# Flow Matching for Accelerated Simulation of Atomic Transport in Crystalline Materials

arXiv: https://arxiv.org/abs/2410.01464 · HTML: https://mlsanity.com/paper/2410.01464/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 72 references that are in the map.
- First posted on arXiv 2 Oct 2024.

## Builds on (most cited first, 27 of 27)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Multisample Flow Matching: Straightening Flows with Minibatch Couplings](https://mlsanity.com/paper/2304.14772/) (2023)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densities](https://mlsanity.com/paper/2006.02425/) (2020)
- [Crystal Structure Prediction by Joint Equivariant Diffusion](https://mlsanity.com/paper/2309.04475/) (2023)
- [Equivariant flow matching](https://mlsanity.com/paper/2306.15030/) (2023)
- [FlowMM: Generating Materials with Riemannian Flow Matching](https://mlsanity.com/paper/2406.04713/) (2024)
- [Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulations](https://mlsanity.com/paper/2210.07237/) (2022)
- [DecompDiff: Diffusion Models with Decomposed Priors for Structure-Based Drug Design](https://mlsanity.com/paper/2403.07902/) (2024)
- [PriorGrad: Improving Conditional Denoising Diffusion Models with Data-Dependent Adaptive Prior](https://mlsanity.com/paper/2106.06406/) (2021)
- [Two for One: Diffusion Models and Force Fields for Coarse-Grained Molecular Dynamics](https://mlsanity.com/paper/2302.00600/) (2023)
- [Timewarp: Transferable Acceleration of Molecular Dynamics by Learning Time-Coarsened Dynamics](https://mlsanity.com/paper/2302.01170/) (2023)
- [EigenFold: Generative Protein Structure Prediction with Diffusion Models](https://mlsanity.com/paper/2304.02198/) (2023)
- [Scalable Diffusion for Materials Generation](https://mlsanity.com/paper/2311.09235/) (2023)
- [SemlaFlow -- Efficient 3D Molecular Generation with Latent Attention and Equivariant Flow Matching](https://mlsanity.com/paper/2406.07266/) (2024)
- [Crystal-GFN: sampling crystals with desirable properties and constraints](https://mlsanity.com/paper/2310.04925/) (2023)
- [Single-model uncertainty quantification in neural network potentials does not consistently outperform model ensembles](https://mlsanity.com/paper/2305.01754/) (2023)
- [Simulate Time-integrated Coarse-grained Molecular Dynamics with Multi-Scale Graph Networks](https://mlsanity.com/paper/2204.10348/) (2022)
- [Score dynamics: scaling molecular dynamics with picoseconds timestep via conditional diffusion model](https://mlsanity.com/paper/2310.01678/) (2023)
- [F3low: Frame-to-Frame Coarse-grained Molecular Dynamics with SE(3) Guided Flow Matching](https://mlsanity.com/paper/2405.00751/) (2024)
- [Force-Guided Bridge Matching for Full-Atom Time-Coarsened Dynamics of Peptides](https://mlsanity.com/paper/2408.15126/) (2024)
- [Generative artificial intelligence for computational chemistry: a roadmap to predicting emergent phenomena](https://mlsanity.com/paper/2409.03118/) (2024)

## Built on by (most cited first, 9 of 9)

- [Force-Free Molecular Dynamics Through Autoregressive Equivariant Networks](https://mlsanity.com/paper/2503.23794/) (2025)
- [OBELiX: A Curated Dataset of Crystal Structures and Experimentally Measured Ionic Conductivities for Lithium Solid-State Electrolytes](https://mlsanity.com/paper/2502.14234/) (2025)
- [Scaling Autoregressive Models for Lattice Thermodynamics](https://mlsanity.com/paper/2603.14695/) (2026)
- [Protein Language Model Embeddings Improve Generalization of Implicit Transfer Operators](https://mlsanity.com/paper/2602.11216/) (2026)
- [Accelerating Long-Term Molecular Dynamics with Physics-Informed Time-Series Forecasting](https://mlsanity.com/paper/2510.01206/) (2025)
- [Inference-Time Compute Scaling For Flow Matching](https://mlsanity.com/paper/2510.17786/) (2025)
- [Teaching Molecular Dynamics to a Non-Autoregressive Ionic Transport Predictor](https://mlsanity.com/paper/2605.09311/) (2026)
- [Stein Kernelized Molecular Dynamics for Active Learning of Interatomic Potentials](https://mlsanity.com/paper/2606.04100/) (2026)
- [FLARE: Flow Matching with Local Axis-Angle Representations for Stochastic Micromagnetic Evolution](https://mlsanity.com/paper/2609.34070/) (2026)

## Abstract (arXiv)

Atomic transport underpins the performance of materials in technologies such as energy storage and electronics, yet its simulation remains computationally demanding. In particular, modeling ionic diffusion in solid-state electrolytes (SSEs) requires methods that can overcome the scale limitations of traditional ab initio molecular dynamics (AIMD). We introduce LiFlow, a generative framework to accelerate MD simulations for crystalline materials that formulates the task as conditional generation of atomic displacements. The model uses flow matching, with a Propagator submodel to generate atomic displacements and a Corrector to locally correct unphysical geometries, and incorporates an adaptive prior based on the Maxwell-Boltzmann distribution to account for chemical and thermal conditions. We benchmark LiFlow on a dataset comprising 25-ps trajectories of lithium diffusion across 4,186 SSE candidates at four temperatures. The model obtains a consistent Spearman rank correlation of 0.7-0.8 for lithium mean squared displacement (MSD) predictions on unseen compositions. Furthermore, LiFlow generalizes from short training trajectories to larger supercells and longer simulations while maintaining high accuracy. With speed-ups of up to 600,000× compared to first-principles methods, LiFlow enables scalable simulations at significantly larger length and time scales.