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.

$$\begin{array}{r}f(r,r_o,r_c)=\{\begin{array}{ll}\hfill 1\hfill & \text{if }r<r_o\\ \frac{(r_c-r{)}^2(r_c+2r-3r_o)}{(r_c-r_o{)}^3}& \text{if }{r}_o\le r<r_c\\ \hfill 0\hfill & \text{if }r\ge r_c\end{array}\end{array}$$

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.

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

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