Question

我正在尝试对具有2个反应物的Python中的两个耦合ODE进行参数优化。我想使用标准化残差作为我的目标函数。

反应是：

da/dt = - k1 * a + k2 * b

db/dt =   k1 * a - k2 * b

初始值：a(0) = 1和b(0) = 0。

初始反应常数：k1 = 1和k2 = 0.1。反应常数在1e-3 < k < 10范围内。这些是要优化的参数。

我设法编写了ODE和目标函数。

到目前为止，这是我的代码。

import numpy as np
from scipy.integrate import odeint
import operator

# My test data
data_b = [0.0244, 0.0842, 0.1208, 0.1724, 0.2315, 0.2634, 0.2831, 0.3084, 0.3079, 0.3097, 0.3324]
data_x = np.linspace(0, 10, 11) # Time points at which the data was measured

# Initial values
x = [1, 0]
k = [1, 0.1]

# My coupled ODE functions with constant reaction constants
def f(x, t):
    k = [1, 0.1]
    a = x[0]
    b = x[1]
    k1 = k[0]
    k2 = k[1]

    dadt = - k1 * a + k2 * b
    dbdt =   k2 * a - k2 * b

    return(dadt, dbdt)

# Trying the function. 
y = odeint(f, x, data_x)
print(y)

# My objective function. Only the concentration of `b` is taken into account. 

def objective(sim, measured):
    # The standard deviation of the data. 
    # The error is normal distributed with mean zero and `sd = 0.015`
    sigma = np.repeat(0.015, len(sim))

    j = list(map(operator.sub, sim, measured)) # Pairwise subtraction
    j = list(map(operator.truediv, j, sigma))  # Division by sigma
    j = list(map(operator.pow, j, np.repeat(2,len(j)))) # Squaring 
    j = sum(j)
    return(j)

# Trying the objective function
j = objective(y[:,1], data_b)
print(j)

# The same ODEs but with reaction constants as parameters
def fb(x, k, t):
    a = x[0]
    b = x[1]
    k1 = k[0]
    k2 = k[1]

    # The ODEs
    dadt = - k1 * a + k2 * b
    dbdt =   k1 * a - k2 * b
    return(dadt, dbdt)

此函数返回以下错误：

error: Extra arguments must be in a tuple

如何解决此错误以及如何进行？我知道我必须结合ODE函数和目标函数并使用函数scipy.optimize.curve_fit进行优化。但是我不知道该怎么做。

耦合ODE的参数估计

0 个答案: