{"paper":{"title":"pyHB: an open-source automatic-differentiation-enhanced semi-analytical solver for nonlinear dynamics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.MS","authors_text":"Hongyuan Fang, Jun Xu, Lei Hou, Qi Liu, Qingye Meng, Yi Chen, Yuhong Jin","submitted_at":"2026-07-20T05:46:25Z","abstract_excerpt":"The Harmonic Balance (HB) method is widely used to compute and analyze the periodic responses of nonlinear systems. However, its application to high-dimensional complex systems is limited by the burden of handling the partial derivatives of the nonlinearities. This work presents pyHB, an open-source, automatic-differentiation-enhanced semi-analytical framework that integrates the complete HB workflow for general user-defined nonlinear systems. The proposed formulation exploits localized nonlinearities and applies PyTorch-based automatic differentiation (AD) only to the reduced nonlinear force,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.17577","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/2607.17577/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"}