Can neural cryptanalysis be applied to AES? In this Wikipedia article about Neural cryptography (section applications) it states:


  In 1995, Sebastien Dourlens applied neural networks to cryptanalyze DES by allowing the networks to learn how to invert the S-tables of the DES. The bias in DES studied through Differential Cryptanalysis by Adi Shamir is highlighted. The experiment shows about 50% of the key bits can be found, allowing the complete key to be found in a short time.


It could very well be that I misunderstood something, but I think that the same "attack" can't be used for AES, since the Inverse Rijndael S-box is public knowledge or am I wrong? Is AES designed this way to prevent an attack by inverting the S-box?
No. Neuro-Cryptanalysis fails on serious ciphers, including DES and AES.
Sebastien Dourlens's Neuro-differential cryptanalysis of DES (in sections 5.4.2 and 5.4.3 of his 1996 mémoire) learns an S-box. Applied to Unix crypt (section 5.4.4), it memorizes passwords/hash pairs (by a training requiring &quot;from several days to several years&quot;) and then merely performs a quick retrieval; something a hash table does routinely and quickly! Neither is relevant to cryptanalysis.
Mohammed M. Alani's Neuro-Cryptanalysis of DES and Triple-DES (in proceedings of ICONIP 2012) claims cryptanalysis of DES or 3DES from 2048 or 4096 examples in an hour of Matlab on a standard PC; but there is no indication that it recovers the key or is  otherwise capable of predicting more input/output mappings than supplied in training (even though the later is a stated objective). My guess is that - at best - it performs similar plaintext/ciphertext memorization thru training.

Update: there recently has been noteworthy progress in the field of neuro cryptanalysys, with Aron Gohr's Improving Attacks on Round-Reduced Speck32/64 using Deep Learning, in proceedings of Crypto 2019. It's further analysed by Adrien Benamira, David Gerault, Thomas Peyrin and Quan Quan Tan in A Deeper Look at Machine Learning-Based Cryptanalysis (eprint, March 2021).