This paper introduces the Chemical Environment Modeling Theory (CEMT), a novel, generalized framework designed to overcome the limitations inherent in traditional atom-centered Machine Learning Force Field (MLFF) models, widely used in atomistic simulations of chemical systems. CEMT demonstrated enhanced flexibility and adaptability by allowing reference points to exist anywhere within the modeled domain and thus, enabling the study of various model architectures. Utilizing Gaussian Multipole (GMP) featurization functions, several models with different reference point sets, including finite difference grid-centered and bond-centered models, were tested to analyze the variance in capabilities intrinsic to models built on distinct reference points. The results underscore the potential of non-atom-centered reference points in force training, revealing variations in prediction accuracy, inference speed and learning efficiency. Finally, a unique connection between CEMT and real-space orbital-free finite element Density Functional Theory (FE-DFT) is established, and the implications include the enhancement of data efficiency and robustness. It allows the leveraging of spatially-resolved energy densities and charge densities from FE-DFT calculations, as well as serving as a pivotal step towards integrating known quantum-mechanical laws into the architecture of ML models.

翻译：本文介绍了化学环境建模理论（CEMT），这是一个新颖的通用框架，旨在克服传统原子中心机器学习力场（MLFF）模型在化学体系原子模拟中固有的局限性。CEMT通过允许参考点存在于建模域内的任意位置，从而支持对各种模型架构的研究，展现了更强的灵活性和适应性。利用高斯多极（GMP）特征化函数，我们测试了包含有限差分网格中心模型和键中心模型在内的多种具有不同参考点集的模型，以分析基于不同参考点构建的模型在能力上的差异。结果表明，非原子中心参考点在力训练中具有潜力，并揭示了预测精度、推理速度和学习效率方面的差异。最后，建立了CEMT与实空间无轨道有限元密度泛函理论（FE-DFT）之间的独特联系，其意义包括提升数据效率和鲁棒性。这使得能够利用FE-DFT计算中的空间分辨能量密度和电荷密度，并成为将已知量子力学定律融入机器学习模型架构的关键一步。