# Graph-Theoretic Neural Network Fragmentation with Covariant Direct Molecular Force Learning: Enabling Coupled-Cluster Accuracy AIMD for Fluxional Systems

arXiv: https://arxiv.org/abs/2607.21779 · HTML: https://mlsanity.com/paper/2607.21779/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 92 references that are in the map.
- First posted on arXiv 23 Jul 2026.

## Builds on (most cited first, 7 of 7)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
- [DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics](https://mlsanity.com/paper/1712.03641/) (2017)
- [Automated Fitting of Neural Network Potentials at Coupled Cluster Accuracy: Protonated Water Clusters as Testing Ground](https://mlsanity.com/paper/1908.08734/) (2019)
- [A large language model-type architecture for high-dimensional molecular potential energy surfaces](https://mlsanity.com/paper/2412.03831/) (2024)

## Abstract (arXiv)

Accurate ab initio molecular dynamics (AIMD) simulations of complex, fluxional chemical systems are severely limited by the high computational scaling of correlated electronic structure methods. To overcome this bottleneck, we present a robust, graph-theoretic molecular fragmentation framework integrated with machine learning to directly model post-Hartree-Fock nuclear forces at coupled cluster accuracy. Bypassing the limitations of automatic differentiation on learned energy surfaces that may struggle with link-atom Jacobians, our approach directly predicts nuclear force vectors. By projecting these vectors onto fragment-fixed principal axes of inertia, we establish co-variant descriptors that naturally preserve rotational, translational, and permutational invariance. The methodology achieves exceptional high parameter efficiency through a vector-valued training protocol that reduces trainable parameters by over an order of magnitude, while an unsupervised mini-batch k-means space tessellation algorithm constructs highly representative training databases using only 10% to 20% of reference configurations. We rigorously validated this framework on the highly fluxional solvated Zundel cation H_{13}O_6^+ ). Our fully machine-learning-predicted AIMD trajectories successfully reproduced complex dynamical signatures and key structural characteristics, including radial distribution functions and the velocity autocorrelation power spectrum. Ultimately, this scalable, systematically improvable framework bridges the gap between high-level correlated wavefunction theories and long-timescale reactive sampling, laying the foundation for advanced, LLM-inspired transfer learning in modern chemical dynamics simulations.