Hey, what trading strategy to use if you know the mathematical equation between price and trading volume? Is there a tool that predicts trading volume?

Your questions suggest that there are deterministic relations between price and volume, which is certainly a bad starting assumption. Google for standard time series methods: ARMA, GARCH, etc.

I will add that the "best" volume predictor will use a combination of backward and forward-looking information. Forward-looking information is found in options and scheduled events, like earnings release days for stocks. 

Now I have a direction for my research, thanks Alan.

You're welcome. One final note is that, in finance, one almost always works with returns or so-called log-returns, not prices. 

@quantiota
what would be the purpose of that trading volume predictor?

I am preparing myself in case I find this mathematical model, I am almost there after seven years of research. I need to understand how the volume prediction algorithm works in a production environment.

I haven't looked at volume as a prediction task, but I've used it before in these contexts:
- conditional for whether a relationship will hold or reverse
- a sign that a lot of people want to trade all of a sudden / I should dig deeper to see what that alpha is
- some alphas like rolling correlation between volatility and volume used to do well.
- had a few alphas that only worked when using volume bars which was neat.

That's about it though, wouldn't see prediction of volume as anything useful - maybe at an HFT timeframe since you are effectively predicting when a lot of people will be trading all of a sudden and that may add tons of jitter (for non-TradFi exchanges) / generally a sign to widen quotes.

I haven't looked at volume as a prediction task, but I've used it before in these contexts:
- conditional for whether a relationship will hold or reverse
- a sign that a lot of people want to trade all of a sudden / I should dig deeper to see what that alpha is
- some alphas like rolling correlation between volatility and volume used to do well.
- had a few alphas that only worked when using volume bars which was neat.

That's about it though, wouldn't see prediction of volume as anything useful - maybe at an HFT timeframe since you are effectively predicting when a lot of people will be trading all of a sudden and that may add tons of jitter (for non-TradFi exchanges) / generally a sign to widen quotes.