I have read articles I and II (I == II almost everywhere..). It's basically BS. I am not going to waste my time with a review but if you have technical questions I will try to answer. I love technical discussions.
The KO punch is when the authors use TensorFlow for AD. It's like a kid with a new toy.
"Concerning AD : from one to thousands dimensions, neural networks are always behind, for all performance indicators and all tests that I performed. It is also lacking of math foundations. I am just more and more confident that this technology is basically crap, but benefit of huge investments and marketing."
More generally, AD is probably a dead-end technology going forward (my words).
def f(t, x):
u = u(t, x)
u_t = tf.gradients(u, t)
u_x = tf.gradients(u, x)
u_xx = tf.gradients(u_x, x)
f = u_t + u*u_x - (0.01/tf.pi)*u_xx
Finally, the term "Physics Informed Deep Learning" is vacuous.