Tabulated pair functions calculator

[Luthaf]

We need some calculator that can take in one or multiple splines, and compute a per atom/per structure functions summed over neighbors.

$$ < n | f > = \sum_j f(r_{ij}) $$

This would enable multiple things:

• calculation of pair potential as a baseline potential (without requiring an external software)
• calculation of basic pair descriptor (the G2 functions for BPSF would be a possibility)

[PicoCentauri]

Before starting on this we might be decide on the parameter/hyper design. Here from the python side

class RadialTableCalculator:
    def __init__(self, cutoff, splines):

I would add a cutoff and list of splines:

splines = [{"species_center": 6,
                  "species_neighbor": 6,
                  "positions": np.array([1,2,3,4]),
                  "values": np.array([1,0.5,0.2,0.1]),
                  "gradients": np.array([1,0.5,0.2,0.1])},
    ...
}

we might also only take values and the calculate the the gradients using some finite difference scheme.

We throw an errors outside of interoplation range. No extrapolation.

[ceriottm]

I think ideally we should take some hint from equistore. You can have e.g. labels that go "center_species" "species_neighbors_1", etc, and then match the samples or keys from a neighbor list. Possibly, the real question here is how we want to implement metadata and group selection for neighbor lists.

On Tue, 4 Oct 2022 at 14:42, Philip Loche @.***> wrote:

Before starting on this we might be decide on the parameter/hyper design. Here from the python side

class RadialTableCalculator: def init(self, cutoff, pairtable, kind):

I would add a cutoff, the interpolation kind and a pairtable dictioary. pairtable contains all elements as keys. Each element is dictionary itself containing the keys positions, energies, forces/gradients, where each of these is a 1D array.

pairtable = { "1": {"positions": np.array([1,2,3,4]), "energies": np.array([1,0.5,0.2,0.1]), "forces": np.array([1,0.5,0.2,0.1])}, ... }

we might also only take energies and the calculathe the gradients using some finite difference scheme.

Any comments?

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[Luthaf]

I think ideally we should take some hint from equistore. You can have e.g. labels that go "center_species" "species_neighbors_1", etc, and then match the samples or keys from a neighbor list. Possibly, the real question here is how we want to implement metadata and group selection for neighbor lists.

I have no idea what you mean here. There is no neighbor list involved in the proposed calculator (from the user point of view). We should also have a separate NeighborList calculator that would just give a raw neighbor list in equistore format (I have this on a branch, I need to clean it up).

[ceriottm]

What I meant is that in practice one will have a list of pair potentials, and they will have to be evaluated for a list of pairs. It would make sense IMO to have the pairs "exploded" into species - basically using the neighbor list to generate a list of pair distances broken down by species.

On Mon, 17 Oct 2022 at 18:31, Guillaume Fraux @.***> wrote:

I think ideally we should take some hint from equistore. You can have e.g. labels that go "center_species" "species_neighbors_1", etc, and then match the samples or keys from a neighbor list. Possibly, the real question here is how we want to implement metadata and group selection for neighbor lists.

I have no idea what you mean here. There is no neighbor list involved in the proposed calculator (from the user point of view). We should also have a separate NeighborList calculator that would just give a raw neighbor list in equistore format (I have this on a branch, I need to clean it up).

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[Luthaf]

So my idea for this calculator would be to do the sum over pairs of the same species (allowing different splines for different species pairs). The output TensorMap would contain species_center and species_neighbor keys, but the samples would be per-atom and not per-pair.