Randomness and Certainty

randomness_certainty.py

# Randomness and Certainty
# https://www.lms.ac.uk/sites/default/files/inline-files/NLMS_505_for%20web.pdf#page=24

import matplotlib.pyplot as plt
import numpy as np
from diffrax import diffeqsolve, ODETerm, Dopri5, SaveAt

N = 300

rng = np.random.default_rng(42)
noise_data = rng.normal(size=N)


def f(t, y, args):
    return y - y**3 + 0.4 * args[t.astype(int)]


term = ODETerm(f)
solver = Dopri5()
saveat = SaveAt(ts=np.arange(start=0, stop=N, step=0.1))
solution = diffeqsolve(
    term,
    solver,
    t0=0,
    t1=N,
    dt0=0.1,
    y0=1,
    saveat=saveat,
    args=noise_data,
)

fig, ax = plt.subplots()
ax.plot(solution.ts, solution.ys)
ax.set_xlabel("$t$")
ax.set_ylabel("$y(t)$")
fig.show()

requirements.txt

numpy
jax[cpu]
diffrax
matplotlib