References Kim, Y.: Convolutional neural networks for sentence classification. arXiv preprint arXiv:1408.5882 (2014) Yang, Z., et al.: Hierarchical attention networks for document classification. In: Proceedings of the 2016 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, 1480–1489 (2016) Devlin, J., Chang, M.-W., Lee, K., & Toutanova, K. Bert:
Machine learning the entropy to estimate free energy differences without sampling transitions – npj Computational Materials
References
-
Frenkel, D. & Smit, B. Understanding molecular simulation: from algorithms to applications (Elsevier, 2023).
-
Barducci, A., Bussi, G. & Parrinello, M. Well-tempered metadynamics: a smoothly converging and tunable free-energy method. Phys. Rev. Lett. 100, 020603 (2008).
Google Scholar
-
Barducci, A., Bonomi, M. & Parrinello, M. Metadynamics. Wiley Interdiscip. Rev.: Computational Mol. Sci. 1, 826–843 (2011).
Google Scholar
-
Valsson, O., Tiwary, P. & Parrinello, M. Enhancing important fluctuations: Rare events and metadynamics from a conceptual viewpoint. Annu. Rev. Phys. Chem. 67, 159–184 (2016).
Google Scholar
-
Sutto, L., Marsili, S. & Gervasio, F. L. New advances in metadynamics. Wiley Interdiscip. Rev.: Computational Mol. Sci. 2, 771–779 (2012).
Google Scholar
-
Bussi, G. & Laio, A. Using metadynamics to explore complex free-energy landscapes. Nat. Rev. Phys. 2, 200–212 (2020).
Google Scholar
-
Kästner, J. Umbrella sampling. Wiley Interdiscip. Rev.: Computational Mol. Sci. 1, 932–942 (2011).
Google Scholar
-
Torrie, G. M. & Valleau, J. P. Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling. J. Computational Phys. 23, 187–199 (1977).
-
Miao, Y., Feher, V. A. & McCammon, J. A. Gaussian accelerated molecular dynamics: unconstrained enhanced sampling and free energy calculation. J. Chem. Theory Comput. 11, 3584–3595 (2015).
-
Invernizzi, M. & Parrinello, M. Rethinking metadynamics: from bias potentials to probability distributions. J. Phys. Chem. Lett. 11, 2731–2736 (2020).
Google Scholar
-
Invernizzi, M., Piaggi, P. M. & Parrinello, M. Unified approach to enhanced sampling. Phys. Rev. X 10, 041034 (2020).
Google Scholar
-
Invernizzi, M. & Parrinello, M. Exploration vs convergence speed in adaptive-bias enhanced sampling. J. Chem. Theory Comput. 18, 3988–3996 (2022).
Google Scholar
-
Invernizzi, M. OPES: On-the-fly probability enhanced sampling method. Nuovo Cimento della Societa Italiana di Fisica C44 (2021). 2101.06991.
-
Rogal, J., Schneider, E. & Tuckerman, M. E. Neural-network-based path collective variables for enhanced sampling of phase transformations. Phys. Rev. Lett. 123, 245701 (2019).
Google Scholar
-
Callen, H. B. Thermodynamics and an introduction to thermostatistics. John Wiley & Sons 2 (1980).
-
Lin, S.-T., Maiti, P. K. & Goddard III, W. A. Two-phase thermodynamic model for efficient and accurate absolute entropy of water from molecular dynamics simulations. J. Phys. Chem. B 114, 8191–8198 (2010).
Google Scholar
-
Desjarlais, M. P. First-principles calculation of entropy for liquid metals. Phys. Rev. E 88, 062145 (2013).
Google Scholar
-
Avinery, R., Kornreich, M. & Beck, R. Universal and accessible entropy estimation using a compression algorithm. Phys. Rev. Lett. 123, 178102 (2019).
Google Scholar
-
Martiniani, S., Chaikin, P. M. & Levine, D. Quantifying hidden order out of equilibrium. Phys. Rev. X 9, 011031 (2019).
Google Scholar
-
Liu, T. & Simine, L. Deltagzip: Computing biopolymer–ligand binding affinity via Kolmogorov complexity and lossless compression. J. Chem. Inf. Modeling 64, 5617–5623 (2024).
Google Scholar
-
Zu, M., Bupathy, A., Frenkel, D. & Sastry, S. Information density, structure and entropy in equilibrium and non-equilibrium systems. J. Stat. Mech.: Theory Exp. 2020, 023204 (2020).
Google Scholar
-
Sorkin, B., Be’er, A., Diamant, H. & Ariel, G. Detecting and characterizing phase transitions in active matter using entropy. Soft Matter 19, 5118–5126 (2023).
Google Scholar
-
Sorkin, B., Ricouvier, J., Diamant, H. & Ariel, G. Resolving entropy contributions in nonequilibrium transitions. Phys. Rev. E 107, 014138 (2023).
Google Scholar
-
Gelman, S. D. & Cohen, G. Nonequilibrium entropy from density estimation. arXiv preprint arXiv:2405.04877 (2024).
-
Noé, F., Olsson, S., Köhler, J. & Wu, H. Boltzmann generators: Sampling equilibrium states of many-body systems with deep learning. Science 365, eaaw1147 (2019).
Google Scholar
-
Schebek, M., Invernizzi, M., Noé, F. & Rogal, J. Efficient mapping of phase diagrams with conditional Boltzmann generators. Mach. Learn.: Sci. Technol. 5, 045045 (2024).
Google Scholar
-
Schebek, M., Noé, F. & Rogal, J. Scalable Boltzmann generators for equilibrium sampling of large-scale materials. arXiv preprint arXiv:2509.25486 (2025).
-
Petersen, M., Roig, G. & Covino, R. Dynamicsdiffusion: Generating and rare event sampling of molecular dynamic trajectories using diffusion models. In NeurIPS 2023 AI for Science Workshop (2023). https://openreview.net/forum?id=pwYCCq4xAf.
-
Klein, & Noé, F. Transferable boltzmann generators. Adv. Neural Inf. Process. Syst. 37, 45281 (2024).
-
Nir, A., Sela, E., Beck, R. & Bar-Sinai, Y. Machine-learning iterative calculation of entropy for physical systems. Proc. Natl. Acad. Sci. 117, 30234–30240 (2020).
Google Scholar
-
Belghazi, M. I. et al. Mutual information neural estimation. In International conference on machine learning, 531–540 (PMLR, 2018).
-
Donsker, M. D. & Varadhan, S. S. Asymptotic evaluation of certain Markov process expectations for large time, I. Commun. pure Appl. Math. 28, 1–47 (1975).
Google Scholar
-
Choi, K. & Lee, S. Combating the instability of mutual information-based losses via regularization. In Uncertainty in Artificial Intelligence, 411–421 (PMLR, 2022).
-
Wolf, M. M., Verstraete, F., Hastings, M. B. & Cirac, J. I. Area laws in quantum systems: mutual information and correlations. Phys. Rev. Lett. 100, 070502 (2008).
Google Scholar
-
Piaggi, P. M., Valsson, O. & Parrinello, M. Enhancing entropy and enthalpy fluctuations to drive crystallization in atomistic simulations. Phys. Rev. Lett. 119, 015701 (2017).
Google Scholar
-
Batzner, S. et al. E (3)-equivariant graph neural networks for data-efficient and accurate interatomic potentials. Nat. Commun. 13, 2453 (2022).
Google Scholar
-
Satorras, V. G., Hoogeboom, E. & Welling, M. E (n) equivariant graph neural networks. In International conference on machine learning, 9323–9332 (PMLR, 2021).
-
Gasteiger, J, Groß, J. & Günnemann, S. In International Conference on Learning Representations (2020).
-
Thompson, A. P. et al. LAMMPS-a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. Computer Phys. Commun. 271, 108171 (2022).
-
Bonomi, M. et al. Plumed: A portable plugin for free-energy calculations with molecular dynamics. Computer Phys. Commun. 180, 1961–1972 (2009).
Google Scholar
-
Promoting transparency and reproducibility in enhanced molecular simulations. Nat. Methods 16, 670–673 (2019).
-
Tribello, G. A., Bonomi, M., Branduardi, D., Camilloni, C. & Bussi, G. Plumed 2: New feathers for an old bird. Computer Phys. Commun. 185, 604–613 (2014).
Google Scholar
-
Wilson, S. R., Gunawardana, K. G. S. H. & Mendelev, M. I. J Chem. Phys. 142, 134705 (2015).
-
Mendelev, M., Kramer, M., Becker, C. A. & Asta, M. Analysis of semi-empirical interatomic potentials appropriate for simulation of crystalline and liquid Al and Cu. Philos. Mag. 88, 1723–1750 (2008).
Google Scholar
-
Bussi, G., Donadio, D. & Parrinello, M. J chem. phys. 126, https://doi.org/10.1063/1.2408420 (2007).
-
Parrinello, M. & Rahman, A. Polymorphic transitions in single crystals: A new molecular dynamics method. J. Appl. Phys. 52, 7182–7190 (1981).
Google Scholar
-
Srivastava, N., Hinton, G., Krizhevsky, A., Sutskever, I. & Salakhutdinov, R. Dropout: A simple way to prevent neural networks from overfitting. J. Mach. Learn. Res. 15, 1929–1958 (2014).
Google Scholar
-
Glorot, X. & Bengio, Y. Understanding the difficulty of training deep feedforward neural networks. In Proceedings of the thirteenth international conference on artificial intelligence and statistics, 249–256 (JMLR Workshop and Conference Proceedings, 2010).
-
Kingma, D. P. & Ba, J. In International Conference on Learning Representations (ICLR) (2015).
-
Ben Shimon, Y., Bar-Sinai, Y. & Hirshberg, B. mice-free-energy. https://github.com/ybs-lab/mice-free-energy (2025). GitHub repository.
Download references
