python - How to fit differential equation to a various data points

Question

I have various data points which want to fit all of them with different differential equations. For example :

t = [0.01, 6, 12, 18, 24, 30, 36, 42, 48, 57, 75]
Ca_data = [64.8, 68.4, 48.0, 36.8, 33.7, 33.4, 29, 33.5, 32.0, 32.2, 0.01]

This is one set of data which I have and I want to fit it with following function:

def fitfunc(t, a, b):
    def myode(Ca, t):
        return a *(Ca ** (2/3)) - b * Ca

    Ca0 = Ca_data[0]
    Casol = odeint(myode, Ca0, t)
    return Casol[:,0]

The following code is the script which I wrote to find the initial values using genetic algorithm and fit the function to data points which is seems that does not work.

import numpy as np
from scipy.optimize import curve_fit
from scipy.integrate import odeint

def generate_Initial_Parameters_genetic(t, d):
    # min and max used for bounds
    maxX = max(t)
    maxY = max(d)
    maxXY = max(maxX, maxY)

    parameterBounds = []
    parameterBounds.append([-maxXY, maxXY])
    parameterBounds.append([-maxXY, maxXY])

    result = differential_evolution(sumOfSquaredError, parameterBounds,         
             seed=3,updating='deferred',workers=2)

    return result.x

def sumOfSquaredError(parameterTuple):
    warnings.filterwarnings("ignore") 
    val = fitfunc(tspan, *parameterTuple)
    return np.sum((Ca_data - val) ** 2.0)

geneticParameters = generate_Initial_Parameters_genetic(tspan, Ca_data)
k_fit, kcov = curve_fit(fitfunc, tspan, Ca_data, p0 = geneticParameters, maxfev = 20000)
                
k_fit, kcov = curve_fit(fitfunc, tspan, Ca_data, p0 = [0,0])

tfit = np.linspace(0,75)
fit = fitfunc(tfit, k_fit[0], k_fit[1])

plt.plot(tspan, Ca_data, 'ro', label='data')
plt.plot(tfit, fit, 'b-', label='fit')
plt.legend(loc='best')

Answer 1

等待大神答复