A while ago; I explored the possibility of using neural networks to calculate colour transforms. My hypothesis was that a trained model would be able to apply a more accurate colour transform in a shorter amount of time compared to an equivalent 64x LUT.
I started tinkering around with Python and Tensorflow and had some promising results, but quickly found that I lacked the time and the computing power to train the models properly. As a result of this, it was tricky to get results good enough that would have made it worth exploring the project further.
Although using neural networks for colour transformations is probably impractical in professional applications. I am still keen to chip away at this as a personal research project when I have time.