dynadojo.systems.lorenz.LorenzSystem#

class dynadojo.systems.lorenz.LorenzSystem#

Bases: SimpleSystem

Generalized Lorenz system. More details and formulation based on [1]

References

Example

>>> from dynadojo.wrappers import SystemChecker
>>> from dynadojo.utils.lds import plot
>>> latent_dim = 3
>>> embed_dim = 3
>>> n = 10
>>> timesteps = 50
>>> system = SystemChecker(LorenzSystem(latent_dim, embed_dim, noise_scale=0, seed=1912))
>>> x0 = system.make_init_conds(n)
>>> y0 = system.make_init_conds(n, in_dist=False)
>>> x = system.make_data(x0, timesteps=timesteps)
>>> y = system.make_data(y0, timesteps=timesteps, noisy=True)
>>> plot([x, y], target_dim=min(latent_dim, 3), labels=["in", "out"], max_lines=15)

>>> from dynadojo.challenges import FixedTrainSize
>>> from dynadojo.baselines.sindy import SINDy
>>> challenge = FixedTrainSize(L=[3, 9, 13, 15], E=None, t=50, n=10, reps=3, system_cls=LorenzSystem, test_examples=1, test_timesteps=50)
>>> data = challenge.evaluate(algo_cls=SINDy)
>>> challenge.plot(data)

Methods

`__init__`([latent_dim, embed_dim, sigma, r, ...])	Initialize the class.
`calc_control_cost`(control)	Calculates the L2 norm / dimension of every vector in the control
`calc_dynamics`(t, x)	Calculates the dynamics for the system.
`calc_error`(x, y)	Returns the MSE error normalized by the embedded dimension.
`make_data`(init_conds, control, timesteps[, ...])	Uses the `calc_dynamics()` method to generate data.
`make_init_conds`(n[, in_dist])	Uniformly samples embedded-dimensional points from an inside or outside distribution

Attributes

`controller`	The controller matrix.
`embed_dim`	The embedded dimension for the system.
`embedder`	The embedder matrix.
`latent_dim`	The latent dimension for the system.
`seed`	The random seed for the system.

__init__(latent_dim=3, embed_dim=3, sigma=10, r=28, a_squared=0.5, b=2.6666666666666665, **kwargs)#

Initialize the class.

Parameters:

latent_dim (int) – Must be an odd number at least 3.
sigma (int) – the Prandtl number
r (int) – normalized Rayleigh number (or heating parameter)
a_squared (float) – \(a^2 = 1 / 2\) Used default value from [1]
b_squared (float) – \(b^2 = 8 / 3\) Used default value from [1]

calc_control_cost(control)#

Calculates the L2 norm / dimension of every vector in the control

Parameters:: control (ndarray) –
Return type:: float

calc_dynamics(t, x)#: Calculates the dynamics for the system. Your class must implement this.

calc_error(x, y)#

Returns the MSE error normalized by the embedded dimension.

Return type:: float

property controller#: The controller matrix. For example, in a system \(\dot{x} = Ax + Bu\), the controller is \(B\).

property embed_dim#: The embedded dimension for the system.

property embedder#: The embedder matrix. An invertible map from the latent space to the embedding space.

property latent_dim#: The latent dimension for the system.

make_data(init_conds, control, timesteps, noisy=False)#

Uses the calc_dynamics() method to generate data. Mathematically, data is generated like \(\dot{x} = f(x) + Bu\). Where \(f(x)\) is given by calc_dynamics().

Parameters:

init_conds (numpy.ndarray) – (n, embed_dim) Initial conditions matrix.
control (numpy.ndarray) – (n, timesteps, embed_dim) Controls tensor.
timesteps (int) – Timesteps per training trajectory (per action horizon).
noisy (bool, optional) – If True, add noise to trajectories. Defaults to False. If False, no noise is added.

Returns:

(n, timesteps, embed_dim) Trajectories tensor.

Return type:

numpy.ndarray

make_init_conds(n, in_dist=True)#

Uniformly samples embedded-dimensional points from an inside or outside distribution

Note

Systems developers determine what counts as in vs out-of-distribution. DynaDojo doesn’t provide any verification that this distinction makes sense or even exists. See LDSystem for a principled example.

Parameters:

n (int) – Number of initial conditions.
in_dist (bool, optional) – If True, generate in-distribution initial conditions. Defaults to True. If False, generate out-of-distribution initial conditions.

Returns:

(n, embed_dim) Initial conditions matrix.

Return type:

numpy.ndarray

property seed#: The random seed for the system.