I want to find the value of the parameter m that minimizes my variable x subject to a system of differential equations. I have the following code
from gekko import GEKKO
def run_model_m(days, population, case, k_val, b_val, u0_val, sigma_val, Kmax0, a_val, c_val):
list_x =[]
list_u =[]
list_Kmax =[]
for i in range(len(days)):
list_xi=[]
list_ui=[]
list_Ki=[]
for j in range(len(days[i])):
#try:
m = GEKKO(remote=False)
#m.time= days[i][j]
eval = np.linspace(days[i][j][0], days[i][j][-1], 100, endpoint=True)
m.time = eval
x_data= population[i][j]
variable= np.linspace(population[i][j][0], population[i][j][-1], 100, endpoint=True)
x = m.Var(value=population[i][j][0], lb=0)
sigma= m.Param(sigma_val)
d = m.Param(c_val)
k = m.Param(k_val)
b = m.Param(b_val)
r = m.Param(a_val)
step = np.ones(len(eval))
step= 0.2*step
step[0]=1
m_param = m.CV(value=1, lb=0, ub=1, integer=True); m_param.STATUS=1
u = m.Var(value=u0_val, lb=0, ub=1)
#m.free(u)
a = m.Param(a_val)
c= m.Param(c_val)
Kmax= m.Param(Kmax0)
if case == 'case0':
m.Equations([x.dt()== x*(r*(1-x/(Kmax))-m_param/(k+b*u)-d), u.dt()== sigma*(m_param*b/((k+b*u)**2))])
elif case == 'case4':
m.Equations([x.dt()== x*(r*(1-u**2)*(1-x/(Kmax))-m_param/(k+b*u)-d), u.dt() == sigma*(-2*u*r*(1-x/(Kmax))+(b*m_param)/(b*u+k)**2)])
p = np.zeros(len(eval))
p[-1] = 1.0
final = m.Param(value=p)
m.Obj(x)
m.options.IMODE = 6
m.options.MAX_ITER=15000
m.options.SOLVER=1
# optimize
m.solve(disp=False, GUI=False)
#m.open_folder(dataset_path+'inf')
list_xi.append(x.value)
list_ui.append(u.value)
list_Ki.append(m_param.value)
list_x.append(list_xi)
list_Kmax.append(list_Ki)
list_u.append(list_ui)
return list_x, list_u, list_Kmax, m.options.OBJFCNVAL
scaled_days[i][j] =[-7.0, 42.0, 83.0, 125.0, 167.0, 217.0, 258.0, 300.0, 342.0]
scaled_pop[i][j] = [0.01762491277346285, 0.020592540360308997, 0.017870838266697213, 0.01690069378982034,0.015512320147187675,0.01506701796298272,0.014096420738841563,0.013991224004743027,0.010543380664478205]
k0,b0,group, case0, u0, sigma0, K0, a0, c0 = (100, 20, 'Size3, Inc', 'case0', 0.1, 0.05, 2, 0, 0.01)
list_x2, list_u2, list_Kmax2,final =run_model_m(days=[[scaled_days[i][j]]], population=
[[scaled_pop[i][j]]],case=case1, k_val=list_b1[i0][0], b_val=b1, u0_val=list_u1[i0][j0],
sigma_val=sigma1, Kmax0=K1, a_val=list_Kmax1[0][0], c_val=c1)
I get the error Data arrays must have the same length, and match time discretization in dynamic problems error but I don't understand why. I have tried making x and m_param arrays, with x=m.Var, m_param =m.MV... But still get the same error, even if they are all arrays of the same length. Is this the right way to find the solution of the minimization problem?
