{"paper":{"title":"Neural operator preconditioning from mixed dataset for the Helmholtz equations: Application to transcranial ultrasound","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Yanfei Xiang","submitted_at":"2026-07-18T17:48:59Z","abstract_excerpt":"This work develops a neural operator preconditioned subspace method for sequences of linear systems arising from the discretization of the two-dimensional Helmholtz equation in transcranial ultrasound applications. The problem involves strongly heterogeneous, patient-dependent velocity fields that induce severe wave distortion and pose significant challenges for standard iterative solvers. Building on neural network preconditioning framework of Giraud et al. (HAL RR-9593, 2025) and the idealized skull dataset used for the learned optimizer of Stanziola et al. (JCP 441, 2021), neural operator p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16906","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/2607.16906/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"}