How can I train a neural network such that the output of
How can I train a neural network such that the output of the network satisfies a certain constraint function in the Neural Network Toolbox 5.0 (R2006a)? I would like to train a neural nework so that the outputs satisfy certain constraints captured by a certain function.
John Williams answered .
2025-11-20
cost = F(y)>0,
then a continuous version of this would need to be created,
cost = -1 ./ (1 + exp(10*F(y))
net.performFcn = 'performance1'; You should be aware that this will result in training a network that will attempt to fit both the target data and the cost function, but may not perfectly fit either, especially in cases where the target data violates the cost function.
function out1=performance1(varargin)
%PERFORMANCE Template performance function with cost function.
%
% WARNING - Future versions of the toolbox may require you to update
% custom functions.
%
% Directions for Customizing
%
% 1. Make a copy of this function with a new name
% 2. Edit your new function according to the code comments marked ***
% 3. Type HELP NNPERFORMANCE to see a list of other performance functions.
%
% Syntax
%
% perf = template_performance(E,Y,X,FP)
% dPerf_dy = template_performance('dy',E,Y,X,perf,FP);
% dPerf_dx = template_performance('dx',E,Y,X,perf,FP);
% info = template_performance(code)
%
% Description
%
% TEMPLATE_PERFORMANCE(E,Y,X,PP) takes E and optional function parameters,
% E - Matrix or cell array of error vectors.
% Y - Matrix or cell array of output vectors. (ignored).
% X - Vector of all weight and bias values (ignored).
% FP - Function parameters (ignored).
% and returns the mean squared error.
%
% TEMPLATE_PERFORMANCE('dy',E,Y,X,PERF,FP) returns derivative of PERF with respect to Y.
% TEMPLATE_PERFORMANCE('dx',E,Y,X,PERF,FP) returns derivative of PERF with respect to X.
% TEMPLATE_PERFORMANCE('name') returns the name of this function.
% TEMPLATE_PERFORMANCE('pnames') returns the name of this function.
% TEMPLATE_PERFORMANCE('pdefaults') returns the default function parameters.
%
% Network Use
%
% To prepare a custom network to be trained with TEMPLATE_PERFORMANCE set
% NET.performFcn to 'template_performance'. This will automatically set
% NET.performParam to the default functions parameters.
% Copyright 1992-2005 The MathWorks, Inc.
fn = mfilename;
boiler_perform
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Name
function n = name
% *** CUSTOMIZE HERE
% *** Define this functions human readable name
n = 'Template';
% ***
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Parameter Defaults
function fp = param_defaults()
fp = struct;
% *** CUSTOMIZE HERE
% *** Defined this functions parameters here
% ***
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Parameter Names
function names = param_names
% *** CUSTOMIZE HERE
% *** Defined human readable names for this functions parameters, if any
names = {'Param One', 'Param Two'};
% ***
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Parameter Check
function err = param_check(fp)
err = [];
% *** CUSTOMIZE HERE
% *** Return an error string if any function parameter is not defined properly.
if (fp.param1 < -1000)
err = 'Argument One is less than -1000';
elseif (fp.param2 == 20)
err = 'Argument Two is 20';
end
% ***
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Apply Performance Function
function perf = performance(e,y,x,fp)
dontcareindices = find(~finite(e));
numdontcares = length(dontcareindices);
e(dontcareindices) = 0;
% *** CUSTOMIZE HERE
% *** Calculate scaler performance from error matrix E, output matrix Y, and
% *** the network weight and bias values vector X.
% *** Zero should indicate perfect performance, with more positive values
% *** indication worse performance.
% *** Don't care elements should effectively be ignored.
numerator = sum(sum(e.^2));
numElements = prod(size(e)) - numdontcares;
if (numElements == 0)
perf = 0;
else
mean_square_error = numerator / numElements;
end
perf = mean_square_error + cost_function(y);
% ***
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Derivative of Perf w/respect to Y
function d = derivative_dperf_dy(e,y,x,perf,fp)
dontcareindices = find(~finite(e));
numdontcares = length(dontcareindices);
e(dontcareindices) = 0;
% *** CUSTOMIZE HERE
% *** Calculate derivative of performance with respect to outputs Y
% *** This should include contributions of both error and any direct effect
% *** of outputs.
numElements = prod(size(e)) - length(dontcares);
if (numElements == 0)
dmse = zeros(size(e));
else
dmse = e * (2/numElements);
end
d = dmse + dcost_function(y);
% ***
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Derivative of Perf w/respect to X
function d = derivative_dperf_dx(t,y,x,perf,fp)
n = length(x);
% *** CUSTOMIZE HERE
% *** Calculate the Nx1 derivative of performance with respect to the networks
% *** weights and biases.
d = zeros(n,1);
% ***
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Function F
function cost = cost_function(y)
% CUSTOMIZE HERE
% Replace with your own output cost function
% Needs to be continuous and return only 0 or positive values
cost = sum(sin(y)+1);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Function F
function dcost = dcost_function(y)
% CUSTOMIZE HERE
% Replace with your own derivative of output cost function
dcost = cos(y);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%