Question: Solve the Coefficient of ODES

Dear Friends,

My present problem is to calculate the coefficients  

of ODES based on the experiment data. In order to simulate the actual experiment, a set of  is given with . Then the experiment data (yexp) can be calculated. Finally, the least-squares method (lsq) is used to calculate the coefficient values. Now the NLPSolve function can be used. However, the globalsolve can’t run.

If it is convenient for you, wish you can solve it.

Code:

restart;
cdm_ode := diff(y1(t), t) = c0*(y6(t)*(1-y3(t))/(s0*(1-y4(t)*(1-y5(t)))))^n/(1-y2(t)), diff(y2(t), t) = ks*y2(t)^(1/3)*(1-y2(t)), diff(y3(t), t) = h1*(1-y3(t)/h2)*c0*(y6(t)*(1-y3(t))/(s0*(1-y4(t)*(1-y5(t)))))^n/(sigma*(1-y2(t))), diff(y4(t), t) = (1/3)*kp*(1-y4(t))^4, diff(y5(t), t) = A*B*y1(t)^(B-1)*c0*(y6(t)*(1-y3(t))/(s0*(1-y4(t)*(1-y5(t)))))^n/(1-y2(t)), diff(y6(t), t) = y6(t)*c0*(y6(t)*(1-y3(t))/(s0*(1-y4(t)*(1-y5(t)))))^n/(1-y2(t));

tol_t := 3600;
sol := dsolve([cdm_ode, y1(0) = 0, y2(0) = 0, y3(0) = 0, y4(0) = 0, y5(0) = 0, y6(0) = 175], numeric, range = 0 .. tol_t, output = listprocedure, parameters = [c0, n, sigma, s0, ks, h1, h2, kp, A, B]);

sol(parameters = [5.7*10^(-6), 10.186, 175, 200, 5*10^(-8), 10000, .269, 1.5*10^(-7), 1.5, 2]);

t := [seq(i^2, i = 0 .. 50, 1)];

y1data := subs(sol, y1(t));
 
y1exp := [seq(y1data(t[i]), i = 1 .. 51)];

err := proc (c0, n, s0, ks, h1, h2, kp, A, B) local y1cal, y1val, lsq; sol(parameters = [c0, n, 175, s0, ks, h1, h2, kp, A, B]); y1cal := subs(sol, y1(t)); y1val := [seq(y1cal(t[i]), i = 1 .. 51)]; lsq := add((y1val[i]-y1exp[i])^2, i = 1 .. 51); lsq end proc;

with(Optimization);
val := NLPSolve(err, 10^(-8) .. 10^(-4), 2 .. 20, 150 .. 250, 10^(-2) .. 1, 100 .. 20000, 10^(-5) .. .4, 10^(-5) .. 1, .5 .. 2, 1 .. 10);
GlobalSolve(err, 10^(-10) .. 10^(-4), 2 .. 20, 150 .. 250, 0 .. 1, 100 .. 15000, 0 .. .5, 0 .. 1, .5 .. 2, 1 .. 5);

Error, (in GlobalOptimization:-GlobalSolve) `InertForms` does not evaluate to a module