Enable multiple spatial_grids and spatiotemporal_grids for multiple trajectories

[znicolaou]

Is your feature request related to a problem? Please describe.

The PDELibrary and WeakPDELibrary classes are initialized with a single spatial_grid and spatiotemporal_grid that are used in derivative calculations, limiting the applicability of multiple_trajectories=True to trajectories that are defined on the same grids.

The current spatial_grid and spatiotemporal_grid are also somewhat memory-wasteful now. We require the grids to be tensor product grids, so they actually only need N_dim vectors to specify rather than a tensor with N_dim+1 axes.

Describe the solution you'd like

We should remove the grid arguments, and instead provide set_spatial_grid and set_spatiotemporal_grid class functions, that take lists of grids. The SINDy.fit function should take optional spatial_grid and spatiotemporal_grid options, and should invoke the library set_spatial_grid and set_spatiotemporal_grid at the time of the fit. The library fit functions should then verify that the the provided x_full has a compatible shape with the grid, and raise an error otherwise. A default grid can be used if None is provide.

Conserving the memory may not be necessary, since the data x_full will always be a similar size to the grids, so we can only reduce the data used by ~1/2.

Additional context

This is a relatively simply fix, but will require changes to the notebooks and tests. I am deferring this for now so that we can complete #185

[Jacob-Stevens-Haas]

Sounds good zach! Two suggestions:

1) Maybe the calls to set_..._grid should be a more functional vs object oriented design (e.g. create_..._grid()). This allows us to test grid creation/validation much faster, without a pytest fixture of a feature library & the expensive fit_transform() method. 2) If y isn't needed, then we could call the code in transform(). Not as sure about this, but lmk your thoughts: Our feature libraries are only feel like estimators to match the Pipeline interface, rather than actual estimators. The splitting of fit and transform seems an unnatural split, saving some intermediate arguments as object attributes, but this seems to break encapsulation (and costs extra memory, though it's probably minimal).