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

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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?

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Anshika Chaurasia
Anshika Chaurasia on 3 Sep 2020
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.

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Tessa Kol
Tessa Kol on 3 Sep 2020
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
Anshika Chaurasia on 4 Sep 2020
Hi Tessa,
The following are the relevant surrogate toolbox documentations:
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.

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