{"paper":{"title":"Exploring Neural Network Surrogates for High-Order Mesh-Free Interpolants","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"physics.comp-ph","authors_text":"Ajay Harish, Georgios Fourtakas, Jack R. C. King, Lucas Gerken Starepravo, Steven Lind","submitted_at":"2025-03-29T21:29:01Z","abstract_excerpt":"Mesh-free numerical methods offer flexibility in the discretisation of complex geometries, showing significant potential for problems where mesh-based methods struggle. Although high-order approximations can be obtained through consistency-correction linear systems, such approaches remain prohibitively expensive for Lagrangian formulations, which commonly exhibit low-order convergence. Here we investigate the use of machine learning (ML) to bridge this gap, developing two strategies to couple multilayer perceptrons (MLPs) with the Local Anisotropic Basis Function Method (LABFM) as an exemplar "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.23230","kind":"arxiv","version":3},"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/2503.23230/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"}