Flow matching for accelerated simulation of atomic transport in crystalline materials

Balluffi, R. W., Allen, S. M. & Carter, W. C. Kinetics of Materials (John Wiley & Sons, 2005).
Yip, S. Molecular Mechanisms in Materials: Insights from Atomistic Modeling and Simulation (MIT Press, 2023).
Bachman, J. C. et al. Inorganic solid-state electrolytes for lithium batteries: mechanisms and properties governing ion conduction. Chem. Rev. 116, 140–162 (2016).
Google Scholar
Friederich, P., Häse, F., Proppe, J. & Aspuru-Guzik, A. Machine-learned potentials for next-generation matter simulations. Nat. Mater. 20, 750–761 (2021).
Google Scholar
Ko, T. W. & Ong, S. P. Recent advances and outstanding challenges for machine learning interatomic potentials. Nat. Comput. Sci. 3, 998–1000 (2023).
Google Scholar
Batatia, I. et al. A foundation model for atomistic materials chemistry. Preprint at https://doi.org/10.48550/arXiv.2401.00096 (2024).
Deng, B. et al. CHGNet as a pretrained universal neural network potential for charge-informed atomistic modelling. Nat. Mach. Intell. 5, 1031–1041 (2023).
Google Scholar
Deng, B. et al. Systematic softening in universal machine learning interatomic potentials. npj Comput. Mater. 11, 9 (2025).
Google Scholar
Fu, X. et al. Forces are not enough: benchmark and critical evaluation for machine learning force fields with molecular simulations. Trans. Mach. Learn. Res. 798 (2023).
Klein, L. et al. Timewarp: transferable acceleration of molecular dynamics by learning time-coarsened dynamics. Adv. Neural Inf. Process. Syst. 36, 52863–52883 (2023).
Schreiner, M., Winther, O. & Olsson, S. Implicit transfer operator learning: multiple time-resolution models for molecular dynamics. Adv. Neural Inf. Process. Syst. 36, 36449–36462 (2023).
Hsu, T., Sadigh, B., Bulatov, V. & Zhou, F. Score dynamics: scaling molecular dynamics with picoseconds time steps via conditional diffusion model. J. Chem. Theory Comput. 20, 2335 (2024).
Google Scholar
Li, S. et al. F3low: frame-to-frame coarse-grained molecular dynamics with SE(3) guided flow matching. Preprint at https://doi.org/10.48550/arXiv.2405.00751 (2024).
Yu, Z., Huang, W. & Liu, Y. Force-guided bridge matching for full-atom time-coarsened dynamics of peptides. Preprint at https://doi.org/10.48550/arXiv.2408.15126 (2024).
Arts, M. et al. Two for one: diffusion models and force fields for coarse-grained molecular dynamics. J. Chem. Theory Comput. 19, 6151–6159 (2023).
Google Scholar
Fu, X., Xie, T., Rebello, N. J., Olsen, B. & Jaakkola, T. S. Simulate time-integrated coarse-grained molecular dynamics with multi-scale graph networks. Trans. Mach. Learn. Res. 1110 (2023).
Ashcroft, N. & Mermin, N. D. Solid State Physics (Saunders College Publishing, 1976).
Schütt, K. et al. SchNet: a continuous-filter convolutional neural network for modeling quantum interactions. Adv. Neural Inf. Process. Syst. 30, 992–1002 (2017).
Marx, D. & Hutter, J. Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods (Cambridge Univ. Press, 2009).
von Bülow, S., Bullerjahn, J. T. & Hummer, G. Systematic errors in diffusion coefficients from long-time molecular dynamics simulations at constant pressure. J. Chem. Phys. 153, 021101 (2020).
Google Scholar
Lipman, Y., Chen, R. T. Q., Ben-Hamu, H., Nickel, M. & Le, M. Flow matching for generative modeling. In Eleventh International Conference on Learning Representations (ICLR, 2023).
Köhler, J., Klein, L. & Noé, F. Equivariant flows: exact likelihood generative learning for symmetric densities. In 37th International Conference on Machine Learning 5361–5370 (PMLR, 2020).
Klein, L., Krämer, A. & Noé, F. Equivariant flow matching. Adv. Neural Inf. Process. Syst. 36, 36725–36744 (2023).
Schütt, K., Unke, O. & Gastegger, M. Equivariant message passing for the prediction of tensorial properties and molecular spectra. In 38th International Conference on Machine Learning 9377–9388 (PMLR, 2021).
Sanchez-Gonzalez, A. et al. Learning to simulate complex physics with graph networks. In 37th International Conference on Machine Learning 8459–8468 (PMLR, 2020).
Neumann, M. et al. Orb: a fast, scalable neural network potential. Preprint at https://doi.org/10.48550/arXiv.2410.22570 (2024).
Lee, S.-G. et al. PriorGrad: improving conditional denoising diffusion models with data-dependent adaptive prior. In International Conference on Learning Representations (ICLR, 2022).
Guan, J. et al. DecompDiff: diffusion models with decomposed priors for structure-based drug design. In 40th International Conference on Machine Learning 11827–11846 (PMLR, 2023).
Jing, B. et al. EigenFold: generative protein structure prediction with diffusion models. Preprint at https://doi.org/10.48550/arXiv.2304.02198 (2023).
Irwin, R., Tibo, A., Janet, J. P. & Olsson, S. SemlaFlow — Efficient 3D Molecular Generation with Latent Attention and Equivariant Flow Matching. In 28th International Conference on Artificial Intelligence and Statistics (AISTATS, 2025).
Pooladian, A.-A. et al. Multisample flow matching: straightening flows with minibatch couplings. In 40th International Conference on Machine Learning 28100–28127 (PMLR, 2023).
Jain, A. et al. Commentary: The Materials Project: a materials genome approach to accelerating materials innovation. APL Mater. 1, 011002 (2013).
Google Scholar
Jun, K., Lee, B., Kam, R. L. & Ceder, G. The nonexistence of a paddlewheel effect in superionic conductors. Proc. Natl Acad. Sci. USA 121, e2316493121 (2024).
Google Scholar
Kimura, T. et al. Stabilizing high-temperature α-Li3PS4 by rapidly heating the glass. J. Am. Chem. Soc. 145, 14466–14474 (2023).
Google Scholar
Lee, B., Jun, K., Ouyang, B. & Ceder, G. Weak correlation between the polyanion environment and ionic conductivity in amorphous Li–P–S superionic conductors. Chem. Mater. 35, 891–899 (2023).
Google Scholar
Kamaya, N. et al. A lithium superionic conductor. Nat. Mater. 10, 682–686 (2011).
Google Scholar
López, C., Rurali, R. & Cazorla, C. How concerted are ionic hops in inorganic solid-state electrolytes? J. Am. Chem. Soc. 146, 8269–8279 (2024).
Google Scholar
Winter, G. & Gómez-Bombarelli, R. Simulations with machine learning potentials identify the ion conduction mechanism mediating non-Arrhenius behavior in LGPS. J. Phys.: Energy 5, 024004 (2023).
Tiwary, P. & Parrinello, M. From metadynamics to dynamics. Phys. Rev. Lett. 111, 230602 (2013).
Google Scholar
Bonati, L., Piccini, G. & Parrinello, M. Deep learning the slow modes for rare events sampling. Proc. Natl Acad. Sci. USA 118, e2113533118 (2021).
Google Scholar
Tiwary, P. et al. Generative artificial intelligence for computational chemistry: a roadmap to predicting emergent phenomena. Preprint at https://doi.org/10.48550/arXiv.2409.03118 (2024).
Dibak, M., Klein, L., Krämer, A. & Noé, F. Temperature steerable flows and Boltzmann generators. Phys. Rev. Res. 4, L042005 (2022).
Google Scholar
Herron, L., Mondal, K., Schneekloth, J. S. & Tiwary, P. Inferring phase transitions and critical exponents from limited observations with thermodynamic maps. Proc. Natl Acad. Sci. USA 121, e2321971121 (2024).
Google Scholar
Diez, J. V., Schreiner, M. J., Engkvist, O. & Olsson, S. Boltzmann priors for implicit transfer operators. In International Conference on Learning Representations (ICLR, 2025).
Mardt, A., Pasquali, L., Noé, F. & Wu, H. Deep learning Markov and Koopman models with physical constraints. In Proc. The First Mathematical and Scientific Machine Learning Conference 451–475 (PMLR, 2020).
Falletta, S. et al. Unified differentiable learning of electric response. Nat. Commun. 16, 4031 (2025).
Google Scholar
Imbalzano, G. et al. Uncertainty estimation for molecular dynamics and sampling. J. Chem. Phys. 154, 074102 (2021).
Google Scholar
Tan, A. R., Urata, S., Goldman, S., Dietschreit, J. C. & Gómez-Bombarelli, R. Single-model uncertainty quantification in neural network potentials does not consistently outperform model ensembles. npj Comput. Mater. 9, 225 (2023).
Google Scholar
Meng, X. & Karniadakis, G. E. A composite neural network that learns from multi-fidelity data: application to function approximation and inverse PDE problems. J. Comput. Phys. 401, 109020 (2020).
Google Scholar
Maginn, E. J., Messerly, R. A., Carlson, D. J., Roe, D. R. & Elliot, J. R. Best practices for computing transport properties: 1.Self-diffusivity and viscosity from equilibrium molecular dynamics [article v1.0. Living J. Comput. Mol. 1, 6324 (2018).
Xie, T., Fu, X., Ganea, O.-E., Barzilay, R. & Jaakkola, T. S. Crystal diffusion variational autoencoder for periodic material generation. In International Conference on Learning Representations (ICLR, 2022).
Jiao, R. et al. Crystal structure prediction by joint equivariant diffusion. Adv. Neural Inf. Process. Syst. 36, 17464–17497 (2023).
AI4Science, M. et al. Crystal-GFN: sampling crystals with desirable properties and constraints. Preprint at https://doi.org/10.48550/arXiv.2310.04925 (2023).
Zeni, C. et al. A generative model for inorganic materials design. Nature 639, 624–632 (2025).
Google Scholar
Yang, S. et al. Scalable diffusion for materials generation. In The Twelfth International Conference on Learning Representations (ICLR, 2024).
Miller, B. K., Chen, R. T. Q., Sriram, A. & Wood, B. M. FlowMM: generating materials with Riemannian flow matching. In Proc. 41st International Conference on Machine Learning 35664–35686 (PMLR, 2024).
He, X., Zhu, Y., Epstein, A. & Mo, Y. Statistical variances of diffusional properties from ab initio molecular dynamics simulations. npj Comput. Mater. 4, 18 (2018).
Google Scholar
Nosé, S. A unified formulation of the constant temperature molecular dynamics methods. J. Chem. Phys. 81, 511–519 (1984).
Google Scholar
Hoover, W. G. Canonical dynamics: equilibrium phase-space distributions. Phys. Rev. A 31, 1695 (1985).
Google Scholar
Larsen, A. H. et al. The atomic simulation environment—a Python library for working with atoms. J. Phys.: Condens. Matter 29, 273002 (2017).
Basconi, J. E. & Shirts, M. R. Effects of temperature control algorithms on transport properties and kinetics in molecular dynamics simulations. J. Chem. Theory Comput. 9, 2887–2899 (2013).
Google Scholar
Riebesell, J., Yang, H., Goodall, R. & Baird, S. G. Pymatviz: visualization toolkit for materials informatics. GitHub https://github.com/janosh/pymatviz (2022).
Paszke, A. et al. PyTorch: an imperative style, high-performance deep learning library. Adv. Neural Inf. Process. Syst. 32, 8026–8037 (2019).
Fey, M. & Lenssen, J. E. Fast graph representation learning with PyTorch Geometric. Preprint at https://doi.org/10.48550/arXiv.1903.02428 (2019).
McCluskey, A. R., Squires, A. G., Dunn, J., Coles, S. W. & Morgan, B. J. kinisi: Bayesian analysis of mass transport from molecular dynamics simulations. J. Open Source Softw. 9, 5984 (2024).
Google Scholar
Hafner, J. Ab-initio simulations of materials using VASP: density-functional theory and beyond. J. Comput. Chem. 29, 2044–2078 (2008).
Google Scholar
McCluskey, A. R., Coles, S. W. & Morgan, B. J. Accurate estimation of diffusion coefficients and their uncertainties from computer simulation. J. Chem. Theory Comput. 21, 79–87 (2025).
Google Scholar
Nam, J. Data for: flow matching for accelerated simulation of atomic transport in materials. Zenodo https://doi.org/10.5281/zenodo.14889658 (2025).
Nam, J. learningmatter-mit/liflow: initial release. GitHub https://github.com/learningmatter-mit/liflow (2025).
Don’t miss more hot News like this! Click here to discover the latest in AI news!
2025-10-16 00:00:00