I want to fit my ode model to experimental data and derive parameters using lsqcurevfit and fmincon

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% Experimental data
t2=[6 12 18 36 48];
t20=[ 6 12 18 24];
nfe20=[ 3.83 3.88 6.27 5.25 ];
nfe2=[ 1.57 2.87 3.9 5.16 4.25];
t=0:1:48;
% ODE equation
ode_eqn = @(x, t) integrate_a(x, t) .* t; %ODE equation to fit
x0 = [1 1 11]; % Initial guess for the parameters
% Least squares curve fitting using lsqcurvefit
x_fit1 = lsqcurvefit(ode_eqn, x0, t2, nfe2);
Unable to perform assignment because the left and right sides have a different number of elements.

Error in solution>integrate_a (line 61)
inf(i) = inf(i-1)+ (f.*x(1) - inf(i-1).*x(2));

Error in solution>@(x,t)integrate_a(x,t).*t (line 9)
ode_eqn = @(x, t) integrate_a(x, t) .* t; %ODE equation to fit

Error in lsqcurvefit (line 251)
initVals.F = feval(funfcn_x_xdata{3},xCurrent,XDATA,varargin{:});

Caused by:
Failure in initial objective function evaluation. LSQCURVEFIT cannot continue.
disp("Fitted parameters using lsqcurvefit:")
disp(x_fit1)
% Nonlinear programming using fmincon
options = optimoptions('fmincon', 'Algorithm', 'interior-point');
x_fit1_constrained = fmincon(@(x) sum((ode_eqn(x, t2) - nfe2).^2), x0,[],[],[],[],[0 0 0],[10 10 3],[],options);
disp("Fitted parameters using fmincon:")
disp(x_fit1_constrained)
% Plotting results
t_fit1 = 0:1:48; % Time points for plotting fitted curve
figure;
plot(t2, nfe2, 'bo', 'MarkerSize', 8, 'LineWidth', 1.5); % Plot experimental data
hold on;
plot(t_fit1, ode_eqn(x_fit1, t_fit1), 'r-', 'LineWidth', 2); % Plot fitted curve using lsqcurvefit
plot(t_fit1, ode_eqn(x_fit1_constrained, t_fit1), 'g--', 'LineWidth', 2); % Plot fitted curve using fmincon
hold off;
legend('Experimental Data', 'lsqcurvefit', 'fmincon');
xlabel('Time');
ylabel('Data');
title('Fitting Experimental Data to ODE Equation');
%%
%{
function [a,b] = nonlcon(x)
f=1:1:6;
a=[];
b=[];
inf=0.9;
for t=0:1:48
if t > x(3)
a = a + (f*x(1) - a.*x(2));
end
end
inf=a-1;
end
%}
function a_int = integrate_a(x, t)
f=[99 38 9 .015 0.06];
inf=0.9;
a_int = zeros;
inf = 0.9;
for i = 1:numel(t)
if t(i) >= x(3)
inf(i) = inf(i-1)+ (f.*x(1) - inf(i-1).*x(2));
end
end
end

Answers (2)

Alan Weiss
Alan Weiss on 14 Jun 2023
There are some examples in the documentation of fitting ODE parameters to data:
Discretized Optimal Trajectory, Problem-Based (maybe not relevant, but might be)
If these don't help, feel free to ask again.
Alan Weiss
MATLAB mathematical toolbox documentation

SWAPNAVA
SWAPNAVA on 15 Jun 2023
Please help me in my code how can I fit this.

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