This website requires JavaScript.

Reconstructing Kernel-based Machine Learning Force Fields with Super-linear Convergence

Stefan Bl\"ucherKlaus-Robert M\"ullerStefan Chmiela
Dec 2022
摘要
Kernel machines have sustained continuous progress in the field of quantumchemistry. In particular, they have proven to be successful in the low-dataregime of force field reconstruction. This is because many physical invariancesand symmetries can be incorporated into the kernel function to compensate formuch larger datasets. So far, the scalability of this approach has however beenhindered by its cubical runtime in the number of training points. While it isknown, that iterative Krylov subspace solvers can overcome these burdens, theycrucially rely on effective preconditioners, which are elusive in practice.Practical preconditioners need to be computationally efficient and numericallyrobust at the same time. Here, we consider the broad class of Nystr\"om-typemethods to construct preconditioners based on successively more sophisticatedlow-rank approximations of the original kernel matrix, each of which provides adifferent set of computational trade-offs. All considered methods estimate therelevant subspace spanned by the kernel matrix columns using differentstrategies to identify a representative set of inducing points. Ourcomprehensive study covers the full spectrum of approaches, starting from naiverandom sampling to leverage score estimates and incomplete Choleskyfactorizations, up to exact SVD decompositions.
展开全部
图表提取

暂无人提供速读十问回答

论文十问由沈向洋博士提出,鼓励大家带着这十个问题去阅读论文,用有用的信息构建认知模型。写出自己的十问回答,还有机会在当前页面展示哦。

Q1论文试图解决什么问题?
Q2这是否是一个新的问题?
Q3这篇文章要验证一个什么科学假设?
0
被引用
笔记
问答