Envelopes

Available Envelopes

graph-pes exposes the Envelope base class, together with implementations of a few common envelope functions:

class graph_pes.models.components.distances.PolynomialEnvelope(cutoff, p=6)

Bases: Envelope

A thrice differentiable envelope function.

\[E_p(r) = 1 - \frac{(p+1)(p+2)}{2}\cdot r^p + p(p+2) \cdot r^{p+1} - \frac{p(p+1)}{2}\cdot d^{p+2}\]

where \(r_\text{cut}\) is the cutoff radius, and \(p \in \mathbb{N}\).

Parameters:

• cutoff (float) – The cutoff radius.

• p (int) – The order of the envelope function.

class graph_pes.models.components.distances.SmoothOnsetEnvelope(cutoff, onset)

Bases: Envelope

A smooth cutoff function with an onset.

\[\begin{split}f(r, r_o, r_c) = \begin{cases} \hfill 1 \hfill & \text{if } r < r_o \\ \frac{(r_c - r)^2 (r_c + 2r - 3r_o)}{(r_c - r_o)^3} & \text{if } r_o \leq r < r_c \\ \hfill 0 \hfill & \text{if } r \geq r_c \end{cases}\end{split}\]

where \(r_o\) is the onset radius and \(r_c\) is the cutoff radius.

Parameters:

• cutoff (float) – The cutoff radius.

• onset (float) – The onset radius.

class graph_pes.models.components.distances.CosineEnvelope(cutoff)

Bases: Envelope

A cosine envelope function.

\[E_c(r) = \frac{1}{2}\left(1 + \cos\left(\frac{\pi r}{r_\text{cut}} \right)\right)\]

where \(r_\text{cut}\) is the cutoff radius.

Parameters:

cutoff (float) – The cutoff radius.

Implementing a new Envelope

class graph_pes.models.components.distances.Envelope(*args, **kwargs)

Any envelope function, \(E(r)\), for smoothing potentials must implement a forward method that takes in a tensor of distances and returns a tensor of the same shape, where the values outside the cutoff are set to zero.

forward(r)

Perform the envelope function.

Parameters:

r (torch.Tensor) – The distances to envelope.

Return type:

Tensor