I was unsure if my parents would notice that the voice on the other end wasn’t mine — or that it was mine, sort of, but it wasn’t me. The voice said hello, asked my dad how he was doing, and asked again when he didn’t respond quickly enough. “What is that, Gaby?” He realized
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
