Can odeint_adjoint solve parametric ODEs?

[mayar-shahin]

Let's say I have some linear system of parametric ODEs:

def f(t, y, params):
    a, b, c = params 
    dydt = torch.zeros_like(y)
    dydt[0] = a*y[0] - b*y[1]
    dydt[1] = b*y[0] - c*y[1]
    return dydt

How do I pass the parameters to odeint/odeint_adjoint? In scipy.integrate.odeint, this would look like this:

odeint(f, y0, t, args=(a,b,c))

[iranroman]

can someone please answer this question?

[ftavella]

Hi! I'm not one of the developers but I think you can do it this way:

import torch
import torch.nn as nn
import matplotlib.pyplot as plt
from torchdiffeq import odeint, odeint_adjoint


class ODEfunc(nn.Module):
    def __init__(self, params):
        super(ODEfunc, self).__init__()
        self.params = params
    
    def forward(self, t, y):
        a, b, c = self.params
        dydt = torch.zeros_like(y)
        dydt[0] = a*y[0] - b*y[1]
        dydt[1] = b*y[0] - c*y[1]
        return dydt

time = torch.linspace(0.0, 10.0, 100)
params = torch.Tensor([1.0, 2.0, 3.0])
y0 = torch.Tensor([1.5, 0.25])

func = ODEfunc(params)
result = odeint(func, y0, time)
result_adjoint = odeint_adjoint(func, y0, time)

plt.plot(time, result[:, 0], color='tab:blue', zorder=0, label="odeint")
plt.scatter(time, result_adjoint[:, 0], color='tab:blue')

plt.plot(time, result[:, 1], color='tab:red', zorder=0)
plt.scatter(time, result_adjoint[:, 1], color='tab:red')

plt.xlabel('Time')
plt.ylabel('Y')
plt.show()

Output:

[Mr-Markovian]

Do this approach work when the parameters are not constant, but different for the samples we want to train on?