Develop toy machine learning model to fit data

Need help building a proof of concept ML model with keras in python. Details: I have four small (N=100) discrete vectors grouped into two XY pairs (i.e., two discrete 1D “dependent variable”/“independent variable“ functions). These 4 vectors are input for a single numerical function Beta (for example, Beta(AX1Vector, Y1Vector, X2Vector, Y2Vector)). Beta returns 30 vectors (each N=300) as predicted output. I have 30 vectors of real data (each with N=300) that can be described as noise on approximately gaussian peaks. I would like to experiment with a machine learning model that can optimize the values of Y1Vector and Y2Vector to minimize the residual between the Beta output and the real world data (I already have manually found Y1 and Y2 vectors that get close). I can understand and write python programs so prefer solutions in this language with something free like tensorflow. I just need help configuring something like keras where the Neural network model optimizes Y1 and Y2 to minimize the residual of Beta(X1, Y1, X2, Y2) output and the real world data. A demonstration with a toy model beta function is perfectly acceptable and in fact preferred. Just need a little guidance!