Python GEKKO-如何在ODE中使用数组中的值

Question

We have a project and we really need help.

Basically what we are tryng to do is to solve a multiple equation system using GEKKO. However, one of the parameters (miu) is predicted by neural networks. However, when we try to put togheter the data predicted and the equations, we obtain multiple errors.

I have two programs: This is the first one, which is the main:

import numpy as np
from gekko import GEKKO, brain
import pandas as pd
import matplotlib.pyplot as plt
from math import e
m = GEKKO(remote=False)    # create GEKKO model --  optimization and accesses solvers of constrained, unconstrained, continuous, and discrete problems

KdQ = 0.001        #degree of degradation of glutamine (1/h)
mG = 1.1e-12# 1.1e-10   #glucose maintenance coefficient (mmol/cell/hour)
YAQ = 0.1#0.90         #yield of ammonia from glutamine
YLG = 0.1 #2            #yield of lactate from glucose
YXG = 2.2e8    #yield of cells from glucose (cells/mmol)
YXQ = 0.5e9#1.5e9    #yield of cells from glutamine (cells/mmol)
KL = 150           #lactate saturation constant (mM)
KA = 40            #ammonia saturation constant (mM)
Kdmax = 0.01       #maximum death rate (1/h)
mumax = 0.044      #maximum growth rate (1/h)
KG = 30#1             #glucose saturation constant (mM)
KQ = 0.22          #glutamine saturation constant (mM)
mQ = 0             #glutamine maintenance coefficient (mmol/cell/hour)
kmu = 0.01         #intrinsic death rate (1/h)
Klysis = 2e-2  #rate of cell lysis (1/h)
Ci_star = 100      #inhibitor saturation concentration (mM)
qi = 2.5e-10   #specific inhibitor production rate (1/h)

#Flow, volume and concentration
Fo = 0         #feed-rate (L/h)
Fi = 0        #feed-rate (L/h)
V = 3              #volume (L)
SG = 653           #glucose concentration in the feed (mM)
SQ = 58.8          #glutamine concentration in the feced (mM)

#Load experimental data
from Experimental_Data import tspan, glucose,glutamine ,glutamate,lact, ammonia, cell_br1, cell_br2
# create GEKKO parameter
t = np.linspace(0,144,99)
m.time = t

XT= m.Var(value=5e8,name='XT')         #total cell density (MMcells/L)
XV = m.Var(value=5e8,lb=0, name='XV')   #viable cell density (MMcells/L)

from test_ann import  b, x
# mu values are given by neural network

mu2 = b.think(x)
mu1 = np.array(mu2)

#mu = m.abs3(mu2)
mu = m.sos1(mu1)
Kd = m.Intermediate(Kdmax*(kmu/(mu+kmu)))    #death rate(1/h)
# create GEEKO equations
m.Equation(XT.dt()== mu*XV )
m.Equation(XV.dt() == ((mu - Kd)*XV ))

# solve ODE
m.options.IMODE  = 4  #Simulation   #2-Regression mode
m.options.SOLVER = 1  #Public software version
m.options.NODES  = 3  #Default
m.options.COLDSTART = 2
# objective
m.solve(display=False)

# objective
#m.Obj(sum([ (z[j]-1)**2 + y for j in range(p)]))
#figure, axes = plt.subplots(nrows=5, ncols=1)
plot1 = plt.figure(1)
plt.plot(t, XV.value, label='viable cell')
#axes[0].plot(t, XT.value, label='total cell')


plt.xlabel='Time [hr]' 
plt.ylabel='Concentration [cells/ml]'
plt.legend()

plot1 = plt.figure(2)

plt.xlabel='Time [hr]' 
plt.ylabel='Concentration [mM]'
plt.legend()

plot1 = plt.figure(3)
plt.plot(tspan,lact,'bx', label = 'Lactate measured')


plt.xlabel='Time [hr]' 
plt.ylabel='Concentration [mM]'
plt.legend()


plot1 = plt.figure(4)

plt.plot(tspan,ammonia,'ro', label = 'Ammonia measured')
plt.plot(tspan,glutamine,'bx', label = 'Glutamine measured')

plt.xlabel='Time [hr]' 
plt.ylabel='Concentration [mM]'
plt.legend()

plot1 = plt.figure(5)
plt.plot(m.time, mu,label='\u03BC')
plt.plot(m.time, Kd,label='Kd')

plt.xlabel='Time [hr]' 
plt.ylabel='Miu[1/h]'
plt.legend()




plt.show()

The data is obtained using Experimental_Data

import pandas as pd

#Load experimental data
df = pd.read_excel(r'path')
sheet = df[0:9] #we have to include row 235  

tspan = sheet['TIME']

cell_br1= sheet['CELL_BR1']
cell_br2= sheet['CELL_BR2']

Since I cannot put the excel file here, the data is the following one:

And the miu is predicted using this module (ann_test)

from gekko import GEKKO
from gekko import brain
import numpy as np
import matplotlib.pyplot as plt  
from numpy import diff
from scipy.interpolate import CubicSpline


xm = np.array([ 0.0 , 23.0 , 47.0  , 71.5 , 95.0 , 119.0 , 143.0 ]) # 47.0,
deriv1 = 0
from Experimental_Data import  cell_br1, cell_br2
def spline(cell):    
    m = GEKKO()
    m.options.IMODE=2
    c = [m.FV(value=0) for i in range(4)]
    x = m.Param(value=xm)
    cell = np.array(cell)
    y = m.CV(value=cell)
    y.FSTATUS = 1
    # polynomial model
    m.Equation(y==c[0]+c[1]*x+c[2]*x**2+c[3]*x**3)
    c[0].STATUS=1
    m.solve(disp=False)
    c[1].STATUS=1
    m.solve(disp=False)
    c[2].STATUS=1
    c[3].STATUS=1
    m.solve(disp=False)
    pbr = [c[3].value[0],c[2].value[0],\
           c[1].value[0],c[0].value[0]]
   # print(pbr)
    xp = np.linspace(0,144,100)
    plot1 = plt.figure(1)
    if cell[0] == cell_br2[0]:
        plt.plot(xm,cell_br2, 'ko', label ='BR2')
        plt.plot(xp,np.polyval(pbr,xp),'g:',linewidth=2)
    elif cell[0]  == cell_br1[0] :
        plt.plot(xm,cell_br1, 'mo', label ='BR1')
        plt.plot(xp,np.polyval(pbr,xp),'r:',linewidth=2)

    plt.xlabel('time(hr)')
    plt.ylabel('cells')
    plt.legend()
    dx = diff(xp)
    dy1 = diff(np.polyval(pbr,xp))
    deriv1 = dy1/dx
    time =np.linspace(0,144,99)
    plot1 = plt.figure(2)
    if cell[0] == cell_br2[0]:
        plt.plot(time,deriv1,'b:',linewidth=2, label ='BR2')
    elif cell[0] == cell_br1[0]:
        plt.plot(time,deriv1,'m:',linewidth=2, label ='BR1')
    plt.xlabel('time(hr)')
    plt.ylabel('miu(1/h)')
    plt.legend()
    #plt.show()
    return(deriv1)

m = GEKKO()



from Experimental_Data import  cell_br1, cell_br2, glucose


b = brain.Brain(remote=True)
b.input_layer(2)
b.layer(linear=5)
b.layer(tanh=3)
b.layer(tanh=5)
b.output_layer(1)

x_s = np.linspace(0,144,99)
xg = np.array([ 0.0 , 23.0 , 47.0 , 71.5 ,\
                95.0 , 119.0 , 144.0 ])
cells_spline = CubicSpline(xm, cell_br1) 
y_cells = cells_spline(x_s)
miu_1 = spline(cell_br1)
miu_2 = spline(cell_br2)
scale = [1.0e6,1.0e4]
x = (x_s, y_cells) #, y_glucose) #Inputs (3)
y1 = (miu_1)    #Output (2)
y2 = (miu_2)    #Output (2)

b.learn(x,y1) # train
b.learn(x,y2) # train
yp = b.think(x) # validate
x_1 = np.linspace(0,144,198)
xp = np.linspace(0,144,99)
yyp = np.array(yp)
miu = np.reshape(yyp, (99,))


plot1 = plt.figure(3)
plt.plot(x_s,miu,'r-', label = 'Predicted ')
plt.plot(x_s,miu_1,'.', label = 'Experimental points')
plt.xlabel('Time [hr]')
plt.ylabel('miu [1/h]')
plt.legend()
plt.show()

The problem is I can't merge the values of miu (from ann_test) with the differential equations.

This is the error I obtained:

TypeError: Cannot cast array data from dtype('O') to dtype('float64') according to the rule 'safe'

Can please someone help?

Answer 1

We have a project and we really need help.

Basically what we are tryng to do is to solve a multiple equation system using GEKKO. However, one of the parameters (miu) is predicted by neural networks. However, when we try to put togheter the data predicted and the equations, we obtain multiple errors.

I have two programs: This is the first one, which is the main:

import numpy as np
from gekko import GEKKO, brain
import pandas as pd
import matplotlib.pyplot as plt
from math import e
m = GEKKO(remote=False)    # create GEKKO model --  optimization and accesses solvers of constrained, unconstrained, continuous, and discrete problems

KdQ = 0.001        #degree of degradation of glutamine (1/h)
mG = 1.1e-12# 1.1e-10   #glucose maintenance coefficient (mmol/cell/hour)
YAQ = 0.1#0.90         #yield of ammonia from glutamine
YLG = 0.1 #2            #yield of lactate from glucose
YXG = 2.2e8    #yield of cells from glucose (cells/mmol)
YXQ = 0.5e9#1.5e9    #yield of cells from glutamine (cells/mmol)
KL = 150           #lactate saturation constant (mM)
KA = 40            #ammonia saturation constant (mM)
Kdmax = 0.01       #maximum death rate (1/h)
mumax = 0.044      #maximum growth rate (1/h)
KG = 30#1             #glucose saturation constant (mM)
KQ = 0.22          #glutamine saturation constant (mM)
mQ = 0             #glutamine maintenance coefficient (mmol/cell/hour)
kmu = 0.01         #intrinsic death rate (1/h)
Klysis = 2e-2  #rate of cell lysis (1/h)
Ci_star = 100      #inhibitor saturation concentration (mM)
qi = 2.5e-10   #specific inhibitor production rate (1/h)

#Flow, volume and concentration
Fo = 0         #feed-rate (L/h)
Fi = 0        #feed-rate (L/h)
V = 3              #volume (L)
SG = 653           #glucose concentration in the feed (mM)
SQ = 58.8          #glutamine concentration in the feced (mM)

#Load experimental data
from Experimental_Data import tspan, glucose,glutamine ,glutamate,lact, ammonia, cell_br1, cell_br2
# create GEKKO parameter
t = np.linspace(0,144,99)
m.time = t

XT= m.Var(value=5e8,name='XT')         #total cell density (MMcells/L)
XV = m.Var(value=5e8,lb=0, name='XV')   #viable cell density (MMcells/L)

from test_ann import  b, x
# mu values are given by neural network

mu2 = b.think(x)
mu1 = np.array(mu2)

#mu = m.abs3(mu2)
mu = m.sos1(mu1)
Kd = m.Intermediate(Kdmax*(kmu/(mu+kmu)))    #death rate(1/h)
# create GEEKO equations
m.Equation(XT.dt()== mu*XV )
m.Equation(XV.dt() == ((mu - Kd)*XV ))

# solve ODE
m.options.IMODE  = 4  #Simulation   #2-Regression mode
m.options.SOLVER = 1  #Public software version
m.options.NODES  = 3  #Default
m.options.COLDSTART = 2
# objective
m.solve(display=False)

# objective
#m.Obj(sum([ (z[j]-1)**2 + y for j in range(p)]))
#figure, axes = plt.subplots(nrows=5, ncols=1)
plot1 = plt.figure(1)
plt.plot(t, XV.value, label='viable cell')
#axes[0].plot(t, XT.value, label='total cell')


plt.xlabel='Time [hr]' 
plt.ylabel='Concentration [cells/ml]'
plt.legend()

plot1 = plt.figure(2)

plt.xlabel='Time [hr]' 
plt.ylabel='Concentration [mM]'
plt.legend()

plot1 = plt.figure(3)
plt.plot(tspan,lact,'bx', label = 'Lactate measured')


plt.xlabel='Time [hr]' 
plt.ylabel='Concentration [mM]'
plt.legend()


plot1 = plt.figure(4)

plt.plot(tspan,ammonia,'ro', label = 'Ammonia measured')
plt.plot(tspan,glutamine,'bx', label = 'Glutamine measured')

plt.xlabel='Time [hr]' 
plt.ylabel='Concentration [mM]'
plt.legend()

plot1 = plt.figure(5)
plt.plot(m.time, mu,label='\u03BC')
plt.plot(m.time, Kd,label='Kd')

plt.xlabel='Time [hr]' 
plt.ylabel='Miu[1/h]'
plt.legend()




plt.show()

The data is obtained using Experimental_Data

import pandas as pd

#Load experimental data
df = pd.read_excel(r'path')
sheet = df[0:9] #we have to include row 235  

tspan = sheet['TIME']

cell_br1= sheet['CELL_BR1']
cell_br2= sheet['CELL_BR2']

Since I cannot put the excel file here, the data is the following one:

And the miu is predicted using this module (ann_test)

from gekko import GEKKO
from gekko import brain
import numpy as np
import matplotlib.pyplot as plt  
from numpy import diff
from scipy.interpolate import CubicSpline


xm = np.array([ 0.0 , 23.0 , 47.0  , 71.5 , 95.0 , 119.0 , 143.0 ]) # 47.0,
deriv1 = 0
from Experimental_Data import  cell_br1, cell_br2
def spline(cell):    
    m = GEKKO()
    m.options.IMODE=2
    c = [m.FV(value=0) for i in range(4)]
    x = m.Param(value=xm)
    cell = np.array(cell)
    y = m.CV(value=cell)
    y.FSTATUS = 1
    # polynomial model
    m.Equation(y==c[0]+c[1]*x+c[2]*x**2+c[3]*x**3)
    c[0].STATUS=1
    m.solve(disp=False)
    c[1].STATUS=1
    m.solve(disp=False)
    c[2].STATUS=1
    c[3].STATUS=1
    m.solve(disp=False)
    pbr = [c[3].value[0],c[2].value[0],\
           c[1].value[0],c[0].value[0]]
   # print(pbr)
    xp = np.linspace(0,144,100)
    plot1 = plt.figure(1)
    if cell[0] == cell_br2[0]:
        plt.plot(xm,cell_br2, 'ko', label ='BR2')
        plt.plot(xp,np.polyval(pbr,xp),'g:',linewidth=2)
    elif cell[0]  == cell_br1[0] :
        plt.plot(xm,cell_br1, 'mo', label ='BR1')
        plt.plot(xp,np.polyval(pbr,xp),'r:',linewidth=2)

    plt.xlabel('time(hr)')
    plt.ylabel('cells')
    plt.legend()
    dx = diff(xp)
    dy1 = diff(np.polyval(pbr,xp))
    deriv1 = dy1/dx
    time =np.linspace(0,144,99)
    plot1 = plt.figure(2)
    if cell[0] == cell_br2[0]:
        plt.plot(time,deriv1,'b:',linewidth=2, label ='BR2')
    elif cell[0] == cell_br1[0]:
        plt.plot(time,deriv1,'m:',linewidth=2, label ='BR1')
    plt.xlabel('time(hr)')
    plt.ylabel('miu(1/h)')
    plt.legend()
    #plt.show()
    return(deriv1)

m = GEKKO()



from Experimental_Data import  cell_br1, cell_br2, glucose


b = brain.Brain(remote=True)
b.input_layer(2)
b.layer(linear=5)
b.layer(tanh=3)
b.layer(tanh=5)
b.output_layer(1)

x_s = np.linspace(0,144,99)
xg = np.array([ 0.0 , 23.0 , 47.0 , 71.5 ,\
                95.0 , 119.0 , 144.0 ])
cells_spline = CubicSpline(xm, cell_br1) 
y_cells = cells_spline(x_s)
miu_1 = spline(cell_br1)
miu_2 = spline(cell_br2)
scale = [1.0e6,1.0e4]
x = (x_s, y_cells) #, y_glucose) #Inputs (3)
y1 = (miu_1)    #Output (2)
y2 = (miu_2)    #Output (2)

b.learn(x,y1) # train
b.learn(x,y2) # train
yp = b.think(x) # validate
x_1 = np.linspace(0,144,198)
xp = np.linspace(0,144,99)
yyp = np.array(yp)
miu = np.reshape(yyp, (99,))


plot1 = plt.figure(3)
plt.plot(x_s,miu,'r-', label = 'Predicted ')
plt.plot(x_s,miu_1,'.', label = 'Experimental points')
plt.xlabel('Time [hr]')
plt.ylabel('miu [1/h]')
plt.legend()
plt.show()

The problem is I can't merge the values of miu (from ann_test) with the differential equations.

This is the error I obtained:

TypeError: Cannot cast array data from dtype('O') to dtype('float64') according to the rule 'safe'

Can please someone help?