Question

我是该论坛的新手，所以如果我违反一些约定，请提醒我。我正在尝试实现ANN以解决PDE，但是我得到标题中引用的错误消息。

这是我的代码：

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import tensorflow as tf
tf.__version__
'2.2.0'

我用于采样域的函数和损失函数（这似乎是问题所在）

# Sampling
def sampler(N1, N2, N3):
    np.random.seed(1)
    # Sampler #1: PDE domain
    t1 = np.random.uniform(low=T0 - 0.5*(T - T0),
                           high=T,
                           size=[N1,1])
    s1 = np.random.uniform(low=S1 - (S2 - S1)*0.5,
                           high=S2 + (S2 - S1)*0.5,
                           size=[N1,1])

    # Sampler #2: boundary condition
    t2 = np.zeros(shape=(1, 1))
    s2 = np.zeros(shape=(1, 1))

    # Sampler #3: initial/terminal condition
    t3 = T * np.ones((N3,1)) #Terminal condition
    s3 = np.random.uniform(low=S1 - (S2 - S1)*0.5,
                           high=S2 + (S2 - S1)*0.5,
                           size=[N3,1])

    return (t1, s1, t2, s2, t3, s3)

# Loss function
def loss(model, t1, x1, t2, x2, t3, x3):
    # Loss term #1: PDE
    V = model(t1, x1)
    V_t = tf.gradients(V, t1)[0]
    V_x = tf.gradients(V, x1)[0]
    V_xx = tf.gradients(V_x, x1)[0]
    f = V_t + r*x1*V_x + 0.5*sigma**2*x1**2*V_xx - r*V 

    L1 = tf.reduce_mean(tf.square(f))

    # Loss term #2: boundary condition
    L2 = tf.reduce_mean(tf.square(V)) 

    # Loss term #3: initial/terminal condition
    L3 = tf.reduce_mean(tf.square(model(t3, x3) - x3))

    return (L1, L2, L3)

模型

# Set random seeds
np.random.seed(42)
tf.random.set_seed(42)


# PDE parameters
r = 0.05            # Interest rate
sigma = 0.25        # Volatility

# Time limits
T0 = 0.0 + 1e-10    # Initial time
T  = 1.0            # Terminal time

# Space limits
S1 = 0.0 + 1e-10    # Low boundary
S2 = 1              # High boundary

#Model specification
num_layers = 3
nodes_per_layer = 6
ann = tf.keras.models.Sequential()

#Adding the Input and hidden layers
i=0
while i != num_layers:
  ann.add(tf.keras.layers.Dense(units=nodes_per_layer, activation='relu'))
  i += 1

#Adding the output layer
ann.add(tf.keras.layers.Dense(units=1, activation='relu'))

# Training parameters
steps_per_sample = 10
sampling_stages = 800

# Number of samples
NS_1 = 1000
NS_2 = 0
NS_3 = 100


t1, s1, t2, s2, t3, s3 = sampler(NS_1, NS_2, NS_3)
t_total = np.concatenate((t1,t2,t3))
s_total = np.concatenate((s1,s2,s3))

tf.compat.v1.disable_eager_execution()
t1_t = tf.compat.v1.placeholder(tf.float32, [None,1])
x1_t = tf.compat.v1.placeholder(tf.float32, [None,1])
t2_t = tf.compat.v1.placeholder(tf.float32, [None,1])
x2_t = tf.compat.v1.placeholder(tf.float32, [None,1])
t3_t = tf.compat.v1.placeholder(tf.float32, [None,1])
x3_t = tf.compat.v1.placeholder(tf.float32, [None,1])

L1_t, L2_t, L3_t = loss(ann, t1_t, x1_t, t2_t, x2_t, t3_t, x3_t)
loss_t = L1_t + L2_t + L3_t

最后一行是我收到此错误消息的地方：

---------------------------------------------------------------------------

AttributeError                            Traceback (most recent call last)

<ipython-input-13-3acdd7516b24> in <module>()
      7 x3_t = tf.compat.v1.placeholder(tf.float32, [None,1])
      8 
----> 9 L1_t, L2_t, L3_t = loss(ann, t1_t, x1_t, t2_t, x2_t, t3_t, x3_t)
     10 loss_t = L1_t + L2_t + L3_t

3 frames

<ipython-input-4-2ab32c0f7a88> in loss(model, t1, x1, t2, x2, t3, x3)
      5     V_t = tf.gradients(V, t1)[0]
      6     V_x = tf.gradients(V, x1)[0]
----> 7     V_xx = tf.gradients(V_x, x1)[0]
      8     f = V_t + r*x1*V_x + 0.5*sigma**2*x1**2*V_xx - r*V
      9 

/usr/local/lib/python3.6/dist-packages/tensorflow/python/ops/gradients_impl.py in gradients_v2(ys, xs, grad_ys, name, gate_gradients, aggregation_method, stop_gradients, unconnected_gradients)
    300         ys, xs, grad_ys, name, True, gate_gradients,
    301         aggregation_method, stop_gradients,
--> 302         unconnected_gradients)
    303   # pylint: enable=protected-access
    304 

/usr/local/lib/python3.6/dist-packages/tensorflow/python/ops/gradients_util.py in _GradientsHelper(ys, xs, grad_ys, name, colocate_gradients_with_ops, gate_gradients, aggregation_method, stop_gradients, unconnected_gradients, src_graph)
    534     xs_set = object_identity.ObjectIdentitySet(xs)
    535     grad_ys = _DefaultGradYs(grad_ys, ys, colocate_gradients_with_ops,
--> 536                              gradient_uid)
    537 
    538     # The approach we take here is as follows: Create a list of all ops in the

/usr/local/lib/python3.6/dist-packages/tensorflow/python/ops/gradients_util.py in _DefaultGradYs(grad_ys, ys, colocate_gradients_with_ops, gradient_uid)
    165   new_grad_ys = []
    166   for i, (y, grad_y) in enumerate(zip(ys, grad_ys)):
--> 167     with _maybe_colocate_with(y.op, gradient_uid, colocate_gradients_with_ops):
    168       if grad_y is None:
    169         if y.dtype.is_complex:

AttributeError: 'NoneType' object has no attribute 'op'

谢谢您的帮助！

Answer 1

错误是由于前一层的输出没有馈送到后续层。下面的代码需要修改以从前面的层中取出

#Adding the Input and hidden layers

i = 0

while i != num_layers:

  ann.add(tf.keras.layers.Dense(units=nodes_per_layer, activation='relu'))

  i += 1

AttributeError：“ NoneType”对象没有属性“ op”

1 个答案: