"Abnormal Termination in LNSRCH" Error

[lhdp0110]

I get the following output:

Parameter Value        Standard Deviation
c_N       3.000000e+00 2.529358e+01
c_bN      6.000000e-01 2.277745e+01
d_N       7.000000e-01 9.629840e+00
f_P       1.000000e+01 6.950825e+01
Status message         ABNORMAL_TERMINATION_IN_LNSRCH
Number of iterations   0
Objective              <symfit.core.objectives.LeastSquares object at 0x0000024443010FA0>
Minimizer              <symfit.core.minimizers.LBFGSB object at 0x0000024443010EB0>

Goodness of fit qualifiers:
chi_squared            0.050448920293983936
objective_value        0.025224460146991968
r_squared              0.9171998963521952

My code is as follows. What does "ABNORMAL_TERMINATION_IN_LNSRCH" mean and what could be causing it? Thank you

from symfit import variables, Parameter, Fit, D, ODEModel
import numpy as np
import matplotlib.pyplot as plt

tdata = np.array([0, 2, 4, 8, 12, 24, 48])
concentration = np.array([1, 1.15, 1.6, 1.8, 1.55, 1.2, 1])
A, t, P, bP, bI, RB, RP, RN, bRN, G = variables('A, t, P, bP, bI, RB, RP, RN, bRN, G')

f_P = Parameter('f_P', 10, min=0)
c_N = Parameter('c_N', 3, min=0)
c_bN = Parameter('c_bN', 0.6, min=0)
d_N = Parameter('d_N', 0.7, min=0)

# supply rates
s_P = 1.5
s_B = 0.5
s_A = 0.5
s_G = 0.2

# degradation/inactivation rates
d_P = 1
d_bP = 0.5
d_bI = 0.5
d_R = 0.5
d_bN = 0.5
d_A = 0.5
d_G = 0.5

# reaction/binding rates
c_P = 0.8
c_I = 0.5
c_B = 4
c_A = 0.8

# proliferation rate
p_G = 2.9       

# mortality rate
m_G = 2      

model = ODEModel({
    D(A, t): s_A + c_A * bRN - d_A * A,
    D(P, t): s_P - c_P * P * G - d_P * P,
    D(bP, t): c_P * P * G - d_bP * bP,
    D(bI, t): c_I * (1-bI) * bP - d_bI * bI,    
    D(RB, t): s_B - c_B * RB * bI - d_R * RB,
    D(RP, t): c_B * RB * bI - f_P * RP - d_R * RP,
    D(RN, t): f_P * RP - c_N * RN + c_bN * bRN - d_N * RN,
    D(bRN, t): c_N * RN - c_bN * bRN - d_bN * bRN,  
    D(G, t): p_G * G - m_G * G * A - d_G * G
    },
    initial={t: tdata[0], A: concentration[0], P: 1, bP: 0, bI: 0, RB: 1, RP: 0, RN: 0, 
             bRN: 0, G: 1}
)

fit = Fit(model, t=tdata, A=concentration, P=None, bP=None, bI=None, RB=None, RP=None, RN=None, 
          bRN=None, G=None)
fit_result = fit.execute()

print(fit_result)

taxis = np.linspace(0, 50)
A_fit, P_fit, bP_fit, bI_fit, RB_fit, RP_fit, RN_fit, bRN_fit, G_fit, = model(t=taxis, **fit_result.params)
plt.scatter(tdata, concentration)
plt.plot(taxis, A_fit, label='[A]')
plt.plot(taxis, P_fit, label='[P]')
plt.plot(taxis, bP_fit, label='[bP]')
plt.plot(taxis, bI_fit, label='[bI]')
plt.plot(taxis, RB_fit, label='[RB]')
plt.plot(taxis, RP_fit, label='[RP]')
plt.plot(taxis, RN_fit, label='[RN]')
plt.plot(taxis, bRN_fit, label='[bRN]')
plt.plot(taxis, G_fit, label='[G]')
plt.xlabel('Hours')
plt.ylabel('[AMP]')
plt.ylim(0, 4)
plt.xlim(0, 50)
plt.legend()
plt.show()

[pckroon]

I don't know exactly what's causing it, since that get really deep into how the BFGS minimizer works. I do know that fitting ODEs can be very difficult, since they tend to be annoyingly sensitive to parameters. You can usually help things along by picking better initial guesses.

[tBuLi]

I should add to this that symfit is a wrapper around scipy's LBFGSB, which has documentation here. So you might find something over there, or by googling for this error in combination with scipy.

Just glossing at your code, I agree with @pckroon that this is probably a difficult ODE to solve, especially given that the amount of datapoints only marginally outweighs the amount of parameters in the problem. Is this your real data, or just an example? More data would probably improve the reliability of the fit.