Equation Modelling/Regression with 3 Independent Variables

I am trying to model a power law equation of the form:

H is a function of 3 variables such that H = f(t, T, x). If I include the effects of T, I can further expand the above equation into:

Now here is where I get stumped. I want to factor x into the equation as an independent variable. I know it as a similar affect on H as T - i.e. H vs t at different values of x and constant T shows a powerlaw dependence to different degrees. Does anyone have suggestions on how I could model this equation or perform regression with MATLAB using actual data to allow H to be calculated as a function of t, T, and x?

Answer 1

[Krishna]

Hello Andrew,

I think the problem you are facing is, you do not have the exact equation to find the value of H from the given variable t, T and x.

In this case what you can do is use Machine learning/ Deep Learning to model the solution.

I would recommend that you use Neural networks for this regression problem. This is because Neural networks are great when you do not have the domain knowledge i.e., you do not understand how the equation works. Also, they are capable to model any regression problem of any complexity if you have enough data.

Please go through the following documentation to get started with neural networks.

https://in.mathworks.com/help/stats/regressionneuralnetwork.html

Apart from this please go through this link to learn more ML techniques for modelling regression problems.

https://in.mathworks.com/help/stats/regression-and-anova.html