ECE$7690$ for Chapter $9$ and NN handouts $($project $6)$: Neural Network Modeling

Construct a three$-$layer neural network with the back$-$propagation learning algorithm to

approximate the same static system that you have designed a fuzzy model for in an earlier project.

Recall that the system's mathematical representation is

$f(x)=e^{\frac{x}{2}}sinx,$xin$[0,6\mathrm{.}5].$

Its graphical representation is

Like before, divide the interval $0,6\mathrm{.}5$ into $100$ equal sub$-$intervals using $99$ points $x_i,i$

$=1,2,$dots,$99.$ Let $x_0=0$ and $x_{100}=6\mathrm{.}5.$ It is required that the neural network meet

for $i=0,1,$dots,$100$

where $F(x)$ represents the neural network output.

You may use Statistics and Machine Learning Toolbox $($in more recent MATLAB$)$ or

Neural Network Toolbox $($in older MATLAB versions$).$

Plot $F(x)$ along with $f(x)$ to show the result.

What are your thoughts in comparison to your previous fuzzy system modeling effort in

Project $2$ and the results obtained then $($note: the error bound there is $0\mathrm{.}8)?$