{"paper":{"title":"Operator Learning with Gaussian Processes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Amin Yousefpour, Carlos Mora, Houman Owhadi, Ramin Bostanabad, Shirin Hosseinmardi","submitted_at":"2024-09-06T18:06:08Z","abstract_excerpt":"Operator learning focuses on approximating mappings $\\mathcal{G}^\\dagger:\\mathcal{U} \\rightarrow\\mathcal{V}$ between infinite-dimensional spaces of functions, such as $u: \\Omega_u\\rightarrow\\mathbb{R}$ and $v: \\Omega_v\\rightarrow\\mathbb{R}$. This makes it particularly suitable for solving parametric nonlinear partial differential equations (PDEs). While most machine learning methods for operator learning rely on variants of deep neural networks (NNs), recent studies have shown that Gaussian Processes (GPs) are also competitive while offering interpretability and theoretical guarantees. In this"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.04538","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2409.04538/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}