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MatthiasSachs authored Nov 3, 2024
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Expand Up @@ -32,9 +32,9 @@ ACEfriction.jl facilitates simulation and machine learning of configuration-depe
```math
{\bf \Gamma}({\bf r}_1, \dots, {\bf r}_N, {z_1},\dots,{z_N}) \in \mathcal{SPSD}_{3N},
```
where $`{\bf r}_i \in \mathbb{R}^3,\; (i=1,\dots,N)`$, are the positions of points in the point cloud, the $`z_i`$s are some discrete features (e.g., chemical element types) and $\mathcal{SPSD}_{3N} \subset \mathbb{R}^{3N \times 3N}$ is the set of $3N\times 3N$-dimensional positive semi-definite matrices.
where $`{\bf r}_i \in \mathbb{R}^3,\; (i=1,\dots,N)`$, are the positions of points/particles in the point cloud, the $`z_i`$s are some discrete features (e.g., chemical element types) and $\mathcal{SPSD}_{3N} \subset \mathbb{R}^{3N \times 3N}$ is the set of $3N\times 3N$-dimensional positive semi-definite matrices.

The underlying representation is based on an equivariant Atomic Cluster Expansion and, as such, size-transferrable, i.e., models can be trained and evaluated on 3D-point clouds comprised of arbitrary number, $N$, of particles.
The underlying representation is based on an equivariant Atomic Cluster Expansion and, as such, size-transferrable, i.e., models can be trained and evaluated on 3D-point clouds comprised of arbitrary number, $N$, of points/particles.

## Documentation

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