Farthest Point Sampling¶

PESMaker uses farthest point sampling (FPS) to choose representative MD frames from a trajectory. The goal is to keep a compact set of structures that covers the descriptor space without labeling every sampled frame with DFT.

Basic Idea¶

Each trajectory frame is mapped to a feature vector:

\[ x_i \in \mathbb{R}^d \]

where \(x_i\) is the descriptor for frame \(i\). PESMaker chooses the production descriptor from the sampling engine:

GPUMD sampling uses Calorine NEP descriptors calculated with the GPUMD sampling potential.
MACE sampling uses invariant descriptors output by the native MACE model configured as sampling.selection.descriptor_model.

Users do not need to select the descriptor backend manually.

FPS starts from one frame, then repeatedly selects the frame whose nearest distance to the already selected set is largest:

\[ i^* = \arg\max_i \min_{j \in S} \|x_i - x_j\|_2 \]

where \(S\) is the set of already selected frames. This picks frames that are far from what has already been selected, so the final set spreads across the trajectory descriptor space.

The method is a greedy coverage rule. Random selection can miss rare regions of a trajectory, especially when most MD frames stay near one basin. FPS instead keeps the frame that currently improves descriptor-space coverage the most. This makes it useful for reducing many correlated MD frames into a smaller DFT labeling set.

FPS is only as meaningful as the descriptor. If the descriptor does not capture the chemistry or distortion that matters for the target potential, far-apart points in descriptor space may not be the most important DFT labels. For production runs, inspect the selected structures and the PCA plot instead of treating the selector as fully automatic.

Stop Criteria¶

PESMaker stops selection when either condition is met:

max_count selected frames have been kept;
the next farthest frame is closer than min_distance to the selected set.

Use max_count to control labeling cost. Use min_distance to avoid spending DFT calculations on frames that are nearly redundant in descriptor space. max_count is optional; if omitted, FPS keeps selecting until the distance rule stops it or all frames have been selected.

Descriptor Invariance And Pooling¶

For MACE, PESMaker calls:

calculator.get_descriptors(
    atoms,
    invariants_only=True,
    num_layers=-1,
)

invariants_only=True is the appropriate default for PESMaker's FPS metric. MACE's \(L=0\) scalar channels are unchanged by rotation, while \(L>0\) channels transform with rotation. A plain Euclidean distance between flattened \(L>0\) components is preserved when the same rotation is applied to both structures, but not when two otherwise equivalent structures have independent orientations. FPS normally treats those rotated copies as the same structure, so PESMaker compares only the invariant channels.

This does not mean equivariant descriptors can never be used for selection. They require a rotation-aware distance, alignment, or another invariant contraction before FPS. PESMaker currently uses direct Euclidean distance and does not implement such a metric.

PESMaker uses every interaction layer, averages atom descriptors separately for each element, and concatenates those element vectors in atomic number order. MACE's official fine_tuning_select.py uses the same get_descriptors(..., invariants_only=True) call, performs per-element averaging, flattens the resulting structure descriptors, and passes them to FPS.

NEP descriptors are atom-level descriptors. PESMaker converts them into one structure-level vector before FPS:

descriptor_pooling: mean: average atom descriptors, the default;
descriptor_pooling: sum: sum atom descriptors;
descriptor_pooling: mean_std: concatenate descriptor means and standard deviations.

mean is usually the safest first choice because it is less sensitive to atom count. mean_std can preserve more information about local-environment spread, but it increases descriptor dimensionality.

Practical Use¶

Minimal selection settings:

sampling:
  engine: gpumd
  potential: /path/to/nep.txt
  selection:
    trajectory_pattern: sampling/**/movie.xyz
    output_dir: selected
    min_distance: 0.2
    max_count: 200  # optional cap
    plot: true

For MACE:

sampling:
  engine: mace
  selection:
    trajectory_pattern: sampling/**/*.lammpstrj
    output_dir: selected
    descriptor_model: /path/to/native-mace.model
    min_distance: 0.0
    max_count: 200

The MACE descriptor model is the native model loaded by ASE. It is separate from the MLIAP-exported model used by LAMMPS.

Run:

pesmaker select run.yaml

The output selected/fps_selection.png shows a PCA projection of all frames and selected frames. Use it as a sanity check: selected frames should be spread over the cloud rather than concentrated in one small region.

PESMaker also writes selected/selection_features.npy. This file stores the actual descriptor matrix used by FPS before PCA:

shape = (number_of_md_frames, descriptor_dimension)

It is not a structure file and does not go into VASP. It is for diagnostics and reproducibility: reload it with numpy.load, rerun PCA or clustering, compare different selection thresholds, and check whether the descriptor space separates physically distinct MD regions. The selected structures themselves are stored in the combined selected/selected.xyz; the manifest records which frames were kept and lets later SCF setup split them into single-point jobs.

References: