Learning QM/MM potential using equivariant multiscale model.

The machine learning (ML) method emerges as an efficient and precise surrogate model for high-level electronic structure theory. Its application has been limited to closed chemical systems without considering external potentials from the surrounding environment. To address this limitation and incorporate the influence of external potentials, polarization effects, and long-range interactions between a chemical system and its environment, the first two terms of the Taylor expansion of an electrostatic operator have been used as extra input to the existing ML model to represent the electrostatic environments. However, high-order electrostatic interaction is often essential to account for external potentials from the environment. The existing models based only on invariant features cannot capture significant distribution patterns of the external potentials. Here, we propose a novel ML model that includes high-order terms of the Taylor expansion of an electrostatic operator and uses an equivariant model, which can generate a high-order tensor covariant with rotations as a base model. Therefore, we can use the multipole-expansion equation to derive a useful representation by accounting for polarization and intermolecular interaction. Moreover, to deal with long-range interactions, we follow the same strategy adopted to derive long-range interactions between a target system and its environment media. Our model achieves higher prediction accuracy and transferability among various environment media with these modifications.

Deep reinforcement learning of transition states.

Combining reinforcement learning (RL) and molecular dynamics (MD) simulations, we propose a machine-learning approach, called RL‡, to automatically unravel chemical reaction mechanisms. In RL‡, locating the transition state of a chemical reaction is formulated as a game, and two functions are optimized, one for value estimation and the other for policy making, to iteratively improve our chance of winning this game. Both functions can be approximated by deep neural networks. By virtue of RL‡, one can directly interpret the reaction mechanism according to the value function. Meanwhile, the policy function allows efficient sampling of the transition path ensemble, which can be further used to analyze reaction dynamics and kinetics. Through multiple experiments, we show that RL‡ can be trained tabula rasa hence allowing us to reveal chemical reaction mechanisms with minimal subjective biases.

A Perspective on Deep Learning for Molecular Modeling and Simulations.

Deep learning is transforming many areas in science, and it has great potential in modeling molecular systems. However, unlike the mature deployment of deep learning in computer vision and natural language processing, its development in molecular modeling and simulations is still at an early stage, largely because the inductive biases of molecules are completely different from those of images or texts. Footed on these differences, we first reviewed the limitations of traditional deep learning models from the perspective of molecular physics and wrapped up some relevant technical advancement at the interface between molecular modeling and deep learning. We do not focus merely on the ever more complex neural network models; instead, we introduce various useful concepts and ideas brought by modern deep learning. We hope that transacting these ideas into molecular modeling will create new opportunities. For this purpose, we summarized several representative applications, ranging from supervised to unsupervised and reinforcement learning, and discussed their connections with the emerging trends in deep learning. Finally, we give an outlook for promising directions which may help address the existing issues in the current framework of deep molecular modeling.

Deep learning for variational multiscale molecular modeling.

Molecular simulations are widely applied in the study of chemical and bio-physical problems. However, the accessible timescales of atomistic simulations are limited, and extracting equilibrium properties of systems containing rare events remains challenging. Two distinct strategies are usually adopted in this regard: either sticking to the atomistic level and performing enhanced sampling or trading details for speed by leveraging coarse-grained models. Although both strategies are promising, either of them, if adopted individually, exhibits severe limitations. In this paper, we propose a machine-learning approach to ally both strategies so that simulations on different scales can benefit mutually from their crosstalks: Accurate coarse-grained (CG) models can be inferred from the fine-grained (FG) simulations through deep generative learning; in turn, FG simulations can be boosted by the guidance of CG models via deep reinforcement learning. Our method defines a variational and adaptive training objective, which allows end-to-end training of parametric molecular models using deep neural networks. Through multiple experiments, we show that our method is efficient and flexible and performs well on challenging chemical and bio-molecular systems.

Locating Transition Zone in Phase Space.

Understanding the reaction mechanism is required for better control of chemical reactions and is usually achieved by locating transition states (TSs) along a proper one-dimensional coordinate called reaction coordinate (RC). The identification of RC can be very difficult for high-dimensional realistic systems. A number of methods have been proposed to tackle this problem. A machine learning method is developed here to incorporate the influence of velocity on the reaction process. The method is also free of the unbalanced label problem resulting from the rather low fraction of configurations near the TS and can be easily extended to large systems. It locates the transition zone in the phase space and defines the dividing surface with a high transmission coefficient. Moreover, considering that the reaction environment can not only change the reaction path but also activate the reactive mode through energy transfer, we devise two measures to quantify the influence of these two factors on the reaction process and find that solvents can assist the reaction by directly doing work along the reactive mode. Not surprisingly, there is a positive correlation between the efficiency of energy transfer into the reactive mode and the reaction rate.

Phase Transition between Crystalline Variants of Ordinary Ice.

Water is one of the most abundant molecules on Earth. However, this common and "simple" material has more than 18 different phases, which poses a great challenge to theoretically study the nature of water and ice. We designed two reaction coordinates that can distinguish between water and various ice states and used them to efficiently sample all possible states of the system in all-atom molecular dynamics simulation at ambient temperature and pressure. Various structural and thermodynamics properties, including the water-ice phase diagrams, can thus be calculated. We also present a simple model that successfully explains the thermodynamic stability of different ice states. Our work provides effective methods and data for theoretical studies of different phases of water and ice.

Dynamic Electric Field Complicates Chemical Reactions in Solutions.

Chemical reactions can be strongly influenced by an external electric field (EEF), but because the EEF is often time-dependent and in case it does not adapt quickly enough to the reaction progress, especially during fast barrier crossing processes, dynamic effects could be important. Here we find that electrostatic interactions can reduce the height of the reaction barrier for a Claissen rearrangement reaction and accelerate the key motions for bonding. Meanwhile, strong electrostatic interactions can modify the barrier into an effective potential well, confining the system into the barrier until solvents adjust themselves to provide an appropriate EEF for charge redistribution. In this case, the otherwise concerted mechanism becomes a stepwise one. Consequently, the motion of solvents modulates the reaction dynamics and leads to heterogeneous reaction paths, even in a seemingly homogeneous aqueous solution. In addition, an excessive stabilization of transition state retards the barrier crossing process, making the thermodynamically favorable pathway less favored dynamically.

Deep Representation Learning for Complex Free-Energy Landscapes.

In this Letter, we analyzed the inductive bias underlying complex free-energy landscapes (FELs) and exploited it to train deep neural networks that yield reduced and clustered representation for the FEL. Our parametric method, called information distilling of metastability (IDM), is end-to-end differentiable and thus scalable to ultralarge data sets. IDM is able to perform clustering in the meantime of reducing the dimensionality. Besides, as an unsupervised learning method, IDM differs from many existing dimensionality reduction and clustering methods in that it requires neither a cherry-picked distance metric nor the ground-true number of clusters defined a priori, and it can be used to unroll and zoom in on the hierarchical FEL with respect to different time scales. Through multiple experiments, we show that IDM can achieve physically meaningful representations that partition the FEL into well-defined metastable states that hence are amenable for downstream tasks such as mechanism analysis and kinetic modeling.