Abstract

Multiscale systems are ubiquitous in science and technology, but are notoriously challenging to simulate as short spatiotemporal scales must be appropriately linked to emergent bulk physics. When expensive high-dimensional dynamical systems are coarse-grained into low-dimensional models, the entropic loss of information leads to emergent physics which are dissipative, history-dependent, and stochastic. To machine learn coarse-grained dynamics from time-series observations of particle trajectories, we propose a framework using the metriplectic bracket formalism that preserves these properties by construction; most notably, the framework guarantees discrete notions of the first and second laws of thermodynamics, conservation of momentum, and a discrete fluctuation-dissipation balance crucial for capturing non-equilibrium statistics. We introduce the mathematical framework abstractly before specializing to a particle discretization. As labels are generally unavailable for entropic state variables, we introduce a novel self-supervised learning strategy to identify emergent structural variables. We validate the method on benchmark systems and demonstrate its utility on two challenging examples: (1) coarse-graining star polymers at challenging levels of coarse-graining while preserving non-equilibrium statistics, and (2) learning models from high-speed video of colloidal suspensions that capture coupling between local rearrangement events and emergent stochastic dynamics. We provide open-source implementations in both PyTorch and LAMMPS, enabling large-scale inference and extensibility to diverse particle-based systems.

For more information, please refer to the following:

• Hernandez, Quercus and Win, Max and O'Connor, Thomas C. and Arratia, Paulo E. and Trask, Nathaniel. "Data-driven particle dynamics: Structure-preserving coarse-graining for emergent behavior in non-equilibrium systems." Arxiv, under review (2025).

Setting it up

First, clone the project.

# clone project
git clone https://github.com/PIMILab/DataDrivenParticleDynamics.git
cd DataDrivenParticleDynamics

Then, install the needed dependencies. The code is implemented in Pytorch. Note that this has been tested using Python 3.11.

# install dependencies
pip install numpy scipy matplotlib pytorch torch-geometric tidynamics MDAnalysis

To download the datasets, you can use the following Googe Drive Link.

How to run the code

Test pretrained nets

The results of the paper (Ideal gas, Star Polymer 11, Star Polymer 51, Viscoelastic and Needle) can be reproduced with the following scripts, found in the executables/ folder.

bash executables/run_ideal_gas_test.sh
bash executables/run_star_polymer_11_test.sh
bash executables/run_star_polymer_51_test.sh
bash executables/run_viscoelastic_test.sh
bash executables/run_needle_test.sh

The data/ folder includes the database and the pretrained parameters of the networks. The resulting time evolution, correlation statistics of the state variables and GIF of the system is plotted and saved in a the outputs/ folder.

Train a custom net

You can run your own experiments for the toy sdpd dataset by setting custom parameters manually. The trained parameters and output plots are saved in the outputs/ folder.

e.g.
python main.py --dset_train 'self_diffusion' --train True --lr 1e-3 ...

General Arguments:

Argument	Description	Options
--train	Train mode	True, False
--gpu	Enable GPU acceleration	True, False

Dataset Arguments:

Argument	Description	Options
--dset_train	Training dataset	self_diffusion, shear_flow, taylor_green, star_polymer, viscoelastic, needle
--dset_test	Test dataset	self_diffusion, shear_flow, taylor_green, star_polymer, viscoelastic, needle
--dt	Time step	Default: 1.0
--h	Cutoff radius	Default: 0.2
--boxsize	Box size of PBCs	Default: 1.0

Network Arguments:

Argument	Description	Options
--n_hidden	Number of MLP hidden layers	Default: 2
--dim_hidden	Dimension of hidden layers	Default: 50
--m	Mass initial value	Default: 1.0
--k_B	Boltzmann constant initial value	Default: 1.0

Training Arguments:

Argument	Description	Options
--lr1	Learning rate networks	Default: 1e-2
--lr2	Learning rate parameters	Default: 1e-2
--batch_size	Training batch size	Default: 50
--shuffle	Shuffle train snapshots	True, False
--max_epoch	Maximum number of training epochs	Default: 3000
--miles	Learning rate scheduler milestones	Default: 1000 2000
--gamma	Learning rate scheduler decay	Default: 1e-1
--N_train	Number of training snapshots	Default: 300

LAMMPS Interface

To use the trained Pytorch model for SDPD simulations in LAMMPS program please refer to its own Github repository.

Citation

If you found this code useful please cite our work as:

@article{hernandez2025data,
  title={Data-driven particle dynamics: Structure-preserving coarse-graining for emergent behavior in non-equilibrium systems},
  author={Hernandez, Quercus and Win, Max and O'Connor, Thomas C and Arratia, Paulo E and Trask, Nathaniel},
  journal={arXiv preprint arXiv:2508.12569},
  year={2025}
}