对于我的数值函数模型，tf.tape.gradient()返回None

Question

我在试着用tf.GradientTape()。但问题是tape.gradient返回None，因此弹出错误输出(TypeError : unsupported operand type(s) for *: 'float' and 'NoneType')。正如您在我的代码中看到的，dloss_dparams = tape.gradient(Cost, [XX,YY])返回none。我不知道问题出在哪里。有人知道它为什么会这样吗？

import tensorflow as tf
import math
import numpy as np
from numpy import loadtxt
import scipy.integrate as inte
from numpy import asarray
from numpy import savetxt

DPA_l=7.68e+5 #Displacements/ion/cm
Na = 6.10e+22 # atomic density atoms/cm3
c=0.0424
S = math.pi*(0.05)**2
rmax=0.23#cm
rmin=-0.23
m=100
n=100
Ndpa =1
Ninitial=1
dx = (rmax-rmin)/m
dy = (rmax-rmin)/n

dfInd = loadtxt('intensity_2c_re2.csv', delimiter =',')
dfRi = loadtxt('p2c_t,ri,sd_re3.csv', delimiter =',')
Fnd = np.full((len(dfInd),m+1,n+1),np.nan)
DPAnd = np.full((len(dfInd),m+1,n+1),np.nan)
Lnd = np.full((len(dfInd),m+1,n+1),np.nan)

def I_V(bb):
    return 2.2e-8+bb*1e-9
def T_D(aa):
    return 7.9e-2 +aa*1e-3

Vnd = np.full((len(dfInd),m+1,n+1),np.nan)
And = np.full((len(dfInd),m+1,n+1),np.nan)
A2nd = np.full((len(dfInd),m+1,n+1),np.nan)
f_x = np.full((len(dfInd),1),np.nan)
f_y = np.full((len(dfInd),1),np.nan)
SSB = np.full((len(dfInd),1),0)
F0nd =np.full((len(dfInd),2),np.nan)

#initial value
for i in range(len(dfInd)): 
    F0nd[i,1] = (0.762*dfInd[i,2]*dfInd[i,0]/S)*0.1*np.sqrt(2)/(2*(np.sqrt(math.pi))*math.erf(1/(5*c*2**2.5))*c)
    F0nd[i,0]= dfInd[i,0]
 
f_x[0,0] = inte.quad(lambda x : np.math.exp((-(x-(rmax))**2)/(2*c**2)),0,rmax-rmin)[0]
f_y[0,0] = inte.quad(lambda y : np.exp((-(y-(rmax))**2)/(2*c**2)),0,rmax-rmin)[0]
F0nd[0,1] = (0.762*dfInd[0,2]*dfInd[1,0]/S)*0.1*math.sqrt(2)/(2*(math.sqrt(math.pi))*math.erf(1/(5*c*2**2.5))*c) ###추가 12/29
DPAnd[0,:,:] = 0
Lnd[0,:,:] = 0
Vnd[0,:,:] = 0

for j in range(m+1):
    for k in range(n+1):
        Fnd[0,j,k] = math.sqrt(F0nd[0,1])*np.math.exp(-(((j*dx-(rmax))**2)/(2*c**2)))*math.sqrt(F0nd[0,1])*np.exp(-(((k*dy-(rmax))**2)/(2*c**2)))
        And[0,j,k] = ((np.exp((-(j*dx-(rmax))**2)/(2*c**2))+np.exp((-((j+1)*dx-(rmax))**2)/(2*c**2)))*0.5*dx/f_x[0])*((np.exp((-(k*dy-(rmax))**2)/(2*c**2))+np.exp((-((k+1)*dy-(rmax))**2)/(2*c**2)))*0.5*dy/f_y[0])
        A2nd[0,j,k] = (1-Vnd[0,j,k])*And[0,j,k]


def predictions(XX,YY):
    i=0
    v=1
    aa=0.0
    bb=0.0
    
    f_x[i+1,0] = inte.quad(lambda x : np.exp((-(x-(rmax-XX))**2)/(2*c**2)),0,rmax-rmin)[0]  #f_x[1,0] #f_x[21,0]
    f_y[i+1,0] = inte.quad(lambda y : np.exp((-(y-(rmax-YY))**2)/(2*c**2)),0,rmax-rmin)[0]  #f_y[1,0] #f_y[21,0]
    for j in range(m+1):
        for k in range(n+1):
            Fnd[i+1,j,k] = F0nd[i+1,1]*np.exp(-(((j*dx-(rmax-XX))**2)/(2*c**2)))*np.exp(-(((k*dy-(rmax-YY))**2)/(2*c**2)))
            And[i+1,j,k] = ((np.exp((-(j*dx-(rmax-XX))**2)/(2*c**2))+np.exp((-((j+1)*dx-(rmax-XX))**2)/(2*c**2)))*0.5*dx/f_x[i+1])*((np.exp((-(k*dy-(rmax-YY))**2)/(2*c**2))+np.exp((-((k+1)*dy-(rmax-YY))**2)/(2*c**2)))*0.5*dy/f_y[i+1])
            DPAnd[i+1,j,k] = DPAnd[i,j,k] + DPA_l*Fnd[i,j,k]/Na
                
            if  DPAnd[i+1,j,k] < T_D(aa) :
                Lnd[i+1,j,k] = DPAnd[i+1,j,k]/(T_D(aa))
            elif DPAnd[i+1,j,k]>=T_D(aa) :
                Lnd[i+1,j,k] = 1.0
                    
            if Lnd[i+1,j,k]<1:
                A2nd[i+1,j,k] = (1.0-Lnd[i+1,j,k])*And[i+1,j,k]*0.79 + 1.0*And[i+1,j,k]*0.21
            elif Lnd[i+1,j,k]==1.0:
                A2nd[i+1,j,k] = (1.0-Lnd[i+1,j,k])*And[i+1,j,k]
                    
    SSB = I_V(bb)*(((A2nd).sum(axis=2)).sum(axis=1))
    loss = (SSB[v]-dfRi[v-1,1])
    return loss


XX = tf.Variable(0.1)
YY = tf.Variable(0.1)
learning_rate = 0.01
for j in range(100):
    with tf.GradientTape() as tape:
        tape.watch([XX,YY])
        Cost = tf.reduce_mean(tf.square(predictions(XX,YY)))
        print('Cost=',Cost)
    dloss_dparams = tape.gradient(Cost, [XX,YY])
    print('dloss_dparams[0] =',dloss_dparams[0],', dloss_dparams[1] =',dloss_dparams[1])
    XX.assign_sub(learning_rate * dloss_dparams[0])
    YY.aasign_sub(learning_rate * dloss_dparams[1])

    if i%10 ==0 :
        print("{:5} I {:10.4f} I {:10.4} I {:10.6f}".format(i, XX.numpy(), YY.numpy(), cost))    

输出结果是

Cost= tf.Tensor(2.803658208007937e-17, shape=(), dtype=float64)
dloss_dparams[0] = None , dloss_dparams[1] = None
Traceback (most recent call last):
File "C:/Users/USER/Downloads/tensorflow_gradient descent14.py", line 103, in <module>
XX.assign_sub(learning_rate * dloss_dparams[0])
TypeError: unsupported operand type(s) for *: 'float' and 'NoneType'

下面是变量(XX，YY)和成本的关系图，以防万一。

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Answer 1

您正在TensorFlow之外进行计算。这将导致渐变为None，请参阅指南：Getting a gradient of None

如果计算退出TensorFlow，磁带将无法记录梯度路径。例如：

X= tf.Variable([1.0，2.0，3.0，4.0]，dtype=tf.float32)，使用tf.GradientTape()作为磁带: x2 = x**2 #此步骤通过NumPy y= np.mean(x2，axis=0) #进行计算#与大多数操作一样，reduce_mean会使用tf.convert\_to\_tensor将NumPy数组转换为常数张量#。Y= tf.reduce_mean(y，axis=0)打印(tape.gradient(y，x))

将打印

无