# Coarse Graining Molecular Dynamics with Graph Neural Networks

arXiv: https://arxiv.org/abs/2007.11412 · HTML: https://mlsanity.com/paper/2007.11412/

## Key facts

- Cited by 56 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jul 2020.

## Built on by (most cited first, 30 of 56)

- [TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentials](https://mlsanity.com/paper/2202.02541/) (2022)
- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [Two for One: Diffusion Models and Force Fields for Coarse-Grained Molecular Dynamics](https://mlsanity.com/paper/2302.00600/) (2023)
- [Smooth Normalizing Flows](https://mlsanity.com/paper/2110.00351/) (2021)
- [Machine Learning Coarse-Grained Potentials of Protein Thermodynamics](https://mlsanity.com/paper/2212.07492/) (2022)
- [Flow-matching -- efficient coarse-graining of molecular dynamics without forces](https://mlsanity.com/paper/2203.11167/) (2022)
- [Graph Neural Networks Accelerated Molecular Dynamics](https://mlsanity.com/paper/2112.03383/) (2021)
- [Learning neural network potentials from experimental data via Differentiable Trajectory Reweighting](https://mlsanity.com/paper/2106.01138/) (2021)
- [Simulate Time-integrated Coarse-grained Molecular Dynamics with Multi-Scale Graph Networks](https://mlsanity.com/paper/2204.10348/) (2022)
- [Navigating protein landscapes with a machine-learned transferable coarse-grained model](https://mlsanity.com/paper/2310.18278/) (2023)
- [Consistent Sampling and Simulation: Molecular Dynamics with Energy-Based Diffusion Models](https://mlsanity.com/paper/2506.17139/) (2025)
- [Generative Coarse-Graining of Molecular Conformations](https://mlsanity.com/paper/2201.12176/) (2022)
- [EquiJump: Protein Dynamics Simulation via SO(3)-Equivariant Stochastic Interpolants](https://mlsanity.com/paper/2410.09667/) (2024)
- [Probabilistic Graph Rewiring via Virtual Nodes](https://mlsanity.com/paper/2405.17311/) (2024)
- [Implicit Transfer Operator Learning: Multiple Time-Resolution Surrogates for Molecular Dynamics](https://mlsanity.com/paper/2305.18046/) (2023)
- [Foundation Inference Models for Markov Jump Processes](https://mlsanity.com/paper/2406.06419/) (2024)
- [Scalable Bayesian Uncertainty Quantification for Neural Network Potentials: Promise and Pitfalls](https://mlsanity.com/paper/2212.07959/) (2022)
- [DiAMoNDBack: Diffusion-denoising Autoregressive Model for Non-Deterministic Backmapping of Cα Protein Traces](https://mlsanity.com/paper/2307.12451/) (2023)
- [Predicting solvation free energies with an implicit solvent machine learning potential](https://mlsanity.com/paper/2406.00183/) (2024)
- [Statistically Optimal Force Aggregation for Coarse-Graining Molecular Dynamics](https://mlsanity.com/paper/2302.07071/) (2023)
- [GraphVAMPNet, using graph neural networks and variational approach to markov processes for dynamical modeling of biomolecules](https://mlsanity.com/paper/2201.04609/) (2022)
- [Contrastive Learning of Coarse-Grained Force Fields](https://mlsanity.com/paper/2205.10861/) (2022)
- [CoarsenConf: Equivariant Coarsening with Aggregated Attention for Molecular Conformer Generation](https://mlsanity.com/paper/2306.14852/) (2023)
- [Conditional Normalizing Flows for Active Learning of Coarse-Grained Molecular Representations](https://mlsanity.com/paper/2402.01195/) (2024)
- [Using pretrained graph neural networks with token mixers as geometric featurizers for conformational dynamics](https://mlsanity.com/paper/2409.19838/) (2024)
- [Top-down machine learning of coarse-grained protein force-fields](https://mlsanity.com/paper/2306.11375/) (2023)
- [EPR-Net: Constructing non-equilibrium potential landscape via a variational force projection formulation](https://mlsanity.com/paper/2301.01946/) (2023)
- [On the Relationships between Graph Neural Networks for the Simulation of Physical Systems and Classical Numerical Methods](https://mlsanity.com/paper/2304.00146/) (2023)
- [AMARO: All Heavy-Atom Transferable Neural Network Potentials of Protein Thermodynamics](https://mlsanity.com/paper/2409.17852/) (2024)
- [Learning Macroscopic Dynamics from Partial Microscopic Observations](https://mlsanity.com/paper/2410.23938/) (2024)

## Abstract (arXiv)

Coarse graining enables the investigation of molecular dynamics for larger systems and at longer timescales than is possible at atomic resolution. However, a coarse graining model must be formulated such that the conclusions we draw from it are consistent with the conclusions we would draw from a model at a finer level of detail. It has been proven that a force matching scheme defines a thermodynamically consistent coarse-grained model for an atomistic system in the variational limit. Wang et al. [ACS Cent. Sci. 5, 755 (2019)] demonstrated that the existence of such a variational limit enables the use of a supervised machine learning framework to generate a coarse-grained force field, which can then be used for simulation in the coarse-grained space. Their framework, however, requires the manual input of molecular features upon which to machine learn the force field. In the present contribution, we build upon the advance of Wang et al.and introduce a hybrid architecture for the machine learning of coarse-grained force fields that learns their own features via a subnetwork that leverages continuous filter convolutions on a graph neural network architecture. We demonstrate that this framework succeeds at reproducing the thermodynamics for small biomolecular systems. Since the learned molecular representations are inherently transferable, the architecture presented here sets the stage for the development of machine-learned, coarse-grained force fields that are transferable across molecular systems.