Can neural networks be used to find features importance? I am wondering if I can use neural networks to find features importances in similar manner as it can be done for random forests or decision trees and if so, how to do it?

I would like to use it on tabular time series data (not images). The reason why I want to find importances on neural networks not on decision trees is that NNs are more complicated algorithms so using NNs might point out some correlations that are not seen by simple algorithms and I need to know what features are found to be more useful with that complicated correlations.

I am not sure if I made it clear enough, please let me know if I have to explain something more.
This should be possible, considering universal approximation theorem you should be able to build a ann that approximates features that gives the most likely best feature set for a different net to train on. I would us a rnn for with a softmax output layer that ranks features by performance.

You can find a good explanation of softmax here: https://developers.google.com/machine-learning/crash-course/multi-class-neural-networks/softmax
basically it will assign probability values for each output node with all of these values adding up to 1.0