Problem Summary: Identify which equation a set of data was most likely generated from
Problem Description: Let's say I have two different equations that are functions of variables X and Y and parameters A and B.
- Class 1: $Z = f(X,Y,A,B)$
- Class 2: $Z = g(X,Y,A,B)$
Now lets say I solve each equation 10k times using provided X and Y values, but randomized parameter values. This will generate two matrices with columns X, Y, and Z and 10k rows which I will now refer to as "snapshots". Below is an example of a visualization with the color representing the Z value.
NOTE: I'm not interested in just building a CNN to classifying the snapshot visualizations below because I hope to generalize this problem to equations with many more variables so they cant really be visualized easily.
My goal is to train a neural net using these snapshots (raw data, not visualizations) that are labeled with the equation that generated them.
However, I'm not really sure which type of neural net I should use. I could perhaps take a simple approach with a few fully-connected layers and the input would be the stretched out snapshot (so 30k long vector). Or maybe I need to use a CNN?
My primary concern is that unlike with an image, the features of these snapshots are kind of meaningless. For example, in a normal image each feature refers a specific pixel. But with these snapshots, each row is just a random simulation of the equation.
Does anyone have a recommendation on which type of neural net to use for this problem? Perhaps recommendations on useful abstractions/transformations of the raw data I could use as features? Any online resources (github/kaggle notebooks, academic papers) that have investigated a similar question would be extremely helpful.
EDIT: Some additional thoughts. Perhaps I need to sort the snapshot based on the Z values so now the rows have meaning (largest output, 2nd largest output, etc).