How to define a temporal PDE library with multiple trajectories?

[itsjacobhere]

I understand when fitting the data multiple trajectories should be passed as a list each with (num_samples, num_features) such as:

model.fit(X, t=t, multiple_trajectories=True)

where both X and t are the list of trajectories. When defining a PDE lib such as:

pde_lib = ps.PDELibrary( derivative_order=2, implicit_terms=True, temporal_grid=t, is_uniform=True, include_bias=True )

how do I pass the proper temporal grid because each trajectory contains a different number of samples?

[znicolaou]

Hi there @itsjacobhere. Enabling differing (spatio)temporal grids for different trajectories is on our list of features to implement (#222), so unfortunately, it isn't possible yet. I've been wanting to do this for a while, and it isn't that hard, but it will require a lot of small changes that will need to be validated.

Instead, the best current solution is to interpolate the trajectories onto a common temporal grid. If you have data x1 and x2 on grids t1=np.arange(0, T1, dt1) and t2=np.arange(0,T2,dt2), then maybe define t=np.arange(0,np.min(T1,T2),np.min(dt1,dt2)) and use scipy.interpolate.interp1d to produce x1_interp=interp1d(x1,t) and x2_interp=interp1d(x2,t), then model.fit([x1_interp,x2_interp],t=t).

[itsjacobhere]

@znicolaou thanks for the quick reply! Doing something like that was my alternative solution as well, originally I was thinking to just truncate or force each trajectory to be the same size, but I wasn't sure if just passing in one (universal) temporal trajectory into the PDE lib would work and if I still need to pass a list for t the same size as X into the model.fit, if that makes sense?

I like your idea of interpolating along one temporal grid though, I'll try that for now. Yeah would be a great feature! thanks for all your work maintaining this package!