这是一个图形化的3D拟合与3D散点图，3D表面图，和3D轮廓图。

import numpy, scipy, scipy.optimize
import matplotlib
from mpl_toolkits.mplot3d import  Axes3D
from matplotlib import cm # to colormap 3D surfaces from blue to red
import matplotlib.pyplot as plt
graphWidth = 800 # units are pixels
graphHeight = 600 # units are pixels
# 3D contour plot lines
numberOfContourLines = 16
def SurfacePlot(func, data, fittedParameters):
    f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)
    matplotlib.pyplot.grid(True)
    axes = Axes3D(f)
    x_data = data[0]
    y_data = data[1]
    z_data = data[2]
    xModel = numpy.linspace(min(x_data), max(x_data), 20)
    yModel = numpy.linspace(min(y_data), max(y_data), 20)
    X, Y = numpy.meshgrid(xModel, yModel)
    Z = func(numpy.array([X, Y]), *fittedParameters)
    axes.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.coolwarm, linewidth=1, antialiased=True)
    axes.scatter(x_data, y_data, z_data) # show data along with plotted surface
    axes.set_title('Surface Plot (click-drag with mouse)') # add a title for surface plot
    axes.set_xlabel('X Data') # X axis data label
    axes.set_ylabel('Y Data') # Y axis data label
    axes.set_zlabel('Z Data') # Z axis data label
    plt.show()
    plt.close('all') # clean up after using pyplot or else thaere can be memory and process problems
def ContourPlot(func, data, fittedParameters):
    f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)
    axes = f.add_subplot(111)
    x_data = data[0]
    y_data = data[1]
    z_data = data[2]
    xModel = numpy.linspace(min(x_data), max(x_data), 20)
    yModel = numpy.linspace(min(y_data), max(y_data), 20)
    X, Y = numpy.meshgrid(xModel, yModel)
    Z = func(numpy.array([X, Y]), *fittedParameters)
    axes.plot(x_data, y_data, 'o')
    axes.set_title('Contour Plot') # add a title for contour plot
    axes.set_xlabel('X Data') # X axis data label
    axes.set_ylabel('Y Data') # Y axis data label
    CS = matplotlib.pyplot.contour(X, Y, Z, numberOfContourLines, colors='k')
    matplotlib.pyplot.clabel(CS, inline=1, fontsize=10) # labels for contours
    plt.show()
    plt.close('all') # clean up after using pyplot or else thaere can be memory and process problems
def ScatterPlot(data):
    f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)
    matplotlib.pyplot.grid(True)
    axes = Axes3D(f)
    x_data = data[0]
    y_data = data[1]
    z_data = data[2]
    axes.scatter(x_data, y_data, z_data)
    axes.set_title('Scatter Plot (click-drag with mouse)')
    axes.set_xlabel('X Data')
    axes.set_ylabel('Y Data')
    axes.set_zlabel('Z Data')
    plt.show()
    plt.close('all') # clean up after using pyplot or else thaere can be memory and process problems
def func(data, a, alpha, beta):
    x = data[0]
    y = data[1]
    return a * (x**alpha) * (y**beta)
if __name__ == "__main__":
    xData = numpy.array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0])
    yData = numpy.array([11.0, 12.1, 13.0, 14.1, 15.0, 16.1, 17.0, 18.1, 90.0])
    zData = numpy.array([1.1, 2.2, 3.3, 4.4, 5.5, 6.6, 7.7, 8.0, 9.9])
    data = [xData, yData, zData]
    initialParameters = [1.0, 1.0, 1.0] # these are the same as scipy default values in this example
    # here a non-linear surface fit is made with scipy's curve_fit()
    fittedParameters, pcov = scipy.optimize.curve_fit(func, [xData, yData], zData, p0 = initialParameters)
    ScatterPlot(data)
    SurfacePlot(func, data, fittedParameters)
    ContourPlot(func, data, fittedParameters)
    print('fitted prameters', fittedParameters)
    modelPredictions = func(data, *fittedParameters) 
    absError = modelPredictions - zData
    SE = numpy.square(absError) # squared errors
    MSE = numpy.mean(SE) # mean squared errors
    RMSE = numpy.sqrt(MSE) # Root Mean Squared Error, RMSE
    Rsquared = 1.0 - (numpy.var(absError) / numpy.var(zData))
    print('RMSE:', RMSE)
    print('R-squared:', Rsquared)

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我不确定你的Model-func的正确性，我确定你传递参数的方式不正确。从James菲利普斯的代码中得到空图，只需绘制他的Model-func以适应他的数据

from scipy.optimize import curve_fit
import numpy as np
x_ = np.array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0])
y_ = np.array([11.0, 12.1, 13.0, 14.1, 15.0, 16.1, 17.0, 18.1, 90.0])
z_ = np.array([1.1, 2.2, 3.3, 4.4, 5.5, 6.6, 7.7, 8.0, 9.9])
def func(data, a, alpha, beta):
    x = data[0]
    y = data[1]
    return a * (x**alpha) * (y**beta)
# Perform curve fitting
popt, pcov = curve_fit(func, (x_, y_), z_)
# As a quick check of whether the model may be overparameterized (resulting depedencies among dims, or Multicollinearity), calculate the condition number of the covariance matrix:
print(np.linalg.cond(pcov))
# Print optimized parameters
print(popt)
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
# Create 3D plot of the data points and the fitted curve
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.scatter(x_, y_, z_, color='blue')
x_range = np.linspace(0, 100, 100)
y_range = np.linspace(0, 100, 100)
X, Y = np.meshgrid(x_range, y_range)
Z = func([X, Y], *popt)
ax.plot_surface(X, Y, Z, color='red', alpha=0.7)
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
plt.show()

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x1c 0d1x的数据
但请始终注意fit中pcov的条件号-np.linalg.cond(pcov)-参见docs
较大的值会引起关注。与拟合的不确定性相关的协方差矩阵的对角元素提供了更多信息：np.diag（pcov）阵列（[1.48814742e+29，3.78596560e-02，5.39253738e-03，2.76417220e+28]）#可以变化-例如注意，第一项和最后一项比其他元素大得多，这表明这些参数的最佳值是模糊的，并且在模型中仅需要这些参数中的一个。
或使用/变更缩放
P.S. ref. curve_fit