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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?

Accepted Answer

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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