{"paper":{"title":"Residual-Based Time Discretization on Nonlinear Approximation Manifolds: Analysis and Gaussian Applications","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","quant-ph"],"primary_cat":"math.NA","authors_text":"Caroline Lasser, Eddy de Leon","submitted_at":"2026-07-16T14:57:44Z","abstract_excerpt":"We study time-discrete parametric approximations of evolution equations in Hilbert spaces based on residual minimization. The solution is represented by a parametrized ansatz belonging to a low-dimensional nonlinear manifold, and time stepping is performed by minimizing suitably defined residuals at each step. Two natural residual formulations are considered: discretization followed by parametrization of the evolution equation, and discretization of the Dirac--Frenkel variational principle governing the parameter dynamics. A unified error analysis is developed for both approaches within the fa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.15086","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/2607.15086/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"}