# Fast Neural Network Approach for Direct Covariant Forces Prediction in Complex Multi-Element Extended Systems

arXiv: https://arxiv.org/abs/1905.02791 · HTML: https://mlsanity.com/paper/1905.02791/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 May 2019.

## Built on by (most cited first, 12 of 12)

- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [Graph Neural Networks Accelerated Molecular Dynamics](https://mlsanity.com/paper/2112.03383/) (2021)
- [Fast Uncertainty Estimates in Deep Learning Interatomic Potentials](https://mlsanity.com/paper/2211.09866/) (2022)
- [Graph Neural Networks for Molecules](https://mlsanity.com/paper/2209.05582/) (2022)
- [Data efficiency and extrapolation trends in neural network interatomic potentials](https://mlsanity.com/paper/2302.05823/) (2023)
- [How simple can you go? An off-the-shelf transformer approach to molecular dynamics](https://mlsanity.com/paper/2503.01431/) (2025)
- [Efficient and Accurate Physics-aware Multiplex Graph Neural Networks for 3D Small Molecules and Macromolecule Complexes](https://mlsanity.com/paper/2206.02789/) (2022)
- [Data-Efficient Machine Learning Potentials via Difference Vectors Based on Local Atomic Environments](https://mlsanity.com/paper/2501.16398/) (2025)
- [Deep Neural Network for Phonon-Assisted Optical Spectra in Semiconductors](https://mlsanity.com/paper/2502.00798/) (2025)
- [Improving the Stability of GNN Force Field Models by Reducing Feature Correlation](https://mlsanity.com/paper/2502.12548/) (2025)
- [On the Connection Between Diffusion Models and Molecular Dynamics](https://mlsanity.com/paper/2504.03187/) (2025)

## Abstract (arXiv)

Neural network force field (NNFF) is a method for performing regression on atomic structure-force relationships, bypassing expensive quantum mechanics calculation which prevents the execution of long ab-initio quality molecular dynamics simulations. However, most NNFF methods for complex multi-element atomic systems indirectly predict atomic force vectors by exploiting just atomic structure rotation-invariant features and the network-feature spatial derivatives which are computationally expensive. We develop a staggered NNFF architecture exploiting both rotation-invariant and covariant features separately to directly predict atomic force vectors without using spatial derivatives, thereby reducing expensive structural feature calculation by ~180-480x. This acceleration enables us to develop NNFF which directly predicts atomic forces in complex ternary and quaternary-element extended systems comprised of long polymer chains, amorphous oxide, and surface chemical reactions. The staggered rotation-invariant-covariant architecture described here can also directly predict complex covariant vector outputs from local physical structures in domains beyond computational material science.