用于 E(3) 等变机器学习粗粒化势的各向异性表示
Anisotropic representations for E(3)-equivariant machine learning coarse-grained potentials
AI总结：
研究旨在通过机器学习实现粗粒化势，提出新型各向异性表示，将原子核表示扩展为椭球状珠子，利用等变消息传递神经网络学习相关量，对比各向同性模型证明方向特征重要性，实现高效模拟，确立该方法对复杂系统模拟的可行性与必要性。
AI中文摘要：
粗粒化（CG）通过将原子组表示为有效相互作用位点来降低原子模拟的计算成本，但常损害结构保真度或需要特定系统参数化。本文引入一种新型各向异性机器学习 CG 势，将原子核的点粒子表示扩展为具有方向依赖特征的大型椭球状珠子，能直接从原子数据学习能量、力和扭矩。该各向异性表示对极性和不对称分子具有物理意义。使用等变消息传递神经网络，模型准确再现了液态水中的径向和角分布函数以及相对取向相关性。与各向同性基线比较表明，缺乏方向信息会导致短程和长程有序的系统误差以及角相关性退化。各向异性模型还揭示了各向同性表示根本无法获得的旋转结构可观测量，且计算开销最小。即使对于仅粗粒化三个自由度的情况，CG 模拟在保持结构保真度的同时实现了 7 - 27 倍的加速，突出了这种系统简化的效率提升。该框架确立了用于各向异性 CG 建模的学习等变表示的可行性和必要性，并为复杂分子液体、聚合物和生物分子系统的准确高效介观模拟提供了一条途径。
英文摘要：
Coarse-graining (CG) lowers the computational cost of atomistic simulations by representing groups of atoms as effective interaction sites, reducing the degrees of freedom of the system but often compromising structural fidelity or requiring system-specific parameterization. Here, we introduce a novel anisotropic machine learning CG potential that extends the point particle representation of atomic nuclei to massive ellipsoidal beads with orientation-dependent features, enabling the learning of energies, forces, and torques directly from atomistic data. The anisotropic representation is physically motivated for polar and asymmetric molecules, where directional interactions and shape anisotropy play important roles in determining structure and dynamics. Using an equivariant message-passing neural network, the model accurately reproduces radial and angular distribution functions as well as relative orientation correlations in liquid water, demonstrating that both translational and rotational dynamics are well captured. Comparison with an isotropic baseline reveals that the lack of orientation information leads to systematic errors in short and long range order and degradation of angular correlations, proving orientation features are essential for accurate coarse-graining. The anisotropic model also exposes rotational structural observables fundamentally inaccessible to isotropic representations, with minimal computational overhead. Even for coarse-graining just three degrees of freedom, CG simulations achieve 7-27$\times$ speedups while preserving structural fidelity, highlighting the efficiency gains of this systemic reduction. This framework establishes the feasibility and necessity of learned equivariant representations for anisotropic CG modeling and provides a path towards accurate and efficient mesoscopic simulations of complex molecular liquids, polymers, and biomolecular systems.
