Predicting the highest phonon peak frequency of a crystal

Predict the frequency of the highest optical phonon peak of a crystal, in 1/cm, from its structure.

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1	# Predicting the highest phonon peak frequency of a crystal
2
3	The highest optical phonon frequency of a crystal sets the scale of its lattice vibrations and is a useful proxy for the dominant longitudinal optical mode. This task asks for it from the structure alone, on 1,265 materials whose phonons were computed with density functional perturbation theory.
4
5	## Task
6
7	Given a crystal structure, predict the frequency of the highest-frequency optical phonon mode peak in units of $\mathrm{cm}^{-1}$. Scoring is the mean absolute error over the five fixed folds.
8
9	## Background
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11	The reference values come from Petretto and co-workers' high-throughput ABINIT phonon database, computed in the harmonic approximation; Matbench kept the entries within 150 meV of the convex hull. Phonon frequencies are expensive to compute and cheap to use downstream, in thermal conductivity, Raman assignment and stability screening, which is why a surrogate is worth having. The task is one of the suite's small structure-based problems, and it rewards models that read bond stiffness off the geometry.
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13	## Data and evaluation
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15	- Data: `matbench_phonons.json.gz` from MPContribs-ML (1,265 records, each a pymatgen Structure and a peak frequency in 1/cm), at <https://ml.materialsproject.org/projects/matbench_phonons> or via `task.load()` in the `matbench` package; the phonon calculations are from Petretto and co-workers.
16	- Split: five folds fixed in `matbench_v0.1_validation.json`, built with scikit-learn's `KFold(n_splits=5, shuffle=True, random_state=18012019)`. Train on each fold's training set, tune inside it only, predict its test set, report the mean. Changing the folds invalidates the comparison.
17	- Metric: mean absolute error in cm^-1 over the five test folds, lower is better. The leaderboard also lists the fold-to-fold standard deviation, RMSE and worst single-sample error.
18	- Official evaluation code: the `matbench` package (MIT), <https://github.com/materialsproject/matbench>; the task's `record(fold, predictions)`, as in `mb.matbench_phonons.record(...)` on a `MatbenchBenchmark` `mb`, scores a fold and `mb.to_file(...)` writes the submission file.
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20	## What is known
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22	- Top of the task leaderboard: MegNet (kgcnn v2.1.0), mean MAE 28.7606 cm^-1 (standard deviation 2.5767).
23	- Close behind: coNGN 28.8874, ALIGNN 29.5385 and coGN 29.7117 cm^-1. Four architectures sit within 1 cm^-1 of each other, less than the fold-to-fold spread.
24	- A dummy regressor scores 323.9822 cm^-1 (mean absolute deviation 323.7870), so the leaders cut the error by more than a factor of ten.
25	- Unmerged claim: pull request [#347](https://github.com/materialsproject/matbench/pull/347) (April 2024) submits DensGNN, whose results file records a mean MAE of 24.52 cm^-1; it has not been reviewed or added to the leaderboard.
26	- The leaderboard's repository has merged no submission since 20 January 2024; newer ones wait as open [pull requests](https://github.com/materialsproject/matbench/pulls), so the official numbers may lag what has been achieved.
27
28	## What would count as progress
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30	- A mean MAE below 28.7606 cm^-1 on the five fixed folds, beating MegNet, kgcnn v2.1.0, submitted as the `matbench` benchmark file so every fold's predictions can be re-scored.
31	- Code and a pinned environment that reproduce the run from the fixed folds.
32	- Per-fold numbers, not just the mean, so that a gain can be compared with the leader fold by fold on the same folds; a small gain should hold on each fold or over repeated training runs. Reproducing the current leader counts too, since the board has not moved since 2024.
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34	## References
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36	1. G. Petretto et al., "High-throughput density-functional perturbation theory phonons for inorganic materials", Scientific Data 5, 180065 (2018). <https://doi.org/10.1038/sdata.2018.65>
37	2. A. Dunn, Q. Wang, A. Ganose, D. Dopp and A. Jain, "Benchmarking materials property prediction methods: the Matbench test set and Automatminer reference algorithm", npj Computational Materials 6, 138 (2020). <https://doi.org/10.1038/s41524-020-00406-3>
38	3. C. Chen, W. Ye, Y. Zuo, C. Zheng and S. P. Ong, "Graph Networks as a Universal Machine Learning Framework for Molecules and Crystals", Chemistry of Materials 31, 3564–3572 (2019). <https://doi.org/10.1021/acs.chemmater.9b01294>
39	4. R. Ruff, P. Reiser, J. Stühmer and P. Friederich, "Connectivity optimized nested line graph networks for crystal structures", Digital Discovery 3, 594–601 (2024). <https://doi.org/10.1039/D4DD00018H>
40
41	## Source
42
43	Imported from [Matbench v0.1 matbench_phonons](https://matbench.materialsproject.org/Leaderboards%20Per-Task/matbench_v0.1_matbench_phonons/), curated by Materials Project (Dunn et al.). Open according to the source as of 2026-10-20. The statement above is written in our own words; see the source for the original wording, history and discussion.