sme_contrib.optimize

[1]:

!pip install -q sme_contrib
import sme
import sme_contrib.optimize as smeopt
import sme_contrib.plot as smeplot
import numpy as np
from matplotlib import pyplot as plt
from IPython.display import HTML
from PIL import Image

Gray-Scott model

A simple two-species model with two reaction rate parameters, that forms spatial patterns and eventually reaches a steady state

[2]:

def simulated_gray_scott(f, k):
    m = sme.open_example_model("gray-scott")
    m.compartments[0].species[
        "V"
    ].analytic_concentration = "exp(-((x-49.5)^2+(y-49.5)^2))"
    m.parameters["f"].value = f"{f}"
    m.parameters["k"].value = f"{k}"
    m.simulate(5000, 50, return_results=False)
    return m


def gray_scott_anim(f, k):
    gray_scott = simulated_gray_scott(f, k)
    return smeplot.concentration_heatmap_animation(
        gray_scott.simulation_results(), ["V"]
    )

[3]:

anim = gray_scott_anim(0.04, 0.06)
HTML(anim.to_html5_video())

2026-04-27 09:47:14,834 - matplotlib.animation - INFO - Animation.save using <class 'matplotlib.animation.FFMpegWriter'>
2026-04-27 09:47:14,835 - matplotlib.animation - INFO - MovieWriter._run: running command: ffmpeg -f rawvideo -vcodec rawvideo -s 640x480 -pix_fmt rgba -framerate 5.0 -loglevel error -i pipe: -vcodec h264 -pix_fmt yuv420p -y /tmp/tmpwnkxmzuy/temp.m4v

[3]:

[4]:

anim = gray_scott_anim(0.051, 0.061)
HTML(anim.to_html5_video())

2026-04-27 09:47:18,888 - matplotlib.animation - INFO - Animation.save using <class 'matplotlib.animation.FFMpegWriter'>
2026-04-27 09:47:18,889 - matplotlib.animation - INFO - MovieWriter._run: running command: ffmpeg -f rawvideo -vcodec rawvideo -s 640x480 -pix_fmt rgba -framerate 5.0 -loglevel error -i pipe: -vcodec h264 -pix_fmt yuv420p -y /tmp/tmpcztb0dgx/temp.m4v

[4]:

[5]:

anim = gray_scott_anim(0.028, 0.062)
HTML(anim.to_html5_video())

2026-04-27 09:47:22,965 - matplotlib.animation - INFO - Animation.save using <class 'matplotlib.animation.FFMpegWriter'>
2026-04-27 09:47:22,966 - matplotlib.animation - INFO - MovieWriter._run: running command: ffmpeg -f rawvideo -vcodec rawvideo -s 640x480 -pix_fmt rgba -framerate 5.0 -loglevel error -i pipe: -vcodec h264 -pix_fmt yuv420p -y /tmp/tmpo_u749ml/temp.m4v

[5]:

Try to fit to the target steady state

Increasing the number of particles and the number of iterations will improve the fit, but take longer to run.

[6]:

def create_target_image(f, k):
    gray_scott = simulated_gray_scott(f, k)
    conc = gray_scott.simulation_results()[-1].species_concentration["V"][0, :]
    conc = 255 * conc / np.max(conc)
    Image.fromarray(conc.astype("uint8")).save("tmp.png")
    gray_scott.export_sbml_file("tmp.xml")

[7]:

def apply_params(model, params):
    model.parameters["f"].value = f"{params[0]}"
    model.parameters["k"].value = f"{params[1]}"

[8]:

create_target_image(0.04, 0.06)
ss = smeopt.SteadyState(
    "tmp.xml",
    "tmp.png",
    ["V"],
    apply_params,
    [0.01, 0.05],
    [0.06, 0.07],
    5000,
    2000,
    90,
)
ss.find(5, 5)
ss.plot_all()

2026-04-27 09:47:26,688 - pyswarms.single.global_best - INFO - Optimize for 5 iters with {'c1': 0.5, 'c2': 0.3, 'w': 0.9}
pyswarms.single.global_best: 100%|██████████|5/5, best_cost=16.3
2026-04-27 09:47:33,371 - pyswarms.single.global_best - INFO - Optimization finished | best cost: 16.268201726018972, best pos: [0.02464089 0.05495265]

[9]:

create_target_image(0.051, 0.061)
ss = smeopt.SteadyState(
    "tmp.xml",
    "tmp.png",
    ["V"],
    apply_params,
    [0.01, 0.05],
    [0.06, 0.07],
    5000,
    2000,
    90,
)
ss.find(5, 5)
ss.plot_all()

2026-04-27 09:47:35,412 - pyswarms.single.global_best - INFO - Optimize for 5 iters with {'c1': 0.5, 'c2': 0.3, 'w': 0.9}
pyswarms.single.global_best: 100%|██████████|5/5, best_cost=54.2
2026-04-27 09:47:42,137 - pyswarms.single.global_best - INFO - Optimization finished | best cost: 54.1962770835492, best pos: [0.03465443 0.05775772]

[10]:

create_target_image(0.028, 0.062)
ss = smeopt.SteadyState(
    "tmp.xml",
    "tmp.png",
    ["V"],
    apply_params,
    [0.01, 0.05],
    [0.06, 0.07],
    5000,
    2000,
    90,
)
ss.find(5, 5)
ss.plot_all()

2026-04-27 09:47:44,043 - pyswarms.single.global_best - INFO - Optimize for 5 iters with {'c1': 0.5, 'c2': 0.3, 'w': 0.9}
pyswarms.single.global_best: 100%|██████████|5/5, best_cost=252
2026-04-27 09:47:50,840 - pyswarms.single.global_best - INFO - Optimization finished | best cost: 252.40159938485198, best pos: [0.03089146 0.0684057 ]

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