Hi Hossein!

I'm not an expert, but I learned that linear tensor factorizations could be generalized by using nonlinear transformations (Please see the attached file). However, I'm not sure if it applies to nonlinear tensors...

I hope it helps (please upvote if it did)

This is a good question. 

There are a number of papers on RG that treat non-linear transformations and tensors:

non-linear transformations:

https://www.researchgate.net/profile/Pavel_Golovinski/publication/257247221_The_complex-valued_encoding_for_dicision-making_based_on_aliasing_data/links/5440f7af0cf2ebb03690e2a8.pdf?origin=publication_detail

https://www.researchgate.net/profile/Vyacheslav_Somsikov/publication/262954644_Non-Linear_Forces_and_Irreversibility_Problem_in_Classical_Mechanics/links/54d0c4670cf298d65668a63d.pdf

https://www.researchgate.net/profile/Julien_Carron/publication/237054106_Optimal_non-linear_transformations_for_large_scale_structure_statistics/links/5473a5110cf29afed60f5897.pdf

non-linear tensors:

https://www.researchgate.net/profile/Gabriel_Bester/publication/7070144_Importance_of_second-order_piezoelectric_effects_in_zinc-blende_semiconductors/links/02bfe50d08f2795fd0000000.pdf

http://www.cs.cmu.edu/~ftorre/ca/ca_final_version/p18.pdf

Article The complex-valued encoding for dicision-making based on aliasing data

Article Non-Linear Forces and Irreversibility Problem in Classical Mechanics

Article Optimal non-linear transformations for large scale structure...

Article Importance of Second-Order Piezoelectric Effects in Zinc-Ble...

Thank you so much Dr.James F Peters

I don't quite understand your question. A tensor is by definition an object  of multilinear algebra. In physics speak, the indices are there to be contracted, and that is a linear process.

However a tensor may depend in a non linear way on position or additional fields. A tensor may also be the lowest order approximation of a non linear transformation:

F(X_1, ....X_N) =

\sum{n_1 + n_2 + ....+n_N = k} T_1...12....23...3....N...NX_1^{n_1}X_2^n_2...X_N^{n_N} + higher order

and the T is a symmetric tensor or order k.

Hi

I advice you to see these documents. You will find what you need.

Best regrds

https://www.google.fr/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&cad=rja&uact=8&ved=0CC0QFjABahUKEwjt8cLE_YXJAhVBNxQKHUe0Cok&url=http%3A%2F%2Farxiv.org%2Fpdf%2Fhep-th%2F0609022&usg=AFQjCNE2qvw27aF7uyLIKYmj_1Ko_eAYrg&sig2=a1MUqdxtBZcBVeJrpHuo6Q&bvm=bv.106923889,d.ZWU

https://www.google.fr/url?sa=t&rct=j&q=&esrc=s&source=web&cd=4&cad=rja&uact=8&ved=0CD0QFjADahUKEwjt8cLE_YXJAhVBNxQKHUe0Cok&url=http%3A%2F%2Flmb.informatik.uni-freiburg.de%2FPublications%2F2006%2FBro06c%2Fbrox_pp113.pdf&usg=AFQjCNGrmx0S-L04lDjF8UE8ur03CTLZTw&sig2=ccpLyCUveW-vLLD--q7V6Q&bvm=bv.106923889,d.ZWU

https://www.google.fr/url?sa=t&rct=j&q=&esrc=s&source=web&cd=5&cad=rja&uact=8&ved=0CEgQFjAEahUKEwjt8cLE_YXJAhVBNxQKHUe0Cok&url=http%3A%2F%2Fwww.math.ucla.edu%2F~tao%2Fpreprints%2Fchapter.pdf&usg=AFQjCNHyPktr7q5crwzhva6nuvU1B2qFZQ&sig2=lX3U__ufLq_2Oxt17JqqdA&bvm=bv.106923889,d.ZWU