利用隐式微分探究原子极小值的参数依赖性
Exploring parameter dependence of atomic minima with implicit differentiation
AI总结：
本研究提出利用隐式导数对原子极小值的能量与结构做势参数泰勒展开，结合稀疏算子法实现大系统高效传播，可准确预测相关物理量、实现高维不确定性量化，还能解决势微调等逆问题。
摘要：
原子间势是突破从头算尺寸限制的关键，但模拟结果对势参数极为敏感。参数变化的前向传播是不确定性量化的核心，而反向传播已在微调、定向设计等新兴逆问题中得到应用。本文将定义为不动点的函数的隐式导数用于对原子极小值的能量和结构进行势参数的泰勒展开，通过自动微分、稠密线性代数或一种新颖的稀疏算子方法计算各项。其中稀疏算子方法可在任意大系统的弛豫结构中实现高效的前向与反向传播。该隐式展开能借助经典势和机器学习势准确预测晶格畸变、缺陷形成能及体积，可在无过高开销的情况下实现高维不确定性传播。随后我们展示了如何利用隐式导数解决具有挑战性的逆问题：通过最小化隐式损失来微调势函数，并稳定钨中位错处由溶质诱导的结构重排。
英文摘要：
Interatomic potentials are essential to go beyond ab initio size limitations, but simulation results depend sensitively on potential parameters. Forward propagation of parameter variation is key for uncertainty quantification, whilst backpropagation has found application for emerging inverse problems such as fine-tuning or targeted design. Here, the implicit derivative of functions defined as a fixed point is used to Taylor expand the energy and structure of atomic minima in potential parameters, evaluating terms via automatic differentiation, dense linear algebra or a novel sparse operator approach. The latter allows efficient forward and backpropagation through relaxed structures of arbitrarily large systems. The implicit expansion accurately predicts lattice distortion and defect formation energies and volumes with classical and machine-learning potentials, enabling high-dimensional uncertainty propagation without prohibitive overhead. We then show how the implicit derivative can be used to solve challenging inverse problems, minimizing an implicit loss to fine-tune potentials and stabilize solute-induced structural rearrangements at dislocations in tungsten.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
