Tensorflow2.0 self defined training method to solve function coefficients

When doing curve fitting and approximation , If you know the approximate equation of fitting , How to find the coefficients of the equation ？
Actually in numpy There are already functions in to find polynomial coefficients , as follows

# x and y Corresponding to the coordinate axis x and y.
z = np.polyfit(x, y, 3) # use 3 Quadratic polynomial fitting , The output coefficient ranges from high to 0
# p Is the equation 
p = np.poly1d(z) # Use degree to synthesize polynomials 

But sometimes curves are more than polynomials , It's an exponential function 、 power function , This requires us to write by ourselves , In fact, it's the same as finding the coefficients of a linear function before , It's just another equation

#  Here we define independent variables and dependent variables x,y.
x = tf.constant([1, 2, 3, 4, 5, 6],dtype=tf.float64)
y = tf.constant([11, 23, 45, 46, 48, 59],dtype=tf.float64)

#  Here we define the parameters that need to be updated during reverse transmission , That is, the parameters we require 
w_a = tf.Variable(-0.0, dtype=tf.float64,name='a')
w_b = tf.Variable(0.1, dtype=tf.float64,name='b')
w_c = tf.Variable(-0.0, dtype=tf.float64,name='c')
w_d = tf.Variable(2.1, dtype=tf.float64,name='d')
#  Put our coefficients in an array , Convenient back transmission 
variables=[w_a, w_b, w_c, w_d]

#  Define the number of cycles 
epoch = 1000
#  Define optimizer 
optimizer=tf.keras.optimizers.Adam(learning_rate=1e-3)

#  loop 
for e in range(epoch):
    with tf.GradientTape() as tape:
        #  Prediction function 
        y_pred=w_a*tf.exp(w_b*x)+w_c*x+w_d
        #  Loss function 
        loss=tf.reduce_sum(tf.square(y_pred-y))
        
    #  Take the derivative of the variable 
    grads=tape.gradient(loss, variables)
    #  Adjust the parameters 
    optimizer.apply_gradients(grads_and_vars=zip(grads, variables))
    
    #  Print the results 
    if e%100==0:
            print(f"step: {
      e}, loss: {
      loss}, a: {
      w_a.numpy()}, b: {
      w_b.numpy()}, c: {
      w_c.numpy()}, d: {
      w_d.numpy()}")
#  Output parameters 
print(variables)

sauce