Xiaoyu Wang

Dongjin Kim, Xiaoyu Wang, Peichen Zhong et al.

Most current machine learning interatomic potentials (MLIPs) rely on short-range approximations, without explicit treatment of long-range electrostatics. To address this, we recently developed the Latent Ewald Summation (LES) method, which infers electrostatic interactions, polarization, and Born effective charges (BECs), just by learning from energy and force training data. Here, we present LES as a standalone library, compatible with any short-range MLIP, and demonstrate its integration with methods such as MACE, NequIP, CACE, and CHGNet. We benchmark LES-enhanced models on distinct systems, including bulk water, polar dipeptides, and gold dimer adsorption on defective substrates, and show that LES not only captures correct electrostatics but also improves accuracy. Additionally, we scale LES to large and chemically diverse data by training MACELES-OFF on the SPICE set containing molecules and clusters, making a universal MLIP with electrostatics for organic systems including biomolecules. MACELES-OFF is more accurate than its short-range counterpart (MACE-OFF) trained on the same dataset, predicts dipoles and BECs reliably, and has better descriptions of bulk liquids. By enabling efficient long-range electrostatics without directly training on electrical properties, LES paves the way for electrostatic foundation MLIPs.

Hengrong Du, Qi Feng, Changwei Tu et al.

We consider the constrained sampling problem where the goal is to sample from a target distribution on a constrained domain. We propose skew-reflected non-reversible Langevin dynamics (SRNLD), a continuous-time stochastic differential equation with skew-reflected boundary. We obtain non-asymptotic convergence rate of SRNLD to the target distribution in both total variation and 1-Wasserstein distances. By breaking reversibility, we show that the convergence is faster than the special case of the reversible dynamics. Based on the discretization of SRNLD, we propose skew-reflected non-reversible Langevin Monte Carlo (SRNLMC), and obtain non-asymptotic discretization error from SRNLD, and convergence guarantees to the target distribution in 1-Wasserstein distance. We show better performance guarantees than the projected Langevin Monte Carlo in the literature that is based on the reversible dynamics. Numerical experiments are provided for both synthetic and real datasets to show efficiency of the proposed algorithms.

Yingli Wang, Changwei Tu, Xiaoyu Wang et al.

The problem of sampling a target probability distribution on a constrained domain arises in many applications including machine learning. For constrained sampling, various Langevin algorithms such as projected Langevin Monte Carlo (PLMC) based on the discretization of reflected Langevin dynamics (RLD) and more generally skew-reflected non-reversible Langevin Monte Carlo (SRNLMC) based on the discretization of skew-reflected non-reversible Langevin dynamics (SRNLD) have been proposed and studied in the literature. This work focuses on the long-time behavior of SRNLD, where a skew-symmetric matrix is added to RLD. Although acceleration for SRNLD has been studied, it is not clear how one should design the skew-symmetric matrix in the dynamics to achieve good performance in practice. We establish a large deviation principle (LDP) for the empirical measure of SRNLD when the skew-symmetric matrix is chosen such that its product with the inward unit normal vector field on the boundary is zero. By explicitly characterizing the rate functions, we show that this choice of the skew-symmetric matrix accelerates the convergence to the target distribution compared to RLD and reduces the asymptotic variance. Numerical experiments for SRNLMC based on the proposed skew-symmetric matrix show superior performance, which validate the theoretical findings from the large deviations theory.