Deep learning is changing many areas in molecular physics, and it has shown great potential to deliver new solutions to challenging molecular modeling problems. Along with this trend arises the increasing demand of expressive and versatile neural network architectures which are compatible with molecular systems. A new deep neural network architecture, Molecular Configuration Transformer (Molecular CT), is introduced for this purpose. Molecular CT is composed of a relation-aware encoder module and a computationally universal geometry learning unit, thus able to account for the relational constraints between particles meanwhile scalable to different particle numbers and invariant with respect to the trans-rotational transforms. The computational efficiency and universality make Molecular CT versatile for a variety of molecular learning scenarios and especially appealing for transferable representation learning across different molecular systems. As examples, we show that Molecular CT enables representational learning for molecular systems at different scales, and achieves comparable or improved results on common benchmarks using a more light-weighted structure compared to baseline models.

The swift progression of machine learning (ML) has not gone unnoticed in the realm of statistical mechanics. ML techniques have attracted attention by the classical density-functional theory (DFT) community, as they enable discovery of free-energy functionals to determine the equilibrium-density profile of a many-particle system. Within DFT, the external potential accounts for the interaction of the many-particle system with an external field, thus, affecting the density distribution. In this context, we introduce a statistical-learning framework to infer the external potential exerted on a many-particle system. We combine a Bayesian inference approach with the classical DFT apparatus to reconstruct the external potential, yielding a probabilistic description of the external potential functional form with inherent uncertainty quantification. Our framework is exemplified with a grand-canonical one-dimensional particle ensemble with excluded volume interactions in a confined geometry. The required training dataset is generated using a Monte Carlo (MC) simulation where the external potential is applied to the grand-canonical ensemble. The resulting particle coordinates from the MC simulation are fed into the learning framework to uncover the external potential. This eventually allows us to compute the equilibrium density profile of the system by using the tools of DFT. Our approach benchmarks the inferred density against the exact one calculated through the DFT formulation with the true external potential. The proposed Bayesian procedure accurately infers the external potential and the density profile. We also highlight the external-potential uncertainty quantification conditioned on the amount of available simulated data. The seemingly simple case study introduced in this work might serve as a prototype for studying a wide variety of applications, including adsorption and capillarity.

This white paper was prepared by the participants of the fall 2016 long program Understanding Many-Particle Systems with Machine Learning. Interactions between many constituent particles, i.e. quarks, electrons, atoms, molecules, or materials, generally give rise to collective or emergent phenomena in matter. Even when the interactions between the particles are well defined and the governing equations of the system are understood, the collective behavior of the system as a whole does not trivially emerge from these equations. Despite many decades of prominent work on interacting many-particle (MP) systems, the problem of N interacting particles is not exactly soluble. In fact, computational complexity typically increases exponentially with N.