Find a function given inputs and output

Dear Matlab community, I would like to ask for an help. I have to find the function "under" a software for building energy efficiency. The input values are Temperature, Area, number of people, etc and the only output value is the energy consumption. Now, is there any matlab tool that can help me find the correlation between ouput-inputs?

Thanks for your time and help.

[Stephen23]

"I have to find the function". That does not make any sense, because for any finite set of data there are infinite functions that exactly fit that data, so there cannot be " the function".

If you really need some function to model your data then practically speaking you have a choice:

1. Use prior knowledge of the underlying system or physics to specify a model, and use curve fitting to obtain the model parameters that describe your data.
2. Use a spline.

Which would you prefer?

[M P]

Thanks for your answer. I absolutely understand that there's not just one function under the software but there are different energy balances equations. My point was to find a function that can mimic with a good approximation what the software does. I have a set of n inputs (xi) and one output (y). The function that I would like to find should be like: y=a+b1*(x1)^c1+b2*(x2)^c2+... I need to find the constants a,b1,c1,b2,c2,... Can spline do something like this? Alternatively, I was thinking about non linear multivariable regression analysis, but stil I don't know any matlab tool that can do it. Thanks again for your time. I hope that my explanation is not confused.

Answer 1

[Star Strider]

You are doing system identification. This can be quite involved, and requires a knowledge of control theory.

The System Identification Toolbox is what you need to estimate the structure and dynamics of your system. See the documentation on Getting Started with System Identification Toolbox (link) to understand how to use it correctly. It can estimate multi-input, single-output (MISO) systems, so you will be able to use it with your problem.

I would use the state space modeling approach, because a state space representation tells you more about your system and its dynamics.