt.

For descriptor systems: E * z’(t).

Parameters:: dz_dt (array-like) – Time derivative of the system states z’(t).
Returns:: Left-hand side of the system ODE.
Return type:: tf.Tensor

aphin.layers.lti_layer module

TensorFlow layers for identification of dynamical systems e.g. LTI systems (LTILayer), port-Hamiltonian systems (PHLayer), … intended for standalone use or the use in the latent space of an autoencoder. All layers approximate the right-hand side of the ODE given states z(t), inputs u(t) and parameters mu and should be trained using reference values of the states, inputs, parameters and the left-hand side of the ODE which is assumed to depend only on the time derivative of the states.

class aphin.layers.lti_layer.LTILayer(*args, **kwargs)[source]

Bases: SystemLayer

Layer for LTI approximation of the time derivative of the latent variable z’(t) = A * z(t) + B * u(t) with A = J - R, J skew. sym., R sym. The system matrix is decomposed into skew-symmetric J and symmetric parts R for conformity with pH layers

property B

Get the (full) input matrix B.

Returns:: Input matrix B.
Return type:: tf.Tensor

property J

Get the skew-symmetric matrix J.

Returns:: Skew-symmetric matrix J.
Return type:: tf.Tensor

property R

Get the symmetric matrix R.

Returns:: Symmetric matrix R.
Return type:: tf.Tensor

call(z, u=None, mu=None, training=False)[source]

Evaluate right-hand side of the ODE system z’(t) = f(z, u, mu) for inputs (z, u, mu).

Parameters:

z (array-like) – System states with shape (n_t * n_s, n).
u (array-like, optional) – System inputs with shape (n_t * n_s, n_u), by default None.
mu (array-like, optional) – Parameters, by default None.
training (bool, optional) – Whether the call is in training mode, by default False.

Returns:

Approximation of z’(t).

Return type:

tf.Tensor

property dof_split

Split of the internal degrees of freedom into J, R, B.

Returns:: Tuple containing the split of degrees of freedom.
Return type:: tuple

get_parameter_dependent_weights(mu)[source]

In case of parameter dependent weights, get the weights for the given parameters.

Parameters:: mu (array-like) – Parameters.
Returns:: Tuple containing dof_J, dof_R, dof_B, and dof_Q.
Return type:: tuple

get_system_matrices(mu=None, n_t=None)[source]

Return matrices in the format (n_sim, r, r).

Parameters:

mu (array-like, optional) – Parameters, by default None.
n_t (int, optional) – Number of time steps, required if mu is not None, by default None.

Returns:

Tuple containing matrices J, R, and B.

Return type:

tuple

init_parameter_dependent_weights()[source]: Initialize trainable variables that depend on parameters (mu).

init_weights()[source]: Initialize trainable variables

property n_matrices_dofs

Number of trainable variables for the matrices.

Returns:: Number of trainable variables.
Return type:: int

aphin.layers.ph_layer module

TensorFlow layers for identification of dynamical systems e.g. LTI systems (LTILayer), port-Hamiltonian systems (PHLayer), … intended for standalone use or the use in the latent space of an autoencoder. All layers approximate the right-hand side of the ODE given states z(t), inputs u(t) and parameters mu and should be trained using reference values of the states, inputs, parameters and the left-hand side of the ODE which is assumed to depend only on the time derivative of the states.

class aphin.layers.ph_layer.PHLayer(*args, **kwargs)[source]

Bases: LTILayer

Layer for port-Hamiltonian (pH) approximation of the time derivative of the latent variable z’(t) = (J - R) * z(t) + B * u(t) with J skew-symmetric and R symmetric positive definite.

property R

Get the symmetric positive definite matrix R.

Returns:: Symmetric positive definite matrix R.
Return type:: tf.Tensor

aphin.layers.phq_layer module

TensorFlow layers for identification of dynamical systems e.g. LTI systems (LTILayer), port-Hamiltonian systems (PHLayer), … intended for standalone use or the use in the latent space of an autoencoder. All layers approximate the right-hand side of the ODE given states z(t), inputs u(t) and parameters mu and should be trained using reference values of the states, inputs, parameters and the left-hand side of the ODE which is assumed to depend only on the time derivative of the states.

class aphin.layers.phq_layer.PHQLayer(*args, **kwargs)[source]

Bases: PHLayer

Layer for port-Hamiltonian (pH) approximation of the time derivative of the latent variable z’(t) = (J - R) * Q * z(t) + B * u(t) with J skew-symmetric, R symmetric positive definite, and Q symmetric positive definite. This is a generalization of PHLayer.

property Q

Get the symmetric positive definite matrix Q.

Returns:: Symmetric positive definite matrix Q.
Return type:: tf.Tensor

call(z, u, mu=None, training=False)[source]

Evaluate right-hand side of the ODE system z’(t) = f(z, u, mu) for inputs (z, u, mu).

Parameters:

z (array-like) – System states with shape (n_t * n_s, n).
u (array-like, optional) – System inputs with shape (n_t * n_s, n_u), by default None.
mu (array-like, optional) – Parameters, by default None.
training (bool, optional) – Whether the call is in training mode, by default False.

Returns:

Approximation of z’(t).

Return type:

tf.Tensor

property dof_split

Split of the internal degrees of freedom into J, R, B, and Q.

Returns:: Tuple containing the split of degrees of freedom.
Return type:: tuple

get_system_matrices(mu=None, n_t=None)[source]

Return matrices in the format (n_sim, r, r).

Parameters:

mu (array-like, optional) – Parameters, by default None.
n_t (int, optional) – Number of time steps, required if mu is not None, by default None.

Returns:

Tuple containing matrices J, R, B, and Q.

Return type:

tuple

init_weights()[source]: Initialize trainable variables

property n_matrices_dofs

Number of trainable variables for the matrices.

Returns:: Number of trainable variables.
Return type:: int

aphin.layers.system_layer module

TensorFlow layers for identification of dynamical systems e.g. LTI systems (LTILayer), port-Hamiltonian systems (PHLayer), … intended for standalone use or the use in the latent space of an autoencoder. All layers approximate the right-hand side of the ODE given states z(t), inputs u(t) and parameters mu and should be trained using reference values of the states, inputs, parameters and the left-hand side of the ODE which is assumed to depend only on the time derivative of the states.

class aphin.layers.system_layer.SystemLayer(*args, **kwargs)[source]

Bases: Layer

Layer for identification of an abstract system z’(t) = f(z, u, mu).

This layer approximates the right-hand side of the ODE given states z(t), inputs u(t), and parameters mu. It is intended for standalone use or for use in the latent space of an autoencoder.

abstract call(z, u=None, mu=None, training=False)[source]

Evaluate rhs of the ODE z’(t) = f(z, u, mu) for inputs (z, u, mu).

Parameters:

z (array-like) – State variables.
u (array-like, optional) – Input variables, by default None.
mu (array-like, optional) – Parameter variables, by default None.
training (bool, optional) – Whether the call is in training mode, by default False.

Returns:

Approximation of z’(t).

Return type:

tf.Tensor

get_config()[source]

Get the configuration of the layer.

Returns:: Configuration dictionary.
Return type:: dict

lhs(dz_dt)[source]

Evaluate left-hand side of the system ODE given z’(t) as dz_dt.

For descriptor systems: E * z’(t).

Parameters:: dz_dt (array-like) – Time derivative of the system states z’(t).
Returns:: Left-hand side of the system ODE.
Return type:: tf.Tensor

aphin.layers package

Submodules

aphin.layers.descriptor_ph_layer module

aphin.layers.lti_layer module

aphin.layers.ph_layer module

aphin.layers.phq_layer module

aphin.layers.system_layer module

Module contents