计算机科学
操作员(生物学)
理论计算机科学
人工智能
生物化学
转录因子
基因
抑制因子
化学
作者
Nicholas H. Nelsen,Andrew M. Stuart
出处
期刊:Siam Review
[Society for Industrial and Applied Mathematics]
日期:2024-05-01
卷期号:66 (3): 535-571
被引量:1
摘要
Supervised operator learning centers on the use of training data, in the form of inputoutput pairs, to estimate maps between infinite-dimensional spaces.It is emerging as a powerful tool to complement traditional scientific computing, which may often be framed in terms of operators mapping between spaces of functions.Building on the classical random features methodology for scalar regression, this paper introduces the function-valued random features method.This leads to a supervised operator learning architecture that is practical for nonlinear problems yet is structured enough to facilitate efficient training through the optimization of a convex, quadratic cost.Due to the quadratic structure, the trained model is equipped with convergence guarantees and error and complexity bounds, properties that are not readily available for most other operator learning architectures.At its core, the proposed approach builds a linear combination of random operators.This turns out to be a low-rank approximation of an operator-valued kernel ridge regression algorithm, and hence the method also has strong connections to Gaussian process regression.The paper designs function-valued random features that are tailored to the structure of two nonlinear operator learning benchmark problems arising from parametric partial differential equations.Numerical results demonstrate the scalability, discretization invariance, and transferability of the function-valued random features method.
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