[2510.22068] Deep Gaussian Processes for Functional Maps

Computer Science > Machine Learning arXiv:2510.22068 (cs) [Submitted on 24 Oct 2025 (v1), last revised 3 Apr 2026 (this version, v2)] Title:Deep Gaussian Processes for Functional Maps Authors:Matthew Lowery, Zhitong Xu, Da Long, Keyan Chen, Daniel S. Johnson, Yang Bai, Varun Shankar, Shandian Zhe View a PDF of the paper titled Deep Gaussian Processes for Functional Maps, by Matthew Lowery and 7 other authors View PDF HTML (experimental) Abstract:Learning mappings between functional spaces, also known as function-on-function regression, is a fundamental problem in functional data analysis with broad applications, including spatiotemporal forecasting, curve prediction, and climate modeling. Existing approaches often struggle to capture complex nonlinear relationships and/or provide reliable uncertainty quantification when data are noisy, sparse, or irregularly sampled. To address these challenges, we propose Deep Gaussian Processes for Functional Maps (DGPFM). Our method constructs a sequence of GP-based linear and nonlinear transformations directly in function space, leveraging kernel integral transforms, GP conditional means, and nonlinear activations sampled from Gaussian processes. A key insight enables a simplified and flexible implementation: under fixed evaluation locations, discrete approximations of kernel integral transforms reduce to direct functional integral transforms, allowing seamless integration of diverse transform designs. To support scalable probabilistic...