Loss function with derivative in TensorFlow 2 - tensorflow

Question

I am using TF2 (2.3.0) NN to approximate the function y which solves the ODE: y'+3y=0
I have defined cutsom loss class and function in which I am trying to differentiate the single output with respect to the single input so the equation holds, provided that y_true is zero:
from tensorflow.keras.losses import Loss
import tensorflow as tf
class CustomLossOde(Loss):
def __init__(self, x, model, name='ode_loss'):
super().__init__(name=name)
self.x = x
self.model = model
def call(self, y_true, y_pred):
with tf.GradientTape() as tape:
tape.watch(self.x)
y_p = self.model(self.x)
dy_dx = tape.gradient(y_p, self.x)
loss = tf.math.reduce_mean(tf.square(dy_dx + 3 * y_pred - y_true))
return loss
but running the following NN:
import tensorflow as tf
from tensorflow.keras.optimizers import Adam
from tensorflow.keras.models import Model
from tensorflow.keras.layers import Dense
from tensorflow.keras import Input
from custom_loss_ode import CustomLossOde
num_samples = 1024
x_train = 4 * (tf.random.uniform((num_samples, )) - 0.5)
y_train = tf.zeros((num_samples, ))
inputs = Input(shape=(1,))
x = Dense(16, 'tanh')(inputs)
x = Dense(8, 'tanh')(x)
x = Dense(4)(x)
y = Dense(1)(x)
model = Model(inputs=inputs, outputs=y)
loss = CustomLossOde(model.input, model)
model.compile(optimizer=Adam(learning_rate=0.01, beta_1=0.9, beta_2=0.99),loss=loss)
model.run_eagerly = True
model.fit(x_train, y_train, batch_size=16, epochs=30)
for now I am getting 0 loss from the fisrt epoch, which doesn't make any sense.
I have printed both y_true and y_test from within the function and they seem OK so I suspect that the problem is in the gradien which I didn't succeed to print.
Apprecitate any help

Answer 1

Defining a custom loss with the high level Keras API is a bit difficult in that case. I would instead write the training loop from scracth, as it allows a finer grained control over what you can do.
I took inspiration from those two guides :
Advanced Automatic Differentiation
Writing a training loop from scratch
Basically, I used the fact that multiple tape can interact seamlessly. I use one to compute the loss function, the other to calculate the gradients to be propagated by the optimizer.
import tensorflow as tf
from tensorflow.keras.optimizers import Adam
from tensorflow.keras.models import Model
from tensorflow.keras.layers import Dense
from tensorflow.keras import Input
num_samples = 1024
x_train = 4 * (tf.random.uniform((num_samples, )) - 0.5)
y_train = tf.zeros((num_samples, ))
inputs = Input(shape=(1,))
x = Dense(16, 'tanh')(inputs)
x = Dense(8, 'tanh')(x)
x = Dense(4)(x)
y = Dense(1)(x)
model = Model(inputs=inputs, outputs=y)
# using the high level tf.data API for data handling
x_train = tf.reshape(x_train,(-1,1))
dataset = tf.data.Dataset.from_tensor_slices((x_train,y_train)).batch(1)
opt = Adam(learning_rate=0.01, beta_1=0.9, beta_2=0.99)
for step, (x,y_true) in enumerate(dataset):
# we need to convert x to a variable if we want the tape to be
# able to compute the gradient according to x
x_variable = tf.Variable(x)
with tf.GradientTape() as model_tape:
with tf.GradientTape() as loss_tape:
loss_tape.watch(x_variable)
y_pred = model(x_variable)
dy_dx = loss_tape.gradient(y_pred, x_variable)
loss = tf.math.reduce_mean(tf.square(dy_dx + 3 * y_pred - y_true))
grad = model_tape.gradient(loss, model.trainable_variables)
opt.apply_gradients(zip(grad, model.trainable_variables))
if step%20==0:
print(f"Step {step}: loss={loss.numpy()}")