FAQ

How would I define a DDE with several delays ?

You just have to specify a delay tensor size that corresponds to the number of delays you desire.

solver = ....
delays = torch.tensor([1.0, 2.0])
history_function = lambda t : ...
ts = ...

def simple_dde(t, y, args, *, history):
    # this correspond to y'(t) = -y(t-1) - y(t-2)
    return - history[0] - history[1]

ys = torchdde.integrate(f, solver, ts[0], ts[-1], ts, history_function, args=None, dt0=ts[1]-ts[0], delays=delays)

How about if I want a neural network to have also several delays ?

Well if it's the same forward pass in the Neural DDE, then nothing needs to be changed ! The term torch.cat([z, *history], dim=-1) unpacks all the delayed terms.

What if my trajectories have different evaluation points ?

torchdde was developed with in mind that the evaluation points ts are the same for all trajectories.
Nonetheless, if this isn't the case, that's not an issue. One could think of doing the following :

# creating different evaluation times ts 
different_ts_list = [torch.linspace(0, 10, torch.randint(1, 10, (1,)).item()) for _ in range(4)]
all_values = torch.cat(different_ts_list)
# taking all unique values from `different_ts_list`
ts, _ = torch.sort(all_values.unique())

# integrate your ODE/DDE with ts 
# after successful integration, we will have to take the values of ys at the times ts_list
ys = torch.rand((4, ts.shape[0], 2))

ys_list_pred = []
for ys_, ts_ in zip(ys, different_ts_list): 
    # creating a mask to get the values of ys at the times ts_list
    mask = torch.where(torch.isin(ts, ts_))
    assert torch.all(different_ts_list[0] == ts[mask]), "Error"
    ys_subset = ys_[mask]
    ys_list_pred.append(ys_subset)