# BIGDML: Towards Exact Machine Learning Force Fields for Materials

arXiv: https://arxiv.org/abs/2106.04229 · HTML: https://mlsanity.com/paper/2106.04229/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 144 references that are in the map.
- First posted on arXiv 8 Jun 2021.

## Builds on (most cited first, 9 of 9)

- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [Machine learning for molecular simulation](https://mlsanity.com/paper/1911.02792/) (2019)
- [SpookyNet: Learning Force Fields with Electronic Degrees of Freedom and Nonlocal Effects](https://mlsanity.com/paper/2105.00304/) (2021)
- [Deep Learning in Protein Structural Modeling and Design](https://mlsanity.com/paper/2007.08383/) (2020)
- [On Invariance and Selectivity in Representation Learning](https://mlsanity.com/paper/1503.05938/) (2015)
- [Machine learning for protein folding and dynamics](https://mlsanity.com/paper/1911.09811/) (2019)
- [Autonomous robotic nanofabrication with reinforcement learning](https://mlsanity.com/paper/2002.11952/) (2020)

## Built on by (most cited first, 5 of 5)

- [Euclidean Fast Attention -- Machine Learning Global Atomic Representations at Linear Cost](https://mlsanity.com/paper/2412.08541/) (2024)
- [A Transferable Recommender Approach for Selecting the Best Density Functional Approximations in Chemical Discovery](https://mlsanity.com/paper/2207.10747/) (2022)
- [Reconstructing Kernel-based Machine Learning Force Fields with Super-linear Convergence](https://mlsanity.com/paper/2212.12737/) (2022)
- [Active Learning Exploration of Transition Metal Complexes to Discover Method-Insensitive and Synthetically Accessible Chromophores](https://mlsanity.com/paper/2208.05444/) (2022)
- [From Peptides to Nanostructures: A Euclidean Transformer for Fast and Stable Machine Learned Force Fields](https://mlsanity.com/paper/2309.15126/) (2023)

## Abstract (arXiv)

Machine-learning force fields (MLFF) should be accurate, computationally and data efficient, and applicable to molecules, materials, and interfaces thereof. Currently, MLFFs often introduce tradeoffs that restrict their practical applicability to small subsets of chemical space or require exhaustive datasets for training. Here, we introduce the Bravais-Inspired Gradient-Domain Machine Learning (BIGDML) approach and demonstrate its ability to construct reliable force fields using a training set with just 10-200 geometries for materials including pristine and defect-containing 2D and 3D semiconductors and metals, as well as chemisorbed and physisorbed atomic and molecular adsorbates on surfaces. The BIGDML model employs the full relevant symmetry group for a given material, does not assume artificial atom types or localization of atomic interactions and exhibits high data efficiency and state-of-the-art energy accuracies (errors substantially below 1 meV per atom) for an extended set of materials. Extensive path-integral molecular dynamics carried out with BIGDML models demonstrate the counterintuitive localization of benzene--graphene dynamics induced by nuclear quantum effects and allow to rationalize the Arrhenius behavior of hydrogen diffusion coefficient in a Pd crystal for a wide range of temperatures.