Which technique to apply if function Y changes with values of X variables other than linear regression

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Python3.3

I have data in two columns, X and Y where the function Y changes for increasing values of the X variable. If Y shows variations with X, the simplest way to do this is by fitting the data with a linear function.(In python), but I am looking for some "advanced" strategy (other than linear regression, i.e., using Neural Networks or other machine learning techniques) to elaborate on these data because the data is quite sparse. Need guidance .

What I have tried:

I have tried linear regression in python