Differential equation fit to my data: incorrect minimization

Question

Marina Batlló RIus 2023-3-29

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1937189-differential-equation-fit-to-my-data-incorrect-minimization

回答： Alan Weiss 2023-3-29

ValuesMaxPeaks.xls

So I have been trying to fit some experimental data that I have in my differential equations. The code I am using is as follows:

Time = table2array(ValuesMaxPeaks(:,1));
x0 = table2array([ValuesMaxPeaks(1,2),ValuesMaxPeaks(1,3),ValuesMaxPeaks(1,4),ValuesMaxPeaks(1,5)]);
Sdata = table2array([ValuesMaxPeaks(:,2),ValuesMaxPeaks(:,3),ValuesMaxPeaks(:,4),ValuesMaxPeaks(:,5)]);
thau = 1/26.61;
model_funct = @(k) ode45(@(t,y) [k(3)*y(3)+k(1)*y(2)+k(5)*y(4)-(k(2)+k(4)+k(6)+thau)*y(1);
             k(2)*y(1)-(k(1)+thau)*y(2);
             k(4)*y(1)-(k(3)+thau)*y(3);
             k(6)*y(1)-(k(5)+thau)*y(4)], Time, x0);
error = @(k) sum(sum((model_funct(k).y - Sdata').^2));
options.StepTolerance = 0.0000000000000000000000000001;
options.MaxFunctionEvaluations = 12000000000000000000000;
options.FunctionTolerance = 0.000000000000000000000000000000000000000001;
k0 = [0.1, 0.01, 0.1, 0.1, 0.1, 0.1]; % Initial guess for k
k_opt = lsqnonlin(@(k) errorfunc(k,Sdata, model_funct),k0,zeros(1,6),[0.2,0.2,0.2,0.2,0.2,0.2], options);

As you can see, I use ode45 to solve the differential equations and lsqnolin to minimize the error of the solutions compared to my experimental data. The code does not return any error, but when I run it, MATLAB returns me the following:

Initial point is a local minimum.
Optimization completed because the size of the gradient at the initial point
is less than 1e-4 times the value of the function tolerance.
<stopping criteria details>

and the result of my minimization stays as my initial values k0. I have already tried to lower the function tolerance and step tolerance, but do not manage to make it solve my constants properly. I also attach some example experimental data in case anyone needs to see it. Do you have any suggestions?