我正在嘗試實作一個物理資訊網路，用于發現漢堡方程的方程（https://arxiv.org/abs/1711.10561）。這包括 2 個預測。流體速度的預測取決于位置和時間點（它們是輸入）以及擴散系數 nu，該系數在所有剖面中都很常見。
我像這樣設定了一個網路
def neural_network (train):
inp_1 = Input(shape=(train.shape[1],)) #setting the size of the input layer
initial = 'he_uniform'
x = Dense(20,kernel_initializer= initial, activation = 'tanh', bias_initializer=initial)(inp_1)
x = Dense(20,kernel_initializer= initial, activation = 'tanh', bias_initializer=initial)(x)
x = Dense(20,kernel_initializer= initial, activation = 'tanh', bias_initializer=initial)(x)
x = Dense(20,kernel_initializer= initial, activation = 'tanh',bias_initializer=initial)(x)
x = Dense(20,kernel_initializer= initial, activation = 'tanh',bias_initializer=initial)(x)
x = Dense(20,kernel_initializer= initial, activation = 'tanh',bias_initializer=initial)(x)
x = Dense(1,kernel_initializer= initial, activation = 'tanh',bias_initializer=initial)(x)
nu = tf.Variable([[1.]], trainable = True, shape=((1,1)))
nu= Dense(1,kernel_initializer= initial, activation = 'tanh',bias_initializer=initial)(nu)
out = tf.concat([x, nu], 1)
return Model(inputs=inp_1, outputs=out)
model = Sequential()
model = neural_network(xt_train)
model.summary()
然后嘗試在一些示例代碼上評估我的運算式：
def residualValOfPDE(xt, nu):
x = xt[:, 0:1] # x coordinate
t = xt[:, 1:2] # t coordinate
with tf.GradientTape(persistent=True) as tape:
tape.watch(x)
tape.watch(t)
u, nu = model( tf.stack([x[:, 0], t[:, 0]], axis=1) )[0]
u_x = tape.gradient(u, x)
u_t = tape.gradient(u, t)
u_xx = tape.gradient(u_x, x)
return u_t u*u_x - nu*u_xx
其中 xt_f 包含位置和時間作為列，不同的點作為行。現在，當我嘗試為一點評估運算式時：
print( residualValOfPDE(xt_f[1:2,:], nu))
它作業正常。但是，當我嘗試傳遞多個點時：
print( residualValOfPDE(xt_f[1:3,:], nu))
我收到以下錯誤：
InvalidArgumentError Traceback (most recent call last) in 19 return u_t u u_x - nu u_xx 20 # ---> 21 print(residualValOfPDE(xt_f[1:3,:], nu)) #計算每個收集點的殘差值
在residualValOfPDE(xt, nu) 11 tape.watch(t) 12 ---> 13 u, nu = model( tf.stack([x[:, 0], t[:, 0]], axis=1) )[0] 14 u_x = tape.gradient(u, x) 15
~/.local/lib/python3.8/site-packages/keras/utils/traceback_utils.py in error_handler(*args, **kwargs) 65 除了例外為 e: # pylint: disable=broad-except 66 filters_tb = _process_traceback_frames (e. traceback ) ---> 67 從 None 68 提高 e.with_traceback(filtered_tb) 最后：69 del filtered_tb
~/.local/lib/python3.8/site-packages/tensorflow/python/framework/ops.py in raise_from_not_ok_status(e, name) 7105 def raise_from_not_ok_status(e, name): 7106 e.message = (" name: " name if name is not None else "") -> 7107 raise core._status_to_exception(e) from None # pylint: disable=protected-access 7108 7109
InvalidArgumentError: Exception encountered when calling layer "tf.concat_28" (type TFOpLambda).
ConcatOp : Dimensions of inputs should match: shape[0] = [2,1] vs. shape[1] = [1,1] [Op:ConcatV2] name: concat
Call arguments received: ? values=['tf.Tensor(shape=(2, 1), dtype=float32)', 'tf.Tensor(shape=(1, 1), dtype=float32)'] ? axis=1 ? name=concat
Any ideas how to solve it? Thanks in advance
uj5u.com熱心網友回復：
問題是您創建的nu變數的硬編碼批量大小為 1。這就是為什么它只能使用 1 的樣本大小而不是更多。很難說你想做什么，但你可以嘗試這樣的事情：
import tensorflow as tf
class NuLayer(tf.keras.layers.Layer):
def __init__(self, batch_dim, initial='he_uniform'):
super(NuLayer, self).__init__()
self.batch_dim = batch_dim
def build(self, input_shape):
self.nu = tf.Variable(initial_value = tf.ones((self.batch_dim,1)), trainable = True)
def call(self, inputs):
return self.nu
inp_1 = tf.keras.layers.Input(shape=(2,)) #setting the size of the input layer
initial = 'he_uniform'
x = tf.keras.layers.Dense(20,kernel_initializer= initial, activation = 'tanh', bias_initializer=initial)(inp_1)
x = tf.keras.layers.Dense(20,kernel_initializer= initial, activation = 'tanh', bias_initializer=initial)(x)
x = tf.keras.layers.Dense(20,kernel_initializer= initial, activation = 'tanh', bias_initializer=initial)(x)
x = tf.keras.layers.Dense(20,kernel_initializer= initial, activation = 'tanh',bias_initializer=initial)(x)
x = tf.keras.layers.Dense(20,kernel_initializer= initial, activation = 'tanh',bias_initializer=initial)(x)
x = tf.keras.layers.Dense(20,kernel_initializer= initial, activation = 'tanh',bias_initializer=initial)(x)
x = tf.keras.layers.Dense(1,kernel_initializer= initial, activation = 'tanh',bias_initializer=initial)(x)
nu = NuLayer(batch_dim=4)
nu = nu(inp_1)
out = tf.keras.layers.Concatenate(axis=1)([x, nu])
model = tf.keras.Model(inputs=inp_1, outputs=out)
def residualValOfPDE(xt):
x = xt[:, 0:1] # x coordinate
t = xt[:, 1:2] # t coordinate
with tf.GradientTape(persistent=True) as tape:
tape.watch(x)
tape.watch(t)
u, nu = model(tf.stack([x[:, 0], t[:, 0]], axis=1) )[0]
u_x = tape.gradient(u, x)
u_t = tape.gradient(u, t)
u_xx = tape.gradient(u_x, x)
return u_t u*u_x - nu*u_xx
xt_f = tf.random.normal((10000, 2))
print( residualValOfPDE(xt_f[1:3,:]))
tf.Tensor(
[[0.5751909]
[0. ]], shape=(2, 1), dtype=float32)
如果要檢查不同的批次大小，請更改Input圖層中的批次大小：
nu = NuLayer(batch_dim=4)
print( residualValOfPDE(xt_f[1:5,:]))
[[-0.51205623]
[ 0. ]
[ 0. ]
[ 0. ]], shape=(4, 1), dtype=float32)
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