Dresden 2020 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 15: Condensed-matter simulations augmented by advanced statistical methodologies (joint session DY/CPP)

DY 15.9: Talk

Monday, March 16, 2020, 17:45–18:00, HÜL 186

Variational autoencoders as a tool to learn collective variables from simulation snapshots — •Miriam Klopotek and Martin Oettel — Institut für Angewandte Phsyik, Eberhard Karls Universität Tübingen, Tübingen, Germany

Variational autoencoders (VAEs) are powerful neural-network architectures capable of learning abstract representations of data (distributions of latent variables) in an unsupervised fashion. We apply a standard formulation of VAEs [1,2] to equilibrium configurations obtained by grand canonical Monte Carlo simulations and formulate a probabilistic model for the VAE which shows that the latent variables are collective variables, and their variances are generalized susceptibilities. Upon application to a lattice model with sticky rods which shows competing gas, liquid and nematic phases we find that the leading collective variables are akin to the two order parameters of the model. Furthermore, the collective variables define coarse-grained configurations. Increasing the number of latent variables leads to finer spatial resolution of the coarse-grained configurations and increasingly preciser physical observables obtained from them. Finally, we discover there is an optimal hyperparameter β in so-called β-VAEs [3] where the collective variables become disentangled with respect to structural correlation length-scales: These disentangled collective variables hence form a hierarchy of different levels-of-detail.

[1] Kingma, D. P. & Welling, M. (2013). arXiv:1312.6114. [2] Rezende, D. J., Mohamed, S., & Wierstra, D. (2014). arXiv:1401.4082. [3] Higgins, I. et al. (2017). ICLR, 2(5), 6.