I am trying to use a new NN architecture named Physics Informed Neural Networks, the aim is to solve a PDE or ODE using NN. So I have to take the derivative of my network with respect to the data, as in the u_prima function below, and then with respect to my model but I have an error. My model definition is:
#Crea el modelo
inputs = ks.Input(shape=(1),dtype=tf.float32,name='entrada')
x1 = ks.layers.Dense(64, activation="relu",name='oculta1')(inputs)
x2 = ks.layers.Dense(64, activation="relu",name='oculta2')(x1)
outputs = ks.layers.Dense(1,name='salida')(x2)
model = ks.Model(inputs=inputs, outputs=outputs)
model.summary()
#Instancia un optimizador
optimizador = ks.optimizers.Adam()
def u_prima(model,t):
with tf.GradientTape() as tp:
tp.watch(t)
u = model(t,training=True)
u_t = 1 + t*tp.gradient(u,t)
return u_t
this derivate will compose my loss function used for the training of my model parameters, I tried to do that as follows:
def loss(model,u_prima,f_x,t):
u_t = u_prima(model,t)
return tf.reduce_mean(tf.square(u_t - f_x(t)))
loss(model,u_prima,f,t)
Finally, I run my training loop and get the error:
epochs = 10
for epoch in range(epochs+1):
with tf.GradientTape() as tp:
perdida = loss(model,u_prima,f,t)
grad = tp.gradient(perdida,model.trainable_variables)
optimizador.apply_gradients(zip(grad,model.trainable_variables))
print(perdida)
The error I get is:
WARNING:tensorflow:Gradients do not exist for variables ['salida/bias:0'] when minimizing the loss. If you're using `model.compile()`, did you forget to provide a `loss`argument?
tf.Tensor(0.9643340489229794, shape=(), dtype=float64)
