Nonlinear function approximation with the use of neural networks with a GA

I'm just starting to work with neural networks and I think I understand the theory, but I don't know how to apply it in practice. I did this exemplary example and the result does not match the function, why? I would also like to compare different models of neural networks

inputs = (1:10);

targets = cos(inputs.^2);

n = 2;

net = feedforwardnet(n);

net = configure(net, inputs, targets);

h = @(x) mse_test(x, net, inputs, targets);

ga_opts = gaoptimset('TolFun', 1e-8,'display','iter');

[x_ga_opt, err_ga] = ga(h, 3*n+1, ga_opts);

net = setwb(net, x_ga_opt);

% 1 model

net.trainFcn = 'trainlm';

net1 = train(net,inputs,targets);

w1 = net1(targets);

plot (inputs,w1)

hold on

plot (inputs,targets);

% 2 model

net.trainFcn = 'traingda';

net2 = train(net,inputs,targets);

w2 = net2(targets);

plot (inputs,w2)

hold on

plot (inputs,targets);

%%%

function mse_calc = mse_test(x, net, inputs, targets)

net = setwb(net, x');

y = net(inputs);

mse_calc = sum((y-targets).^2)/length(y);

end

Answer 1

[Nomit Jangid]

In my understanding, you're trying to train neural networks with one hidden layer (containing 2 neurons). You’re using genetic algorithm to optimize your neural networks. If you’re using MATLAB version R2018b or later, I'd suggest using "optimoptions" instead of "gaoptimset". The only difference between using “optimoptions” and the other functions is, for “optimoptions”, you can include the solver name as the first argument. For example, to set iterative display in ga,

ga_opts = optimoptions('ga','Display','iter');
%instead of
ga_opts = gaoptimset('Display','iter');

By executing this function, "net" will be be optimized such that the mean squared error is minimized

Also, I am sharing a few links which will help you start practising Deep Learning in MATLAB with a few hands-on session and theory as well.

• https://matlabacademy.mathworks.com/R2020a/portal.html?course=deeplearning
• https://www.mathworks.com/help/deeplearning/getting-started-with-deep-learning-toolbox.html
• https://blogs.mathworks.com/loren/2015/08/04/artificial-neural-networks-for-beginners/