One way to do this would be by using a Generalized Regression Neural Network (GRNN). GRNN is particularly useful for function approximation and regression tasks, making it well-suited for your problem. Refer the code snippet below for the general steps that you can follow:
% Load dataset (assuming data to be the variable that stores your data)
X = data.inputs; % Independent variables
Y_actual = data.observed_values; % Actual observations
% Train GRNN model
sigma = 0.1; % Smoothing parameter (adjust as needed)
grnnModel = newgrnn(X', Y_actual', sigma);
% Generate predictions using equations
Y_pred_eq1 = equation1(X); % Replace with actual equation
Y_pred_eq2 = equation2(X); % Replace with actual equation
% Compute GRNN predictions
Y_pred_grnn = sim(grnnModel, X');
% Compare errors
mse_eq1 = mean((Y_pred_eq1 - Y_pred_grnn).^2);
mse_eq2 = mean((Y_pred_eq2 - Y_pred_grnn).^2);
% Determine best equation using errors
Refer the following documentation to read more about the function: https://www.mathworks.com/help/deeplearning/ref/newgrnn.html
