Predicting exfoliation energy of 2D materials

Peeling a single layer off a layered crystal costs energy, and that cost decides whether a material can become a two-dimensional one. This task asks for the computed exfoliation energy from the crystal structure, on 636 candidates from the JARVIS-DFT database.

Task

Given a crystal structure, predict the exfoliation energy in meV per atom as computed with the OptB88vdW and TBmBJ functionals. Scoring is the mean absolute error over the five fixed folds. The target has a long upper tail: every submission's worst single-sample error exceeds 1,400 meV/atom, which is where the difficulty sits.

Background

The data was adapted from the JARVIS-DFT two-dimensional dataset of Choudhary and co-workers, who screened layered compounds for exfoliable candidates. It entered Matbench v0.1 as one of the two smallest tasks, and it is the suite's hardest regression problem in relative terms: a model that halves the error still misses by tens of meV per atom. Because exfoliation energy is a weak van der Waals quantity, small structural differences matter and the DFT values themselves carry functional-dependent uncertainty.

Data and evaluation

• Data: matbench_jdft2d.json.gz from MPContribs-ML (636 records, each a pymatgen Structure and an exfoliation energy in meV/atom), at https://ml.materialsproject.org/projects/matbench_jdft2d or via task.load() in the matbench package; the structures and energies come from JARVIS-DFT.
• 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.
• Metric: mean absolute error in meV/atom over the five test folds, lower is better. The leaderboard also lists the fold-to-fold standard deviation, RMSE and worst single-sample error.
• Official evaluation code: the matbench package (MIT), https://github.com/materialsproject/matbench; the task's record(fold, predictions), as in mb.matbench_jdft2d.record(...) on a MatbenchBenchmark mb, scores a fold and mb.to_file(...) writes the submission file.

What is known

• Top of the task leaderboard: MODNet v0.1.12, mean MAE 33.1918 meV/atom (standard deviation 7.3428 across folds).
• Runners-up: MODNet v0.1.10 34.5368, coNGN 36.1698 and coGN 37.1652 meV/atom.
• A dummy regressor scores 67.2851 meV/atom (the target's mean absolute deviation is 67.2020), so the best entry halves the error and no more.
• Fold-to-fold standard deviations are large here (7–14 meV/atom), so improvements below a few meV/atom are hard to distinguish from noise.
• Unmerged claim: pull request #347 (April 2024) submits DensGNN, whose results file records a mean MAE of 31.97 meV/atom; it has not been reviewed or added to the leaderboard.
• The leaderboard's repository has merged no submission since 20 January 2024; newer ones wait as open pull requests, so the official numbers may lag what has been achieved.

What would count as progress

• A mean MAE below 33.1918 meV/atom on the five fixed folds, beating MODNet v0.1.12, submitted as the matbench benchmark file so every fold's predictions can be re-scored.
• Code and a pinned environment that reproduce the run from the fixed folds.
• 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.

References

1. K. Choudhary, I. Kalish, R. Beams and F. Tavazza, "High-throughput Identification and Characterization of Two-dimensional Materials using Density functional theory", Scientific Reports 7, 5179 (2017). https://doi.org/10.1038/s41598-017-05402-0
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
3. P.-P. De Breuck, M. L. Evans and G.-M. Rignanese, "Robust model benchmarking and bias-imbalance in data-driven materials science: a case study on MODNet", Journal of Physics: Condensed Matter 33, 404002 (2021). https://doi.org/10.1088/1361-648X/ac1280
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

Source

Imported from Matbench v0.1 matbench_jdft2d, 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.