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在PYMC3中求解ODE

在这里,我的目的是估算由下式给出的阻尼谐波振荡器的参数(伽马和ω)

dX ^ 2 / dt ^ 2 +γ* dX / dt +(2 * pi * omega)^ 2 * X = 0。(我们可以向系统中添加高斯白噪声。)


 import pymc
 import numpy as np
 import scipy.io as sio
 import matplotlib.pyplot as plt; 
 from scipy.integrate import odeint

 #import data
 xdata = sio.loadmat('T.mat')['T'][0]  #time
 ydata1 = sio.loadmat('V1.mat')['V1'][0]  #  V2=dV1/dt, (X=V1),
 ydata2 = sio.loadmat('V2.mat')['V2'][0]  # dV2/dt=-(2pi*omega)^2*V1-gama*V2

 #time span for solving the equations
 npts= 500   
 dt=0.01
 Tspan=5.0
 time = np.linspace(0,Tspan,npts+1) 

 #initial condition
 V0 = [1.0, 1.0]

# Priors for unknown …
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python porting pymc pymc3 probabilistic-programming

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