Xianbin Liu

Yang Li, Shenglan Yuan, Linghongzhi Lu et al.

In this paper, we present large deviation theory that characterizes the exponential estimate for rare events of stochastic dynamical systems in the limit of weak noise. We aim to consider next-to-leading-order approximation for more accurate calculation of mean exit time via computing large deviation prefactors with the research efforts of machine learning. More specifically, we design a neural network framework to compute quasipotential, most probable paths and prefactors based on the orthogonal decomposition of vector field. We corroborate the higher effectiveness and accuracy of our algorithm with a practical example. Numerical experiments demonstrate its powerful function in exploring internal mechanism of rare events triggered by weak random fluctuations.

Kaipeng Zeng, Xianbin Liu, Yu Zhang et al.

Organic synthesis stands as a cornerstone of the chemical industry. The development of robust machine learning models to support tasks associated with organic reactions is of significant interest. However, current methods rely on hand-crafted features or direct adaptations of model architectures from other domains, which lack feasibility as data scales increase or ignore the rich chemical information inherent in reactions. To address these issues, this paper introduces RAlign, a novel chemical reaction representation learning model for various organic reaction-related tasks. By integrating atomic correspondence between reactants and products, our model discerns the molecular transformations that occur during the reaction, thereby enhancing comprehension of the reaction mechanism. We have designed an adapter structure to incorporate reaction conditions into the chemical reaction representation, allowing the model to handle various reaction conditions and to adapt to various datasets and downstream tasks. Additionally, we introduce a reaction-center-aware attention mechanism that enables the model to concentrate on key functional groups, thereby generating potent representations for chemical reactions. Our model has been evaluated on a range of downstream tasks. Experimental results indicate that our model markedly outperforms existing chemical reaction representation learning architectures on most of the datasets. We plan to open-source the code contingent upon the acceptance of the paper.

Yang Li, Jinqiao Duan, Xianbin Liu

The emergence of transition phenomena between metastable states induced by noise plays a fundamental role in a broad range of nonlinear systems. The computation of the most probable paths is a key issue to understand the mechanism of transition behaviors. Shooting method is a common technique for this purpose to solve the Euler-Lagrange equation for the associated action functional, while losing its efficacy in high-dimensional systems. In the present work, we develop a machine learning framework to compute the most probable paths in the sense of Onsager-Machlup action functional theory. Specifically, we reformulate the boundary value problem of Hamiltonian system and design a neural network to remedy the shortcomings of shooting method. The successful applications of our algorithms to several prototypical examples demonstrate its efficacy and accuracy for stochastic systems with both (Gaussian) Brownian noise and (non-Gaussian) Lévy noise. This novel approach is effective in exploring the internal mechanisms of rare events triggered by random fluctuations in various scientific fields.