MLP_cannonball4

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Author: Copyright � 2008, MetaQuotes Software Corp.
MLP_cannonball4

This script implements a foundational Artificial Intelligence concept known as a Multi-Layer Perceptron (MLP). In simple terms, it is a type of neural network designed to learn from data by identifying patterns and relationships between different variables.

The Objective: Predicting Projectile Motion

The specific task this script performs is solving the "cannonball problem." Imagine firing a projectile (like a cannonball): if you know the initial speed and the angle at which it is fired, you can predict where it will land. This script aims to teach a computer to calculate those horizontal (X) and vertical (Y) positions automatically based on those two starting inputs.

How the Logic Works

The script operates through four main phases:

1. Data Generation

Before the "learning" begins, the script generates a large dataset of scenarios. It creates 1,000 different examples consisting of random speeds and angles. For each example, it uses standard physics formulas to calculate the exact correct landing positions. This serves as the "answer key" for the AI.

2. Building the Network (The Brain)

The script constructs a simplified neural network architecture. Think of this as a series of interconnected layers:

  • Input Layer: Receives the raw data (speed and angle).
  • Hidden Layer: This is where the "thinking" happens. It processes the inputs using mathematical weights that the computer will adjust over time to find patterns.
  • Output Layer: Produces the final estimate of the X and Y coordinates.

3. The Training Process (Learning)

The script uses a method called Stochastic Gradient Descent. This is an iterative learning process:

  • Forward Pass: The AI takes a set of inputs (e.g., "Speed: 50, Angle: 45") and makes a guess at the landing position.
  • Error Calculation: The script compares the AI's guess against the "answer key" from the dataset to see how wrong it was. This difference is called the Mean Squared Error (MSE).
  • Backward Pass (Backpropagation): This is the core learning step. The script looks at the error and works backward through the network, slightly adjusting the internal "weights" of the neurons. It tries to tweak these values so that the next time it sees similar inputs, the error will be smaller.

4. Validation and Refinement

The script repeats this training cycle hundreds of times. It maintains two sets of data:

  • Training Data: Used to teach the AI (like a student practicing with a textbook).
  • Test Data: Used to check the AI's performance on problems it hasn't seen before (like a final exam).

The program continues running until the error rate becomes sufficiently small, meaning the neural network has "learned" the underlying physics of the trajectory without being explicitly told the formulas.

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MLP_cannonball4 
//+------------------------------------------------------------------+
//|                                               MLP_cannonball.mq4 |
//|                      Copyright © 2008, MetaQuotes Software Corp. |
//|                                        http://www.metaquotes.net |
//+------------------------------------------------------------------+
#property copyright "Copyright © 2008, MetaQuotes Software Corp."
#property link      "http://www.metaquotes.net"
/* This program implements a simple Multi Layer Perceptron to solve the canonball problem (regression)
   Adapted by Sebastien Marcel (2003-2004) from D. Collobert
   The goal is to estimate the position X of a bullet at time t (fixed) given the initial speed (v) and angle (a)
	  
   y
   
  / \
   |
   |
   |
   |               . X
   |            .
   |          .
   |        .
   |      .
   |     .
   |    .
   |   .
   |  .
   | .
   |.   (v,a)
   --------------------------> x
   
*/

#define PI 3.14159265358979323846
#define RAND_MAX 32767.0

//
// Datasets
#define N_PATTERNS_TRAIN 500
#define N_PATTERNS_TEST 500
#define N_PATTERNS_TRAIN_TEST 1000 //N_PATTERNS_TRAIN + N_PATTERNS_TEST

//  w1[N_HU1][IN1]=>w1[4][3]
//     H  In
//     |  |
//  w1[0][0] w1[0][1] w1[0][2]  
//  w1[1][0] w1[1][1] w1[1][2]          
//  w1[2][0] w1[2][1] w1[2][2]          
//  w1[3][0] w1[3][1] w1[3][2]
//  forward train:
//  aHidden[0] = xBias;
//  aHidden[1] = xBias*w1[1][0] + (In0)*w1[1][1] + (In1)*w1[1][2];
//  aHidden[2] = xBias*w1[2][0] + (In0)*w1[2][1] + (In1)*w1[2][2];
//  aHidden[3] = xBias*w1[3][0] + (In0)*w1[3][1] + (In1)*w1[3][2];
//  yHidden[0] = xBias;
//  yHidden[1] = f(aHidden[1]);
//  yHidden[2] = f(aHidden[2]);
//  yHidden[3] = f(aHidden[3]);
//
//  w2[OUT][N_HU1]=>w2[2][4]
//
//  w2[0][0] w2[0][1] w2[0][2] w2[0][3]
//  w2[1][0] w2[1][1] w2[1][2] w2[1][3]
//     |  |
//    Out H
// forward train:
//	aOutput[0] = 0.0;
//	aOutput[1] = 0.0;
//	aOutput[0] = aOutput[0] + yHidden[0]*w2[0][0];
//	aOutput[1] = aOutput[1] + yHidden[0]*w2[1][0];
//	aOutput[0] = aOutput[0] + yHidden[1]*w2[0][1];
//	aOutput[1] = aOutput[1] + yHidden[1]*w2[1][1];
//	aOutput[0] = aOutput[0] + yHidden[2]*w2[0][2];
//	aOutput[1] = aOutput[1] + yHidden[2]*w2[1][2];
//	aOutput[0] = aOutput[0] + yHidden[3]*w2[0][3];
//	aOutput[1] = aOutput[1] + yHidden[3]*w2[1][3];
//

//	out0 = f(aOutput[0]);
//	out1 = f(aOutput[1]);

#define IN 4
#define IN1 5 //IN+1
#define OUT 2
#define N_HU 6
#define N_HU1 7 //N_HU + 1
//*****************************
// Inputs
//
	double DataIn0[N_PATTERNS_TRAIN_TEST]; // speed of bullet
	double DataIn1[N_PATTERNS_TRAIN_TEST]; // angle of bullet
	double DataIn2[N_PATTERNS_TRAIN_TEST]; // speed of bullet
	double DataIn3[N_PATTERNS_TRAIN_TEST]; // angle of bullet	
// X[N_PATTERNS_TRAIN + N_PATTERNS_TEST];
//*****************************
// Targets
//
	double DataOut0[N_PATTERNS_TRAIN_TEST]; // x position at time t
	double DataOut1[N_PATTERNS_TRAIN_TEST]; // y position at time t
// Y[N_PATTERNS_TRAIN + N_PATTERNS_TEST];

//*****************************
// to create the data
//
double vmax;
double gravity;

//*****************************
// to train the MLP
//
double lambda =  0.01;     // learning rate
double mu = 0.6;           // inertia momentum rate
double mse_min = 0.001;    // minimum Mean Squared Error
int max_iterations = 500; // maximum number of iterations

//*****************************
// MLP data


// weights between hidden neurons and inputs
double w1[N_HU1][IN1];
double w1old[N_HU1][IN1];

// weights between outputs and hidden neurons
double w2[OUT][N_HU1];
double w2old[OUT][N_HU1];

// values of integration function
double aHidden[N_HU1];
double aOutput[OUT];

// values of transfert function
double yHidden[N_HU1];

// constant value of bias
double xBias = 1.0;


int init()
{
  vmax = 1.0/10;
  gravity = 1.0/200;
  
  return(0);
}
//+------------------------------------------------------------------+
//| script program start function                                    |
//+------------------------------------------------------------------+
int start()
  {
//----
   initrand();
   main();
//----
   return(0);
  }
//+------------------------------------------------------------------+

//*****************************
// Sigmoid transfer function
//
double f(double x)
{
	return (1.0 /(1.0 + MathExp(-x)));
}

//*****************************
// Derivative of Sigmoid
//
double f_prime(double x)
{
   double z = MathExp(-x);
	double one_plus_z = 1.0 + z;
	
	return (z / (one_plus_z * one_plus_z));
}



//*****************************
// Compute the x position of bullet at time t
//
double xpos(double t, double v, double teta)
{
	return( v * t * MathCos(teta*PI/180.0));
}

//*****************************
// Compute the y position of bullet at time t
//
double ypos(double t, double v, double teta)
{
	return( -0.5 * gravity * t * t + v * t * MathSin(teta*PI/180.0));
}

//*****************************
// Compute the MSE
//
double MSE(
            double a0, 
            double a1, 
            double b0,
            double b1
          )
{
	return (0.5*((a0 - b0)*(a0 - b0) + (a1 - b1)*(a1 - b1)));
}

//*****************************
// Create the MLP  
//
void createMLP()
{
	int i, j;
	// weights between hidden neurons and inputs
	for (i = 0; i<IN1; i++)
	{
		for (j = 0; j< N_HU1; j++)
		{	 
			w1[j][i] = Random(-1.0, 1.0);
			w1old[j][i] = w1[j][i];
		}
	}
   // weights between outputs and hidden neurons
	for (i = 0; i<OUT; i++)
	{
		for (j = 0; j< N_HU1; j++)
		{	 
			w2[i][j] = Random(-1.0, 1.0);
			w2old[i][j] = w2[i][j];
		}
	}
}

//*****************************
// Create the datasets
//
void createDatasets()
{
	int i;

	i = 0;
	while (i < (N_PATTERNS_TRAIN + N_PATTERNS_TEST))
	{  
		DataIn0[i] = (Random(0.0, vmax)) / vmax;
		DataIn1[i] = (Random(0.0, 90.0)) / 90.0;
		DataIn2[i] = (Random(0.0, vmax)) / vmax;
		DataIn3[i] = (Random(0.0, 90.0)) / 90.0;
		
		DataOut0[i] = xpos(10, DataIn0[i] * vmax, (DataIn1[i])*90.0);
		DataOut1[i] = ypos(10, DataIn0[i] * vmax, (DataIn1[i])*90.0);

		if (DataOut1[i] > 0.0) i = i + 1;
   }
}

//*****************************
// Forward the input in the MLP
//
void forward(
             double In0,
             double In1,
             double In2,
             double In3,             
             double &out0,
             double &out1
             )
{
	int i;

	aHidden[0] = xBias;
	yHidden[0] = xBias;
	
	for (i = 1; i <= N_HU; i++)
	{
		aHidden[i] = xBias*w1[i][0] + (In0)*w1[i][1] + (In1)*w1[i][2] + 
		                              (In2)*w1[i][3] + (In3)*w1[i][4];
		yHidden[i] = f(aHidden[i]);
	}

	aOutput[0] = 0.0;
	aOutput[1] = 0.0;

	for (i = 0; i <= N_HU; i++)
	{
		aOutput[0] = aOutput[0] + yHidden[i]*w2[0][i];
		aOutput[1] = aOutput[1] + yHidden[i]*w2[1][i];
	}

	out0 = f(aOutput[0]);
	out1 = f(aOutput[1]);
} 

//*****************************
// Backward (back-propagate the gradient of error)
//
void backward(
               double Yestimate0, 
               double Yestimate1, 
               double Outwant0,
               double Outwant1,
               double In0, 
               double In1, 
               double In2, 
               double In3,                
               double lambda, 
               double mu
               )
{
	double wnew, Goutput[OUT], Ghidden[N_HU1];
	int i,j;

	// 
	Goutput[0] = (Yestimate0 - Outwant0) * f_prime(aOutput[0]);
	Goutput[1] = (Yestimate1 - Outwant1) * f_prime(aOutput[1]); 

	//
	for (i = 0; i<=N_HU; i++)
		Ghidden[i] = (Goutput[0]*w2[0][i] + Goutput[1]*w2[1][i])*f_prime(aHidden[i]);

	//
	for (j = 0; j<OUT;j++)
	{
		for (i = 0; i<=N_HU; i++)
		{
			wnew = w2[j][i] - lambda * yHidden[i] * Goutput[j] + mu * (w2[j][i] - w2old[j][i]);
			w2old[j][i] = w2[j][i];
			w2[j][i] = wnew;
		}
	}

	//
	for (i = 0; i<=N_HU; i++)
	{
		wnew = w1[i][0] - lambda * xBias * Ghidden[i] + mu * (w1[i][0] - w1old[i][0]);
		w1old[i][0] = w1[i][0];
		w1[i][0] = wnew;
	   
		wnew = w1[i][1] - lambda * In0 * Ghidden[i] + mu * (w1[i][1] - w1old[i][1]);
		w1old[i][1] = w1[i][1];
		w1[i][1] = wnew;
	   
		wnew = w1[i][2] - lambda * In1 * Ghidden[i] + mu * (w1[i][2] - w1old[i][2]);
		w1old[i][2] = w1[i][2];
		w1[i][2] = wnew;

		wnew = w1[i][3] - lambda * In2 * Ghidden[i] + mu * (w1[i][3] - w1old[i][3]);
		w1old[i][3] = w1[i][3];
		w1[i][3] = wnew;
	   
		wnew = w1[i][4] - lambda * In3 * Ghidden[i] + mu * (w1[i][4] - w1old[i][4]);
		w1old[i][4] = w1[i][4];
		w1[i][4] = wnew;		
	}
}

//*****************************
// Stochastic gradient training
//
double train(int P)
{
   double Yestimate0;
   double Yestimate1; 
	double mse_;
	double mse_total;

	mse_total = 0.0;
   
	// For each train patterns
	for(int p = 0 ; p < P ; p++)
	{
		// Forward current train pattern into the MLP
		forward(
		          //X[p], 
               DataIn0[p],
               DataIn1[p],
               DataIn2[p],
               DataIn3[p],               
		          //&Yestimate
               Yestimate0,
               Yestimate1		          
		        );
      
		// Computes the MSE
		mse_ = MSE(
		             //Y[p], 
            DataOut0[p], 
            DataOut1[p], 
		             //Yestimate
            Yestimate0,
            Yestimate1
		          );
      
		// Accumulate the MSE
		mse_total = mse_total + mse_;

		// Backward MSE gradient
		backward(
		          //Yestimate, 
                Yestimate0, 
                Yestimate1, 
		          //Y[p], 
                DataOut0[p], //Outwant
                DataOut1[p], //Outwant
		          //X[p], 
                DataIn0[p], 
                DataIn1[p], 
                DataIn2[p], 
                DataIn3[p],                	          
		          lambda, 
		          mu
		          ); 
	}

	// Return normalized train MSE
	double P1=P;
	return (mse_total /P1);
}


//
int main()
{
	double mse_train;
	double mse_test;
   double mse_;
   double Yestimate0; 
   double Yestimate1; 
	//*****************************
	createMLP();
	//*****************************
	createDatasets();
	//*****************************	
	//for (int i = 0; i< N_PATTERNS_TRAIN; i++) printf(" TRN: x=[%f %f] y=[%f %f]\n", X[i].v, X[i].a, Y[i].x, Y[i].y);
	//for (int i = N_PATTERNS_TRAIN; i<(N_PATTERNS_TRAIN + N_PATTERNS_TEST); i++) printf(" TST: x=[%f %f] y=[%f %f]\n", X[i].v, X[i].a, Y[i].x, Y[i].y);
	Print("Stochastic gradient training:");
	//
	int pf_train = FileOpen("mse_train_mt4_in4.txt",FILE_CSV|FILE_WRITE,' ');//FileOpen("mse_train.txt", "w");
	int pf_test = FileOpen("mse_test_mt4_in4.txt",FILE_CSV|FILE_WRITE,' ');//FileOpen("mse_test.txt", "w");

	int iter;
	
	for(iter = 1 ; iter <= max_iterations ; iter++)
	{
		//*****************************
		// train
		//*****************************		
		mse_train = train(N_PATTERNS_TRAIN);
		FileWrite(pf_train,mse_train);
		//*****************************
		// test
		//*****************************		
		mse_test = 0.0;
		// For each test pattern
		// (N_PATTERNS_TRAIN + N_PATTERNS_TEST)                       N_PATTERNS_TRAIN                            0
		// +-----------------------------------------------------------+------------------------------------------+
		//
		for(int i = N_PATTERNS_TRAIN ; i < (N_PATTERNS_TRAIN + N_PATTERNS_TEST) ; i++)
		{
			Yestimate0 = 0.0;
			Yestimate1 = 0.0;
			// forward current pattern into the MLP
			//forward(X[i], &Yestimate);
		    forward(
		          //X[p], 
               DataIn0[i],
               DataIn1[i],
               DataIn2[i],
               DataIn3[i],               
		          //&Yestimate
               Yestimate0,
               Yestimate1		          
		        );			
			// computes MSE
			//mse_ = MSE(Y[i], Yestimate);
			mse_ = MSE(
		             //Y[p], 
            DataOut0[i], 
            DataOut1[i], 
		             //Yestimate
            Yestimate0,
            Yestimate1
		          );
			// accumulate MSE
			mse_test += mse_;
  		}       
		// Normalize the MSE
		mse_test /= N_PATTERNS_TEST;
		FileWrite(pf_test,mse_test);
		Print("->",iter); 
		//fflush(stdout);
		if (mse_train < mse_min) break;
   }
	//Print("\n");
	//
	FileClose(pf_test);
	FileClose(pf_train);
	//*****************************
	// Print info about training
	//
	Print("Number of iterations = ", iter);
	Print("Final MSE train = ", mse_train);
	Print("Final MSE test = ", mse_test);
	Print("End of program.");

	return (0);
}

//use this first function to seed the random number generator,
//call this before any of the other functions
void initrand()
{
    //srand((unsigned)(time(0)));
    MathSrand(TimeLocal());
}
//generates a psuedo-random double between 0.0 and 0.999...
double randdouble0()
{
    return (MathRand()/((RAND_MAX)+1));
}
//generates a psuedo-random double between min and max
double randdouble2(double min, double max)
{
    if (min>max)
    {
        return (randdouble0()*(min-max)+max);    
    }
    else
    {
        return (randdouble0()*(max-min)+min);
    }
}


// Random generator
double Random(double inf, double sup)
{
        return(randdouble2(inf,sup));
}

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