def simulate_default():
# initial conditions
x0 = np.array([-8.0, 7.0, 27])
# time domain and step size
t0, T, h = 0, 25, 0.01
time_points, data = train_lmmNet.create_training_data(t0, T, h, f_lorenz, x0)
return time_points, data
def simulate_default():
"""
Simulate the default 2-D damped harmonic oscillator cubic dynamics
"""
# time domain
t0, T, h = 0, 25, 0.01
x0 = np.array([2, 0]) # initial conditions -- default cubic problem
time_points, cubic_data = train_lmmNet.create_training_data(
t0, T, h, f_cubic, x0)
return time_points, cubic_data
def simulate_custom(tstart=0, tend=25, step=.01, xinit=2, yinit=0):
"""
Simulate the default 2-D damped harmonic oscillator cubic dynamics
"""
# time domain
t0, T, h = tstart, tend, step
x0 = np.array([xinit,
yinit]) # initial conditions -- default cubic problem
time_points, cubic_data = train_lmmNet.create_training_data(
t0, T, h, f_cubic, x0)
return time_points, cubic_data
def report_linear_sindy():
error_list = []
for _ in range(10):
error_dict = {}
xi = np.random.uniform(-4, 4, 1)[0]
yi = np.random.uniform(-4, 4, 1)[0]
zi = np.random.uniform(0, 2, 1)[0]
time_points, test_data = linear.simulate_custom(xinit=xi, yinit=yi, zinit=zi)
t0, T, h = 0, 50, .01
_, pred = train_lmmNet.create_training_data(t0, T, h, sindy_linear, test_data[0,0,:])
predictions = pred[0]
e1 = wasserstein_distance(predictions[:,0], test_data[0,:,0])
e2 = wasserstein_distance(predictions[:,1], test_data[0,:,1])
e3 = wasserstein_distance(predictions[:,2], test_data[0,:,2])
error_dict['wasserstein'] = (e1, e2, e3)
e1, _ = fastdtw(predictions[:,0], test_data[0,:,0], dist=euclidean)
e2, _ = fastdtw(predictions[:,1], test_data[0,:,1], dist=euclidean)
e3, _ = fastdtw(predictions[:,2], test_data[0,:,2], dist=euclidean)
e1 /= np.linalg.norm(test_data[0,:,0], 2)**2
e2 /= np.linalg.norm(test_data[0,:,1], 2)**2
e3 /= np.linalg.norm(test_data[0,:,2], 2)**2
error_dict['dtw'] = (e1, e2, e3)
e1 = predict_lmmNet.compute_MSE(predictions, test_data[0], 0)
e2 = predict_lmmNet.compute_MSE(predictions, test_data[0], 1)
e3 = predict_lmmNet.compute_MSE(predictions, test_data[0], 2)
error_dict['mse'] = (e1, e2, e3)
# plot
plt.plot(time_points, test_data[0,:,0], 'r.', label='x_1')
plt.plot(time_points, test_data[0,:,1], 'y.', label='x_2')
plt.plot(time_points, test_data[0,:,2], 'g.', label='x_3')
plt.plot(time_points, predictions[:,0], 'b--', label='predicted x_1')
plt.plot(time_points, predictions[:,1], 'b--')
plt.plot(time_points, predictions[:,2], 'b--')
plt.legend()
plt.show()
error_list.append(error_dict)
return error_list
def simulate_custom(tfirst=0, tlast=300, step_size=0.2, cyclin=0, MPF=0,
wee1_total=1, cdc25_total=5, APC_total=1, IE_total=1,
k1=1, v2_1 = .005, v2_2 = .25, noise=0.):
"""
Simulate the Novak Tyson Cell Cycle Model with custom parameters.
Arguments:
- cdc25_total = Total cdc25 (needed to maintain cyclin and MPF oscillations)
- k1 = synthesis of cyclin
- v2_1 = degradation of cyclin by APC off
- v2_2 = degradation of cyclin by APC on
- noise = strength of Gaussian noise to be added to the integrated dynamics
Returns:
- time points
- virtual time-series measurements for each biochemical species
"""
globals()['wee1_total'] = wee1_total
globals()['cdc25_total'] = cdc25_total
globals()['APC_total'] = APC_total
globals()['IE_total'] = IE_total
globals()['k1'] = k1
globals()['v2_1'] = v2_1
globals()['v2_2'] = v2_2
# define initial conditions
preMPF = 0
cdc25P = 0
wee1P = 0
IEP = 1
APC = 1
x0 = np.array([cyclin,MPF,preMPF,cdc25P,wee1P,IEP,APC])
# define default parameters
default = {'k3':0.005, 'ka':.02,'Ka':.1,'kb':.1,'Kb':1, 'kc':.13, 'Kc':.01, 'kd':.13, 'Kd':1,
'vwee_1':.01, 'vwee_2':1, 'v25_1':0.5*.017, 'v25_2':0.5*.17,
'ke':.02, 'Ke':1, 'kf':.1, 'Kf':1, 'kg':.02, 'Kg':.01, 'kh':.15, 'Kh':.01, 'PPase':1, 'CDK_total':100, 'IE_total':1, 'APC_total':1}
for key,val in default.items():
globals()[key]=val
time_points, novak_data = create_training_data(tfirst, tlast, step_size, f_NovakTyson, x0, noise_strength=noise)
return time_points, novak_data
def simulate_default(debug=False):
"""
Simulate the Novak Tyson Cell Cycle Model with default parameters.
The parameters can be categorized into a few classes:
* The lowercase k's are maximal rates (usually kcat)
* The uppercasse K's are Michaelis constants
* Total protein concentrations
* The v's are weighting parameters for computing intermediate constants
Returns:
- time points
- virtual time-series measurements for each biochemical species
"""
# define the simulation time
tfirst, tlast = 0, 1500
step_size = 0.2
# define initial conditions
cyclin = 0
MPF = 0
preMPF = 0
cdc25P = 0
wee1P = 0
IEP = 1
APC = 1
x0 = np.array([cyclin,MPF,preMPF,cdc25P,wee1P,IEP,APC])
# define default parameters
default = {'k1':1, 'k3':0.005,
'ka':.02,'Ka':.1,'kb':.1,'Kb':1, 'kc':.13, 'Kc':.01, 'kd':.13, 'Kd':1,
'v2_1':.005, 'v2_2':.25, 'vwee_1':.01, 'vwee_2':1, 'v25_1':0.5*.017, 'v25_2':0.5*.17,
'ke':.02, 'Ke':1, 'kf':.1, 'Kf':1, 'kg':.02, 'Kg':.01, 'kh':.15, 'Kh':.01,
'wee1_total':1, 'PPase':1, 'CDK_total':100, 'cdc25_total':5,'IE_total':1, 'APC_total':1}
for key,val in default.items():
globals()[key]=val
if debug:
return f_NovakTyson(x0, 0)
time_points, novak_data = create_training_data(tfirst, tlast, step_size, f_NovakTyson, x0)
return time_points, novak_data