How to use gaussian process regression to find the optimal set of parameters?

In a physical experiment I measured some outcome A.

Then I set up a simulation of the experiment where I vary two parameters B and C over the range 0.1 up to 0.8 with an interval of 0.1 (thus, 0.1:0.1:0.8). I want to find the optimal combination of B and C that predicts the measured outcome A as close as possible using gaussian process regression and Latin hypercube design.

Since it is very time consuming to simulate all the possible combinations of B and C (8^2 = 64 simulations), I have the predicted outcome A in a data file for certain combinations of B and C. How can I use the data from these simulations to find the best prediction of A in matlab using gaussian process regression in combination with Latin hypercube design?

Answer 1

[Anshika Chaurasia]

Hi Tessa,

It is my understanding you want to know how to find optimal set of parameters using Latin Hypercube Design in combination with Gaussian process regression in MATLAB.

Using Latin Hypercube Design you could produce simulation data as shown below:

data = lhsdesign(n,p); % here p represents variables i.e. p = 2 in your case, and for each variables (B and C),
% the n values are randomly distributed with one from each interval (0,1/n), (1/n,2/n), ..., (1-1/n,1)

Then, fit Gaussian process regression model on the data using fitrgp.

• Refer to lhsdesign and lhsnorm documentations to produce Latin Hypercube samples.
• Refer to LHS DOE app which generates Latin Hypercube distribution.
• Refer to RegressionGP class and fitrgp documentations to fit Gaussian process regression model.

[Tessa Kol]

Hello Anshika,

You understood my problem. Indeed I found the same documentations, but I felt that there would be like an surrogate toolbox or somesort to help me find the optimal set of parameters. By using Latin Hypercube Design you reduce the number of runs necessary to achieve a reasonably accurate result. Then I want to use some kind of surrogate modeling toolbox that uses gaussian process regression to find the optimal set of input parameters that achieves a reasonable/realistic respond. Does something like that exist without me having to build a whole function/script in matlab?

[Anshika Chaurasia]

Hi Tessa,

The following are the relevant surrogate toolbox documentations:

• In MATLAB Global Optimization Toolbox has surrogate optimization solver.
• Surrogate Model Optimization Toolbox is one of the several submissions in MATLAB File Exchange on MATLAB Central which is a forum for our product users to interact, exchange information and knowledge, without MathWorks' involvement. Feel free to contact the author of this submission directly for specific questions about the implementation.

In MATLAB Regression Learner App has Gaussian Regression Process model option that will help you to build your model without writing any script in MATLAB.

[Tessa Kol]

Thank you for you suggestions and effort. I will look into that.