问题描述
我将根据以下函数对数据集进行采样进行模拟：
def sampler(N1,N2,N3):
np.random.seed(42)
# Sampler #1: PDE domain
t1 = np.random.uniform(low=T0,high=T,size=[N1,1])
s1 = np.random.uniform(low=S1,high=S2,1])
# Sampler #2: boundary condition
t2 = np.random.uniform(low=T0,size=[N2,1])
s2 = np.zeros(shape=(N2,1))
# Sampler #3: initial/terminal condition
t3 = T * np.ones((N3,1)) #Terminal condition
s3 = np.random.uniform(low=S1,size=[N3,1])
return (t1,s1,t2,s2,t3,s3)
在损失函数中，每个子集(t1,s1)，(t2,s2)和(t3,s3)应该用唯一的项求值：
def loss(model,t1,x1,x2,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(model(t2,x2) - 0))
# Loss term #3: initial/terminal condition
L3 = tf.reduce_mean(tf.square(model(t3,x3) - tf.math.maximum(x3-K,0)))
我已经建立了以下参数：
# Set random seeds
np.random.seed(123)
tf.random.set_seed(123)
# Strike price
K = 0.5
# PDE parameters
r = 0.02 # Interest rate
sigma = 0.18 # 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 = 1.0 # High boundary
# Number of samples
NS_1 = 1000
NS_2 = 100
NS_3 = 100
模型
class DGM(tf.keras.Model):
def __init__(self,n_layers,n_nodes,dimensions=1):
"""
Parameters:
- n_layers: number of layers
- n_nodes: number of nodes in (inner) layers
- dimensions: number of spacial dimensions
"""
super().__init__()
self.n_layers = n_layers
self.initial_layer = DenseLayer(dimensions + 1,activation="relu")
self.lstmlikelist = []
for _ in range(self.n_layers):
self.lstmlikelist.append(LSTMLikeLayer(dimensions + 1,activation="relu"))
self.final_layer = DenseLayer(n_nodes,1,activation=None)
def call(self,t,x):
X = tf.concat([t,x],1)
S = self.initial_layer.call(X)
for i in range(self.n_layers):
S = self.lstmlikelist[i].call({'S': S,'X': X})
result = self.final_layer.call(S)
return result
# Neural network layers
class DenseLayer(tf.keras.layers.Layer):
def __init__(self,n_inputs,n_outputs,activation):
"""
Parameters:
- n_inputs: number of inputs
- n_outputs: number of outputs
- activation: activation function
"""
super(DenseLayer,self).__init__()
self.n_inputs = n_inputs
self.n_outputs = n_outputs
self.W = self.add_weight(shape=(self.n_inputs,self.n_outputs),initializer='random_normal',trainable=True)
self.b = self.add_weight(shape=(1,trainable=True)
self.activation = _get_function(activation)
def call(self,inputs):
S = tf.add(tf.matmul(inputs,self.W),self.b)
S = self.activation(S)
return S
class LSTMLikeLayer(tf.keras.layers.Layer):
def __init__(self,activation):
"""
Parameters:
- n_inputs: number of inputs
- n_outputs: number of outputs
- activation: activation function
"""
super(LSTMLikeLayer,self).__init__()
self.n_outputs = n_outputs
self.n_inputs = n_inputs
self.Uz = self.add_weight("Uz",shape=[self.n_inputs,self.n_outputs])
self.Ug = self.add_weight("Ug",self.n_outputs])
self.Ur = self.add_weight("Ur",self.n_outputs])
self.Uh = self.add_weight("Uh",self.n_outputs])
self.Wz = self.add_weight("Wz",shape=[self.n_outputs,self.n_outputs])
self.Wg = self.add_weight("Wg",self.n_outputs])
self.Wr = self.add_weight("Wr",self.n_outputs])
self.Wh = self.add_weight("Wh",self.n_outputs])
self.bz = self.add_weight("bz",shape=[1,self.n_outputs])
self.bg = self.add_weight("bg",self.n_outputs])
self.br = self.add_weight("br",self.n_outputs])
self.bh = self.add_weight("bh",self.n_outputs])
self.activation = _get_function(activation)
def call(self,inputs):
S = inputs['S']
X = inputs['X']
Z = self.activation(tf.add(tf.add(tf.matmul(X,self.Uz),tf.matmul(S,self.Wz)),self.bz))
G = self.activation(tf.add(tf.add(tf.matmul(X,self.Ug),self.Wg)),self.bg))
R = self.activation(tf.add(tf.add(tf.matmul(X,self.Ur),self.Wr)),self.br))
H = self.activation(tf.add(tf.add(tf.matmul(X,self.Uh),tf.matmul(tf.multiply(S,R),self.Wh)),self.bh))
Snew = tf.add(tf.multiply(tf.subtract(tf.ones_like(G),G),H),tf.multiply(Z,S))
return Snew
def _get_function(name):
f = None
if name == "tanh":
f = tf.nn.tanh
elif name == "sigmoid":
f = tf.nn.sigmoid
elif name == "relu":
f = tf.nn.relu
elif not name:
f = tf.identity
assert f is not None
return f
这将是我使用示例模型的方法：
model = DGM(n_layers=2,n_nodes = 3)
model.compile(
optimizer = "Adam",loss = loss
)
model.fit()
错误回溯：
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
<ipython-input-12-f781fe65eb00> in <module>()
----> 1 model.fit()
2 frames
/usr/local/lib/python3.6/dist-packages/tensorflow/python/keras/engine/training.py in _method_wrapper(self,*args,**kwargs)
106 def _method_wrapper(self,**kwargs):
107 if not self._in_multi_worker_mode(): # pylint: disable=protected-access
--> 108 return method(self,**kwargs)
109
110 # Running inside `run_distribute_coordinator` already.
/usr/local/lib/python3.6/dist-packages/tensorflow/python/keras/engine/training.py in fit(self,x,y,batch_size,epochs,verbose,callbacks,validation_split,validation_data,shuffle,class_weight,sample_weight,initial_epoch,steps_per_epoch,validation_steps,validation_batch_size,validation_freq,max_queue_size,workers,use_multiprocessing)
1030 version_utils.disallow_legacy_graph('Model','fit')
1031 self._assert_compile_was_called()
-> 1032 self._check_call_args('fit')
1033 _disallow_inside_tf_function('fit')
1034
/usr/local/lib/python3.6/dist-packages/tensorflow/python/keras/engine/training.py in _check_call_args(self,method_name)
2468 'Models passed to `' + method_name + '` can only have `training` '
2469 'and the first argument in `call` as positional arguments,'
-> 2470 'found: ' + str(extra_args) + '.')
2471
2472 def _validate_compile(self,optimizer,metrics,**kwargs):
ValueError: Models passed to `fit` can only have `training` and the first argument in `call` as positional arguments,found: ['x'].
现在如何根据已设置的惯常损失函数拟合模型？
解决方法
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