Need help! I try to build Neural Network but it does not fit well with the training data!

I check my feed forward and backpropagation but cant find error, please help! Thank you so much.

Here is my code:

%% Prepare data
% train data:                               
I=1;                                % number of independent variables
F=1;                                % number of dependent varaiables
Ib=[-pi:0.1:(4*pi)].';              % input matrix
Yb= sin(Ib);                        % (actual) output matrix
P=size(Ib,1);                       % number of observations
% Normalize:
Input(:,1)=(Ib(:,1)-min(Ib(:,1)))/(max(Ib(:,1))-min(Ib(:,1)));
Y(:,1)=(Yb(:,1)-min(Yb(:,1)))/(max(Yb(:,1))-min(Yb(:,1)));

%% Neural Network:
% hyperparameter for NN:
Gen=10^8;                   % number of times train neural network
Epsi= 10^(-7);              % tolerance
SSEold=999;                 % sum squared error

m=0;                        % update step size
A=1;
B=10000;
mu=A/(B+m);                 % step size or rate of learning


% layer:
N=1;                        % number of hidden layers
H=15;                       % number of hidden nodes
g=0.01;

% Initial parameter:
W1=rand(I+1,H);                 
X=g.*rand(H,F);

bias=g*rand(P,1);           % bias node
bias1=g*rand(1,1);          % bias weight to output layer

% Add bias node to Input layer:
Input=cat(2,Input,bias);
Err=10;

while (Err >Epsi && m < Gen)
%% Forward probagation:
    Vp=Input*W1;
    Vp=1./(1+exp(-Vp));        
    Yhat=bias1+Vp*X;
    SSEnew=sum(abs(Y-Yhat).^2,1);   
%% Backward probagation:
    Yerr=Y-Yhat;
    bias1=bias1+mu*sum(Yerr);
    W1=W1+mu*(Input.')*(Yerr*(X.').*Vp.*(1-Vp));
    X=X+mu*(Yerr'*Vp).';
%% Update:
    m=m+1;
    mu=A/(B+m);
%% Calculate Sum Squared Error:
    Err=abs(SSEnew-SSEold);
    SSEold=SSEnew;
end

%% plot
figure1=figure;
grid on
plot(Y)
hold on
plot(Yhat)

Answer 1

[Greg Heath]

>> Vp = Input * W1;

Error using *

>> size(Input), size(W1)

ans =

158 4

ans =

2 15

Hope this helps

Thank you for formally accepting my answer

Greg

[Quang Cung]

Hi Greg Heath, that was a good catch, thanks for that, but I still got a problem with the code, the result from NN does not fit well with the train data set. Here is the code after I modified, please help me to fix it. Thanks.

clear all
clc
%% Prepare data
% =========train data===========                               
Ib=[-pi:0.1:(4*pi)].';              % input matrix
Yb= sin(Ib);                        % (actual) output matrix
% ==========Normalize============
Input(:,1)=(Ib(:,1)-min(Ib(:,1)))/(max(Ib(:,1))-min(Ib(:,1)));
Y(:,1)=(Yb(:,1)-min(Yb(:,1)))/(max(Yb(:,1))-min(Yb(:,1)));
%% Neural Network:
P=size(Input,1);            % number of observations
I=size(Input,2);            % number of independent variables
F=size(Y,2);                % number of dependent varaiables
% =========operational parameter for NN===========
Gen= 10^(6);                 % number of times train neural network
Epsi= 10^(-7);              % tolerance
m=0;                        % update step size
A=1;                        
B=10000;
mu=A/(B+m);                 % step size or rate of learning
SSEold=999;                 % sum squared error
% ============layer================================
N=1;                        % number of hidden layers
H=15;                       % number of hidden nodes
g=0.5;
% ============Initial parameter====================
W1=rand(I+1,H);                 
X=g.*rand(H,F);
bias=g*rand(P,1);           % bias node
bias1=g*rand(1,1);          % bias weight to output layer
% =============Add bias node to Input layer========
Input=cat(2,Input,bias);
Err=10;
while (Err >Epsi && m < Gen)
%% Forward probagation:   
    Vp=Input*W1;
    Vp=1./(1+exp(-Vp));        
    Yhat=bias1+Vp*X;
    SSEnew=sum(abs(Y-Yhat).^2,1);
%% Backward probagation:
    Yerr=Y-Yhat;
    bias1=bias1+mu*sum(Yerr);
    W1=W1+mu*(Input.')*(Yerr*(X.').*Vp.*(1-Vp));
    X=X+mu*(Yerr.'*Vp).';
%% Update:
    m=m+1;
    mu=A/(B+m);   
%% Calculate Sum Squared Error:
    Err=abs(SSEnew-SSEold);
    SSEold=SSEnew;
end
%% plot
figure1=figure;
grid on
plot(Y)
hold on
plot(Yhat)