发表机构
Massachusetts Institute of Technology; École Polytechnique Fédérale de Lausanne; University of Warwick（麻省理工学院; 洛桑联邦理工学院; 华威大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文首次将多元共形方法应用于多任务原子模拟，通过校准能量、力和应力并传播到弹性常数等下游量，捕获误差抵消，提升不确定性量化可靠性。
AI 中文摘要
机器学习已成为设计兼顾效率与精度的原子间势的标准工具，但不确定性量化仍是一个开放问题。多尺度模拟引入了额外挑战：跨尺度的稳健不确定性量化。即使在同一尺度内，计算也常是多阶段的，产生一系列目标量，每个量依赖于前一个，且每个量都有一定的不确定性。共形方法已成为一种模型无关的框架，用于重新校准代理预测，以生成以用户指定速率包含真实值的集合。对于多阶段工作流，我们需要针对多种化学性质和原子构型进行不确定性校准，并希望将不确定性集合传播到下游感兴趣的量。这种传播应捕获材料科学中许多下游目标中出现的误差抵消；例如，近似能量差通常比单个能量预测更准确。我们首次探索了化学性质的多元共形方法，包括Bonferroni校正的超矩形、基于马氏距离的超椭球集合，以及共形风险控制中的自定义损失函数。校准直接应用于预测的能量、原子力和维里应力，然后通过材料建模中常用的多种近似协议传播到弹性常数和空位形成能。我们强调了在共形过程中构建相关性预测的优势，这使得构建能够捕获近对称性和误差抵消的集合成为可能。最后，我们讨论了所用近似计算协议与共形保证之间的相互作用。
英文摘要
Machine learning has become the standard tool for the design of interatomic potentials which balance efficiency and accuracy, but uncertainty quantification remains an open problem. Multiscale simulations introduce an additional challenge: robust uncertainty quantification across scales. Even within one scale, computations are often multistage, producing a sequence of target quantities, each dependent on the previous, and each with some uncertainty. Conformal methods have emerged as a model agnostic framework for recalibrating surrogate predictions to produce sets which contain the truth at a user-specified rate. For multistage workflows, we require uncertainty calibration for multiple chemical properties and atomistic configurations, and we want to propagate uncertainty sets to downstream quantities of interest. Such propagation should capture the error cancellations which occur in many downstream targets in materials science; for instance, an approximate energy difference is often more accurate than individual energy predictions. We present the first exploration of multivariate conformal methods for chemical properties, including Bonferroni-corrected hyperrectangles, hyperellipsoidal sets based on the Mahalanobis distance, and custom loss functions within conformal risk control. Calibration is applied directly to predicted energies, atomic forces, and virial stresses, then propagated to elastic constants and vacancy formation energies employing a variety of commonly considered approximate protocols in materials modeling. We highlight the benefits of building correlation predictions into the conformal procedure, making it possible to build sets which capture near symmetries and error cancellation. We conclude with a discussion of the interplay of the employed approximate computational protocol and conformal guarantees.
Commentsmain: 17 pages, 7 figures + appendix: 9 pages, 10 figures
