发表机构
School of Mathematical Sciences, Institute of Natural Sciences and MOE-LSC, Shanghai Jiao Tong University; Department of Mathematics, National University of Singapore（上海交通大学数学科学学院、自然科学研究院和教育部线性科学中心; 新加坡国立大学数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对机器学习原子间势的能量-力平衡问题，提出力约束拟合方法，通过原对偶优化替代权重选择，在多个体系上实现6.7-8.9倍加速并改善模型选择。
AI 中文摘要
机器学习原子间势通常通过加权和标量化进行拟合，将能量和力的误差合并到单一损失中。然而，名义权重仅相对于完整的拟合协议才能确定一个势。因此，我们将能量-力平衡视为一个依赖于协议的物理模型选择问题。对于熔融LiCl、液态H2O和Si的固定基原子团簇展开模型，所得的标量化路径在极端权重下包含被支配状态。其非支配子集依赖于求解器，且分布外Si路径是非单调的。我们将直接权重选择替换为在归一化力损失上界约束下最小化正则化能量目标。投影对偶上升法根据力约束残差调整拉格朗日乘子。随后，冻结乘子的有限记忆拟牛顿细化返回最终模型。在三个系统中，约束过程达到了与求解器匹配的低误差区域，并在所述计时约定下，相对于完成的标量化扫描获得了6.7至8.9倍的实测加速。物理性质计算表明，第一壳层几何对所选平衡相对不敏感，而输运和固态观测量变化更为显著。这些结果将拟合的模型-协议对确定为能量-力模型选择的相关对象，并支持力约束拟合作为显式选择规则。
英文摘要
Machine-learned interatomic potentials are commonly fitted by weighted-sum scalarization, which combines energy and force errors in a single loss. A nominal weight, however, identifies a potential only relative to the complete fitting protocol. We therefore treat energy--force balancing as a protocol-dependent problem of physical model selection. For fixed-basis atomic cluster expansion models of molten LiCl, liquid H$_2$O, and Si, the resulting scalarization paths contain dominated states at extreme weights. Their nondominated subsets depend on the solver, and the out-of-distribution Si path is nonmonotone. We replace direct weight selection by minimizing the regularized energy objective subject to an upper bound on the normalized force loss. Projected dual ascent adjusts the Lagrange multiplier from the force-constraint residual. A frozen-multiplier limited-memory quasi-Newton refinement then returns the final model. Across the three systems, the constrained procedure reaches the solver-matched low-error region and gives measured speedups of $6.7$--$8.9$ over completed scalarization scans under the stated timing convention. Physical-property calculations show that first-shell geometry is comparatively insensitive to the selected balance, whereas transport and solid-state observables vary more strongly. These results identify the fitted model--protocol pair as the relevant object of energy--force model selection and support force-constrained fitting as an explicit selection rule.
