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我想拟合以下模型： 在此处输入图像描述 一些荧光测量（[YFP] 随着时间的推移）。基本上我可以测量YFP随时间的变化，但不能测量x的变化。在浏览了溢出中的不同解决方案（并尝试了各种提出的解决方案）之后，我完成了与Symfit非常接近的工作。但是，当我尝试将模型拟合到实验结果时，我得到以下拟合结果：

Parameter Value        Standard Deviation
TauOFF    4.425923e-02 2.173698e+00
TauON     9.687891e+00 1.945774e+02
TauONx    4.539607e-02 2.239210e+00
x_SS      7.968579e+00 2.726591e+02
Status message         Maximum number of function evaluations has been exceeded.
Number of iterations   443
Objective              <symfit.core.objectives.LeastSquares object at 0x000002640701C898>
Minimizer              <symfit.core.minimizers.NelderMead object at 0x000002640701CEF0>

Goodness of fit qualifiers:
chi_squared            480161.4690600715
objective_value        240080.73453003576
r_squared              0.9677940481847731

在此处输入图像描述

我不明白为什么 X 的预测如此之低，而且几乎是一个常数（几乎是因为当我放大时，它实际上会发生一点变化）。此外，它说“已超过最大功能评估次数”。我究竟做错了什么？？我使用了错误的最小化器吗？初始参数估计值错误？

下面是我的代码：

# %% Importing modules
import symfit
from symfit import parameters, variables, ODEModel, Fit, Parameter, D
from symfit.core.objectives import LogLikelihood
from symfit.core.minimizers import NelderMead
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
from sympy.solvers import ode

# %% Experimental data. Inputs is time, outputs is fluorescence measurements ([YFP])
inputs = np.array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
   18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34,
   35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51,
   52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66])
outputs = [73.64756293519015, 44.83500717360115, 66.59467242620596, 49.65998568360771, 46.484859217283514, 72.37530519707008, 74.47354904982025, 61.437468439656605, 80.15204098496119, 93.11740890688259, 74.73900664346728, 87.38835848475512, 94.96499329658872, 116.07910576096306, 126.95045168354777, 123.76237623762376, 147.73432650527624, 168.04489072652098, 183.3221551531411, 321.22186495176834, 356.38957816377166, 389.03440885819737, 321.22186495176834, 356.38957816377166, 389.03440885819737, 582.1501961516907, 607.139657798083, 651.6151143860851, 682.4329863103533, 716.422610612502, 749.3927432822223, 777.726234656009, 809.6079246328624, 847.2845376012857, 870.6370831711431, 895.512942218847, 914.3568311720239, 1002.7537605116663, 1019.3525890625908, 1028.7006485379452, 1073.162564875272, 1080.7277331278212, 1106.8392267287595, 1119.0425361584034, 1139.207233729366, 1145.790182270091, 1177.2867420349437, 1185.0114126299773, 1196.1818638533032, 1213.7383689107828, 1208.2922013820337, 1209.8943558642277, 1225.7463589296947, 1232.9657629893582, 1221.7722725107194, 1237.6858956142842, 1240.1111320399323, 1240.6384572177496, 1249.767333643555, 1247.0462864291337, 1259.6783113651027, 1258.188648128636, 1267.006026296567, 1272.2310666363428, 1260.6866757617101, 1266.8857660924748]

# %% Model Definitions
x, y, t = variables('x, y, t')
TauONx = Parameter('TauONx', 0.1)
TauON = Parameter('TauON', 0.180854297)
### For a moment, I thought of fixing TauOFF, obtaining this value from other experiments
TauOFF = Parameter('TauOFF', 10.53547354)
#TauOFF = 10.53547354
x_SS = Parameter('x_SS', 0.1)

#### All of this is using symfit package!
model_dict = {
    D(x, t): TauONx*(x_SS - x),
    D(y, t): TauON*x - TauOFF*y,
}
# %% Execute data
ode_model = ODEModel(model_dict, initial={t: 0.0, x: 54 * 10e-4, y: 54 * 10e-4})
    
fit = Fit(ode_model, t=inputs, x=None, y=outputs, minimizer=NelderMead)
#fit = Fit(ode_model, outputs, objective=LogLikelihood)
fit_result = fit.execute()
print(fit_result)

# %% Plot the data generated vs the output
tvec = np.linspace(0, 60, 1000)
X, Y = ode_model(t=tvec, **fit_result.params)
plt.plot(tvec, X, label='[x]')
plt.plot(tvec, Y, label='[y]')
plt.scatter(inputs, outputs)
plt.legend()
plt.show()
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