dynadojo.baselines.sindy.SINDy#

class dynadojo.baselines.sindy.SINDy#

Bases: AbstractAlgorithm

Sparse Identification of Nonlinear Dynamical systems (SINDy). Wrapper for ``pysindy``[1]_.

References

Note

For an example of how to use SINDy with a challenge, see LorenzSystem.

Example

from dynadojo.systems.lorenz import LorenzSystem
from dynadojo.wrappers import SystemChecker, AlgorithmChecker
from dynadojo.utils.lds import plot
from dynadojo.baselines.sindy import SINDy

latent_dim = 3
embed_dim = latent_dim
n = 50
test_size = 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(30, 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=["IND", "OOD"], max_lines=test_size)

sindy = AlgorithmChecker(SINDy(embed_dim, timesteps, max_control_cost=0, seed=100))
sindy.fit(x)
y_pred = sindy.predict(y[:, 0], timesteps)
y_err = system.calc_error(y, y_pred)
print(f"{y_err=}")
plot([y_pred, y], target_dim=min(3, latent_dim), labels=["pred", "true"], max_lines=15)

The error should be around 5.38 and the prediction looks like this:

Methods

`__init__`(embed_dim, timesteps[, ...])	Initialize the class.
`act`(x, **kwargs)	Determines the control for each action horizon.
`fit`(x, **kwargs)	Fits the algorithm on a tensor of trajectories.
`predict`(x0, timesteps, **kwargs)	Predict how initial conditions matrix evolves over a given number of timesteps.

Attributes

`embed_dim`	The embedded dimension of the dynamics.
`max_control_cost`	The maximum control cost.
`seed`	The random seed for the algorithm.
`timesteps`	The timesteps per training trajectory.

__init__(embed_dim, timesteps, max_control_cost=0, differentiation_method=None, **kwargs)#

Initialize the class.

Parameters:

embed_dim (int) – The embedded dimension of the system. Recommended to keep embed dimension small (e.g., <10).
timesteps (int) – The timesteps of the training trajectories. Must be greater than 2.
differentiation_method (str, optional) – The differentiation used in SINDy. See PySINDy documentation for more details.
max_control_cost (float, optional) – Ignores control, so defaults to 0.

act(x, **kwargs)#

Determines the control for each action horizon. control.

Parameters:

x (numpy.ndarray) – (n, timesteps, embed_dim) Trajectories tensor.
**kwargs – Additional keyword arguments.

Returns:

(n, timesteps, embed_dim) controls tensor.

Return type:

numpy.ndarray

property embed_dim#: The embedded dimension of the dynamics.

fit(x, **kwargs)#

Fits the algorithm on a tensor of trajectories.

Parameters:

x (np.ndarray) – (n, timesteps, embed_dim) Trajectories tensor.
**kwargs – Additional keyword arguments.

Return type:

None

property max_control_cost#: The maximum control cost.

predict(x0, timesteps, **kwargs)#

Predict how initial conditions matrix evolves over a given number of timesteps.

Note

The timesteps argument can differ from the ._timesteps attribute. This allows algorithms to train on a dataset of a given size and then predict trajectories of arbitrary lengths.

Note

The first coordinate of each trajectory should match the initial condition x0.

Parameters:

x0 (np.ndarray) – (n, embed_dim) initial conditions matrix
timesteps (int) – timesteps per predicted trajectory
**kwargs – Additional keyword arguments.

Returns:

(n, timesteps, embed_dim) trajectories tensor

Return type:

np.ndarray

property seed#: The random seed for the algorithm.

property timesteps#: The timesteps per training trajectory.