# Simulate Time-integrated Coarse-grained Molecular Dynamics with Multi-Scale Graph Networks

arXiv: https://arxiv.org/abs/2204.10348 · HTML: https://mlsanity.com/paper/2204.10348/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 85 references that are in the map.
- First posted on arXiv 21 Apr 2022.

## Builds on (most cited first, 29 of 29)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics](https://mlsanity.com/paper/1707.09571/) (2017)
- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentials](https://mlsanity.com/paper/2202.02541/) (2022)
- [Learning Gradient Fields for Molecular Conformation Generation](https://mlsanity.com/paper/2105.03902/) (2021)
- [VAMPnets: Deep learning of molecular kinetics](https://mlsanity.com/paper/1710.06012/) (2017)
- [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)
- [Machine Learning of coarse-grained Molecular Dynamics Force Fields](https://mlsanity.com/paper/1812.01736/) (2018)
- [Coarse Graining Molecular Dynamics with Graph Neural Networks](https://mlsanity.com/paper/2007.11412/) (2020)
- [TorchMD: A deep learning framework for molecular simulations](https://mlsanity.com/paper/2012.12106/) (2020)
- [Variational approach for learning Markov processes from time series data](https://mlsanity.com/paper/1707.04659/) (2017)
- [Graph Neural Networks Accelerated Molecular Dynamics](https://mlsanity.com/paper/2112.03383/) (2021)
- [Coarse-Graining Auto-Encoders for Molecular Dynamics](https://mlsanity.com/paper/1812.02706/) (2018)
- [Deep Generative Markov State Models](https://mlsanity.com/paper/1805.07601/) (2018)
- [Molecular Latent Space Simulators](https://mlsanity.com/paper/2007.00728/) (2020)
- [Physics-aware, probabilistic model order reduction with guaranteed stability](https://mlsanity.com/paper/2101.05834/) (2021)
- [Transferable neural networks for enhanced sampling of protein dynamics](https://mlsanity.com/paper/1801.00636/) (2018)
- [Graph Neural Network Based Coarse-Grained Mapping Prediction](https://mlsanity.com/paper/2007.04921/) (2020)
- [Accelerating amorphous polymer electrolyte screening by learning to reduce errors in molecular dynamics simulated properties](https://mlsanity.com/paper/2101.05339/) (2021)

## Built on by (most cited first, 23 of 23)

- [Timewarp: Transferable Acceleration of Molecular Dynamics by Learning Time-Coarsened Dynamics](https://mlsanity.com/paper/2302.01170/) (2023)
- [Generative Modeling of Molecular Dynamics Trajectories](https://mlsanity.com/paper/2409.17808/) (2024)
- [Scalable Equilibrium Sampling with Sequential Boltzmann Generators](https://mlsanity.com/paper/2502.18462/) (2025)
- [Erwin: A Tree-based Hierarchical Transformer for Large-scale Physical Systems](https://mlsanity.com/paper/2502.17019/) (2025)
- [EquiJump: Protein Dynamics Simulation via SO(3)-Equivariant Stochastic Interpolants](https://mlsanity.com/paper/2410.09667/) (2024)
- [Force-Free Molecular Dynamics Through Autoregressive Equivariant Networks](https://mlsanity.com/paper/2503.23794/) (2025)
- [FlashMD: long-stride, universal prediction of molecular dynamics](https://mlsanity.com/paper/2505.19350/) (2025)
- [Amortized Sampling with Transferable Normalizing Flows](https://mlsanity.com/paper/2508.18175/) (2025)
- [Scalable Normalizing Flows Enable Boltzmann Generators for Macromolecules](https://mlsanity.com/paper/2401.04246/) (2024)
- [Flow Matching for Accelerated Simulation of Atomic Transport in Crystalline Materials](https://mlsanity.com/paper/2410.01464/) (2024)
- [UniSim: A Unified Simulator for Time-Coarsened Dynamics of Biomolecules](https://mlsanity.com/paper/2506.03157/) (2025)
- [Force-Guided Bridge Matching for Full-Atom Time-Coarsened Dynamics of Peptides](https://mlsanity.com/paper/2408.15126/) (2024)
- [MarS-FM: Generative Modeling of Molecular Dynamics via Markov State Models](https://mlsanity.com/paper/2509.24779/) (2025)
- [Protein Language Model Embeddings Improve Generalization of Implicit Transfer Operators](https://mlsanity.com/paper/2602.11216/) (2026)
- [Learning Macroscopic Dynamics from Partial Microscopic Observations](https://mlsanity.com/paper/2410.23938/) (2024)
- [Data-driven particle dynamics: Structure-preserving coarse-graining for emergent behavior in non-equilibrium systems](https://mlsanity.com/paper/2508.12569/) (2025)
- [Enhanced Sampling for Efficient Learning of Coarse-Grained Machine Learning Potentials](https://mlsanity.com/paper/2510.11148/) (2025)
- [Improving the Stability of GNN Force Field Models by Reducing Feature Correlation](https://mlsanity.com/paper/2502.12548/) (2025)
- [Natively Trainable Sparse Attention for Hierarchical Point Cloud Datasets](https://mlsanity.com/paper/2508.10758/) (2025)
- [Generative Quasi-Continuum Modeling of Confined Fluids at the Nanoscale](https://mlsanity.com/paper/2509.08223/) (2025)
- [Scalable learning of macroscopic stochastic dynamics](https://mlsanity.com/paper/2511.12842/) (2025)
- [Teaching Molecular Dynamics to a Non-Autoregressive Ionic Transport Predictor](https://mlsanity.com/paper/2605.09311/) (2026)
- [MinkowskiPE: Minkowski Positional Encoding for Spatiotemporal Perception](https://mlsanity.com/paper/2609.33804/) (2026)

## Abstract (arXiv)

Molecular dynamics (MD) simulation is essential for various scientific domains but computationally expensive. Learning-based force fields have made significant progress in accelerating ab-initio MD simulation but are not fast enough for many real-world applications due to slow inference for large systems and small time steps (femtosecond-level). We aim to address these challenges by learning a multi-scale graph neural network that directly simulates coarse-grained MD with a very large time step (nanosecond-level) and a novel refinement module based on diffusion models to mitigate simulation instability. The effectiveness of our method is demonstrated in two complex systems: single-chain coarse-grained polymers and multi-component Li-ion polymer electrolytes. For evaluation, we simulate trajectories much longer than the training trajectories for systems with different chemical compositions that the model is not trained on. Structural and dynamical properties can be accurately recovered at several orders of magnitude higher speed than classical force fields by getting out of the femtosecond regime.