Training an accurate regressive neural network on synthetic image data?

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Background: I'm currently doing research that involves automating this niche physics task with input from a camera. Basically given a certain shape/brightness of a pattern of light coming in, I can get these coordinates. Normally this is done with a large matrix inversion algorithm, but this takes a lot of time. Since the task is meant to be done in real-time, the idea is to make a neural network that can substitute for the inversion algorithm. I come from a physics background so while I know the basics of ML, all this image processing and more advanced neural network stuff is really new to me.