Hi all. I want to create a custom loss function for a simple neural network so that it computes the data mean squared error and satisfies a simple equation.

I want to combine the data loss function and an equation to constrain my NN output. The data loss function can be a mean squared error and the equation is as follows: Q_pred - (m*Cp*(T1_pred - T2). The neural net is a simple ANN with some inputs and Q_pred and T1_pred as its outputs. Can anybody help me to figure this out?

Answer 1

[Subhajyoti Halder]

Hi Seyed Navid,

It is my understanding that you want to combine the data loss function and an equation to constrain a Neural Network output.

Before we train the model, we need to define the equation constraint function. Then in each epoch, when computing the mean squared loss, also compute the equation constraint term and combine them to get the total loss.

Here, in the following sample code, I have implemented the same in MATLAB R2023a.

% Generate sample data
input_data = rand(100, 2);              % Example input data with two features

% Define the target output values (ground truth)
target_output = zeros(size(Q_pred));    % Example target output

% Initialize
Q_pred = rand(100, 1);      % Example predicted Q values
T1_pred = rand(100, 1);     % Example predicted T1 values
T2 = 10;                    % Constant T2 value for the equation constraint 

% Define the equation constraint function
equation_constraint = @(Q_pred, T1_pred, T2) Q_pred - (m * Cp * (T1_pred - T2));

Then in each epoch, while calculating the the loss

% Compute the equation constraint term
equation_term = equation_constraint(Q_pred, T1_pred, T2);

% Compute the mean squared error loss
mse_loss = mean((Q_pred - target_output).^2);

% Define the total loss combining MSE and equation constraint
total_loss = mse_loss + equation_term;
    
% Perform backpropagation and update the neural network parameters to minimize the total loss
% ...

% Rest of your neural network training code goes here
% ...

Kindly note to adjust the equation constraint function, sample data, target output, and other parameters based on your specific problem and requirements.

For more details on the ’Neural Networks’, kindly go through the following documentation

https://www.mathworks.com/help/stats/neural-networks-for-classification.html