6. Data Library¶

The orc.data module provides a collection of ODE and PDE benchmark systems commonly used to evaluate reservoir computing methods. Each function returns a solution array U and time vector t.

In [1]:

import functools
import time

import jax
jax.config.update("jax_enable_x64", True)
import jax.numpy as jnp
import jax.random
import diffrax
import numpy as np
import matplotlib.pyplot as plt

import orc.data
import orc.utils.visualization as vis

import functools import time import jax jax.config.update("jax_enable_x64", True) import jax.numpy as jnp import jax.random import diffrax import numpy as np import matplotlib.pyplot as plt import orc.data import orc.utils.visualization as vis

ODE Systems¶

Lorenz63 — 3D chaotic attractor and the canonical RC benchmark. Lyapunov time $\approx$ 1.1 time units.

In [2]:

u,t = orc.data.lorenz63(tN = 20, dt = 0.01)
vis.plot_time_series(u,t, title="Lorenz63 Time Series")

u,t = orc.data.lorenz63(tN = 20, dt = 0.01) vis.plot_time_series(u,t, title="Lorenz63 Time Series")

Rössler — 3D chaotic system with simpler attractor geometry than Lorenz.

In [3]:

u,t = orc.data.rossler(tN = 100, dt = 0.01)
vis.plot_time_series(u,t, title="Rossler Time Series")

u,t = orc.data.rossler(tN = 100, dt = 0.01) vis.plot_time_series(u,t, title="Rossler Time Series")

Sakaraya — 3D chaotic system from ecological modeling (predator-prey dynamics).

In [4]:

u,t = orc.data.sakaraya(tN = 20, dt = 0.01)
vis.plot_time_series(u,t, title="Sakaraya Time Series")

u,t = orc.data.sakaraya(tN = 20, dt = 0.01) vis.plot_time_series(u,t, title="Sakaraya Time Series")

Colpitts — 3D chaotic oscillator originating from electronic circuit theory.

In [5]:

u,t = orc.data.colpitts(tN = 100, dt = 0.01)
vis.plot_time_series(u,t, title="Colpitts Time Series")

u,t = orc.data.colpitts(tN = 100, dt = 0.01) vis.plot_time_series(u,t, title="Colpitts Time Series")

Hyper Lorenz63 — 4D hyperchaotic extension of the Lorenz system (two positive Lyapunov exponents).

In [6]:

u,t = orc.data.hyper_lorenz63(tN = 20, dt = 0.01)
vis.plot_time_series(u,t, title="Hyper Lorenz63 Time Series")

u,t = orc.data.hyper_lorenz63(tN = 20, dt = 0.01) vis.plot_time_series(u,t, title="Hyper Lorenz63 Time Series")

Hyper Xu — 4D hyperchaotic system with complex attractor structure.

In [7]:

u,t = orc.data.hyper_xu(tN = 20, dt = 0.01)
vis.plot_time_series(u,t, title="Hyper Xu Time Series")

u,t = orc.data.hyper_xu(tN = 20, dt = 0.01) vis.plot_time_series(u,t, title="Hyper Xu Time Series")

Double Pendulum — 4D Hamiltonian system exhibiting chaos. Supports optional damping.

In [8]:

u,t = orc.data.double_pendulum(tN = 40, dt = 0.01, damping=0.0)
vis.plot_time_series(u,t, title="Double Pendulum Time Series")

u,t = orc.data.double_pendulum(tN = 40, dt = 0.01, damping=0.0) vis.plot_time_series(u,t, title="Double Pendulum Time Series")

Spatiotemporal Systems¶

Lorenz96 — $N$-dimensional spatiotemporal chaos with adjustable dimension. Commonly used for testing high-dimensional forecasting methods.

In [9]:

u,t = orc.data.lorenz96(tN = 40, dt = 0.05, N=200)
vis.imshow_1D_spatiotemp(u,t[-1], title="Lorenz96 Time Series", interpolation='bicubic')

u,t = orc.data.lorenz96(tN = 40, dt = 0.05, N=200) vis.imshow_1D_spatiotemp(u,t[-1], title="Lorenz96 Time Series", interpolation='bicubic')

Kuramoto-Sivashinsky (1D) — Spatiotemporally chaotic PDE integrated with a spectral method. A standard benchmark for high-dimensional RC forecasting (see ks.ipynb).

In [10]:

u,t = orc.data.KS_1D(tN=1000)
vis.imshow_1D_spatiotemp(u,t[-1], title="Kuramoto-Sivashinsky 1D Time Series", interpolation='bicubic')

u,t = orc.data.KS_1D(tN=1000) vis.imshow_1D_spatiotemp(u,t[-1], title="Kuramoto-Sivashinsky 1D Time Series", interpolation='bicubic')

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