Ali:

Lets suppose that you want to train a NN for regression, some inputs and one target like this:

hiddenLayerSize = [6 2];

net = fitnet(hiddenLayerSize);

[net,tr] = train(net,inputs,targets);

The following code in MATLAB should print the NN configuration, weights, activation function and bias. Then you can build your equation... you may try to adapt it to your personal problem. If you found any error, please, let me know.

clc;

fprintf('Network Configuration\n');

fprintf('Internal weights for each layer\n\n');

fprintf(':::: Input Layer/Hidden1 ::::\n');

for R=1:net.inputs{1}.size

fprintf('X%d\n',R)

for S=1:hiddenLayerSize(1)

fprintf('W(%d,%d)=%f\n',R,S,net.IW{1}(S,R));

end

fprintf('-------\n');

end

fprintf('Node Bias\n');

for R=1:net.layers{1}.dimensions

fprintf('b(%d)=%f\n',R,net.b{1}(R));

end

fprintf('-------\n');

fprintf('Activation function: %s\n',net.layers{1}.transferFcn);

fprintf('*********************************\n');

for R=2:net.numLayers-1

fprintf(':::: Input Hidden %d ::::\n',R);

%fprintf('%d,%d\n',R,R-1);

[NODES,IN_NODES]=size(net.LW{R,R-1});

for K=1:IN_NODES

fprintf('Node %d \n',K)

for S=1:NODES

fprintf('W(%d,%d)=%f\n',K,S,net.LW{R,R-1}(S,K));

end

fprintf('-------\n');

end

fprintf('Node Bias\n');

for m=1:net.layers{R}.dimensions

fprintf('b(%d)=%f\n',m,net.b{R}(m));

end

fprintf('-------\n');

fprintf('Activation function: %s\n',net.layers{R}.transferFcn);

fprintf('---------------------------------\n');

end

fprintf('*********************************\n');

fprintf(':::: Output Layer ::::\n');

R=R+1;

[NODES,IN_NODES]=size(net.LW{R,R-1});

for K=1:IN_NODES

fprintf('Node %d \n',K)

for S=1:NODES

fprintf('W(%d,%d)=%f\n',K,S,net.LW{R,R-1}(S,K));

end

fprintf('-------\n');

end

fprintf('Output bias\n');

fprintf('b=%f\n',net.b{net.numLayers}(1));

fprintf('-------\n');

fprintf('Activation function: %s\n',net.layers{R}.transferFcn);

fprintf('*********************************\n');

fprintf('Done...!\n');

why do not try curve fitting toolbox in Matlab?

just type cftool in command window and insert your data

you should clarify the function type(i.e. linear, non-linear, sin,...) and the toolbox returns you the parameters you want

Good Luck

The latest command for curve fitting is nftool. 

Thanks dear hossein, I know that it's possible by curve fitting but I want to drive out the equation by neural network which correlates the inputs to the outputs so that I can use it as an objective function in order to be optimized by Genetic Algorithm and combine NN and GA.

Ali:

Lets suppose that you want to train a NN for regression, some inputs and one target like this:

hiddenLayerSize = [6 2];

net = fitnet(hiddenLayerSize);

[net,tr] = train(net,inputs,targets);

The following code in MATLAB should print the NN configuration, weights, activation function and bias. Then you can build your equation... you may try to adapt it to your personal problem. If you found any error, please, let me know.

clc;

fprintf('Network Configuration\n');

fprintf('Internal weights for each layer\n\n');

fprintf(':::: Input Layer/Hidden1 ::::\n');

for R=1:net.inputs{1}.size

fprintf('X%d\n',R)

for S=1:hiddenLayerSize(1)

fprintf('W(%d,%d)=%f\n',R,S,net.IW{1}(S,R));

end

fprintf('-------\n');

end

fprintf('Node Bias\n');

for R=1:net.layers{1}.dimensions

fprintf('b(%d)=%f\n',R,net.b{1}(R));

end

fprintf('-------\n');

fprintf('Activation function: %s\n',net.layers{1}.transferFcn);

fprintf('*********************************\n');

for R=2:net.numLayers-1

fprintf(':::: Input Hidden %d ::::\n',R);

%fprintf('%d,%d\n',R,R-1);

[NODES,IN_NODES]=size(net.LW{R,R-1});

for K=1:IN_NODES

fprintf('Node %d \n',K)

for S=1:NODES

fprintf('W(%d,%d)=%f\n',K,S,net.LW{R,R-1}(S,K));

end

fprintf('-------\n');

end

fprintf('Node Bias\n');

for m=1:net.layers{R}.dimensions

fprintf('b(%d)=%f\n',m,net.b{R}(m));

end

fprintf('-------\n');

fprintf('Activation function: %s\n',net.layers{R}.transferFcn);

fprintf('---------------------------------\n');

end

fprintf('*********************************\n');

fprintf(':::: Output Layer ::::\n');

R=R+1;

[NODES,IN_NODES]=size(net.LW{R,R-1});

for K=1:IN_NODES

fprintf('Node %d \n',K)

for S=1:NODES

fprintf('W(%d,%d)=%f\n',K,S,net.LW{R,R-1}(S,K));

end

fprintf('-------\n');

end

fprintf('Output bias\n');

fprintf('b=%f\n',net.b{net.numLayers}(1));

fprintf('-------\n');

fprintf('Activation function: %s\n',net.layers{R}.transferFcn);

fprintf('*********************************\n');

fprintf('Done...!\n');

Maybe you might want to have a look at

https://it.mathworks.com/matlabcentral/answers/394478-problem-with-mathematical-expression-of-neural-network

and

https://it.mathworks.com/help/nnet/ug/deploy-neural-network-functions-and-objects.html.

Best wishes,

Algo

I've got the same question. Could you finally derive an equation from your neural network? I'd appreciate if you could keep me posted. Ali Naderi

I think its impossible to get a certain equation between all input and target data, because the NN involve with some weights so that the best answer not obtained by equation but the best answer achieved by the distance concept(MSE) between input and target data.

Kindly refer

Deleted research item The research item mentioned here has been deleted