使用Matlab神经工具箱求解差分方程

Question

我正在尝试使用Matlab的神经网络工具箱来模拟差分方程。等式的形式为：

  

y [k + 1] = y [k] + d_t *（-a * y [k] + x [k]）

a 和 d_t 由NN中的2个可调权重表示。 a 是第一层的权重，第二层的两个权重都等于1，第三层（无延迟权重）是 d_t ，最后一个权重是1

网络如下所示：

产生网络的代码是：

%% input 
t = 1:100;
x = ones(1,length(t));

%% difference equation
% consntants 
d_t = 0.1;
a = 1;
% initialization
y0 = 0;
% output signal
y = zeros(length(t), 1);
y(1) = y0;

for ii = 1:(length(t)-1)
   y(ii+1) = y(ii) + d_t * (-a*y(ii) + x(ii));
end

% input
plot(t, x, 'b--')
hold on
% difference equation output 
plot(t, y, 'r' )

%% NN
net = network;
% structure
net.numInputs = 1;
net.numLayers = 3;
% neurons
net.inputs{1}.size = 1;
net.layers{1}.size = 1;
net.layers{2}.size = 1;
net.layers{3}.size = 1;

%names
net.inputs{1}.name  = 'x';
net.layers{1}.name  = '1st';
net.layers{2}.name  = '2nd';
net.layers{3}.name  = '3rd';
net.outputs{3}.name = 'y';

% connections
net.biasConnect  = [0; 0; 0]; % exclude biases
net.inputConnect = [0; 1; 0];  % input connected to 2nd layer
net.layerConnect = [0 0 1; ... % 3rd to 1st {1,3}
                    1 0 0; ... % 1st to 2nd
                    0 1 1];    % 2nd to 3rd; 3rd to 3rd
net.outputConnect= [0 0 1];   % 3rd layer connected to output

% set the weights
% input weight
net.IW{2,1} = 1;
net.inputWeights{2,1}.learn = 0;

% 3rd to 1st
net.LW{1,3} = 1; % value
net.layerWeights{1,3}.learn = 0; % do not change

% 1st to 2nd
net.LW{2,1} = -1; % TO BE TRAINED
net.layerWeights{2,1}.learn = 1; % train

% 2nd to 3rd
net.LW{3,2} = 0.1; % delta T (finite time difference)
net.layerWeights{3,2}.learn = 0; % do not change

% 3rd to 3rd
net.LW{3,3} = 1; % value
net.layerWeights{3,3}.learn = 0; % do not change

% add delay
net.layerWeights{1,3}.delays = 1;
net.layerWeights{3,3}.delays = 1;

view(net)

hold on;
plot(net(x),'g--')

但是结果看起来像这样：

似乎延迟被忽略，输入信号仅通过常数 d_t = 0.1。

有什么想法，为什么先前的输出似乎没有进入第一层和第二层？