StandardScript.m

clear; clc; close all;
%% Import Data
n=20;
x=linspace(-2,2,n);
y=linspace(-2,2,n);
n1=numel(x); n2=n1;
count=0;
for j=1:n2
    for k=1:n1
        count=count+1;
        Data(1,count)=x(j);
        Data(2,count)=y(k);
        u=x(j)^2+y(k)^2;
        Label(1,count)=(log(1+(x(k)-4/3)^2+3*(x(k)+y(j)-x(k)^3)^2));
        Label(2,count)=exp(-u/2).*cos(2*u);
    end
end

%% Network Structure Set Up
InputDimension=2; OutputDimension=2;
LayerStruct=[InputDimension,5,8,OutputDimension];
NN.ActivationFunction='Gaussian';
NN.Cost='SSE';
NN.NetworkType='ANN';
NN=Initialization(NN,LayerStruct);

%% First Order Solver Set Up

option.Solver='ADAM';
option.s0=10e-3;
option.MaxIteration=200;
option.BatchSize=100;
NN=OptimizationSolver(Data,Label,NN,option);

%% Quasi-Newton Solver Set Up

option.Solver='BFGS';
option.MaxIteration=300;
NN=OptimizationSolver(Data,Label,NN,option);



%%
plot(log10(NN.OptimizationHistory))


%% Validation
Prediction=NN.Evaluate(Data);
Error=Label-Prediction;

%% Statistics
figure; histogram(Error);
title('Error Distribution')
figure
scatter3(Data(1,:),Data(2,:),Label(1,:),'black')
hold on
[X,Y]=meshgrid(x,y);
n1=numel(x); n2=numel(y);
surf(X,Y,reshape(Prediction(1,:),n1,n2))
title('Neural Network Fit')
legend('Data','Fitting')