I am no math guru, but I have some math knowledge from high school.
The goal of this task is to approximate a 4-variable function in Quadratic form.
Let's say Mark is cooking some dinner for his family
The variables include:
1) His mood
2) The ambient temperature
3) The conditions of the cooking wares
4) The Quality of the food

We have about 50 samples, with one variable, I can easily develop a function in quadratic form or even higher degrees using convolution technique. but I am not sure how I can do the same thing with many variables? it is not straight a superpositional problem, right?

What problem is he trying to solve, precisely? Predict the quality of the food given the other three variables?

18 hours ago, lucky6969b said:

it is not straight a superpositional problem, right?

Probably not in general, but given your specific inputs it might be. Mood as a scalar is likely linear or cubic, temperature is likely a square, cooking tools is likely cubic, and food quality is likely cubic. Those aren't particularly complicated decision surfaces to compose together.

If the results were more varied or in a more general case, and if you're looking to build a model to represent a wide variation of samples and a single scalar output, there are a few neural net techniques that could be used. 

Without knowing anything more of your problem than you described, you've got 4 scalar inputs, a scalar output, a smooth gradient decision surface, and 50 sample values containing all 5 values.  A back propagation network or RBF network could cover that, and there are plenty of existing libraries for them.  You've got a small number of samples to build from, but considering the simple nature of your decision surface it might be enough.