{"paper":{"title":"MPINeuralODE: Multiple-Initial-Condition Physics-Informed Neural ODEs for Globally Consistent Dynamical System Learning","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Combining a soft physics residual with multiple-initial-condition shooting lets Neural ODEs recover the true vector field from few trajectories.","cross_cats":["math.DS","physics.chem-ph"],"primary_cat":"cs.LG","authors_text":"Antonio Malpica-Morales, Frank Ioannis Papadakis Wood, Lake Yang, Serafim Kalliadasis","submitted_at":"2026-05-13T10:18:18Z","abstract_excerpt":"Neural ordinary differential equations (Neural ODEs) often fit training trajectories while generalizing poorly to unseen initial conditions and long horizons. We propose MPINeuralODE, which combines a soft physics-informed residual with a Multiple-Initial-Condition (MIC) multiple-shooting curriculum whose ingredients are structurally complementary: the physics term anchors the vector-field magnitude on the support that MIC enlarges. We evaluate along three axes: out-of-sample error, long-horizon stability, and Hamiltonian drift, which together expose whether the learned dynamics recover the un"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"On Lotka-Volterra, MPINeuralODE achieves the lowest out-of-sample and long-horizon MSE among data-driven methods, with a 26% reduction over the baseline Neural ODE, while essentially matching the PINN ablation on Hamiltonian drift.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the soft physics-informed residual and MIC multiple-shooting curriculum are structurally complementary such that the physics term anchors the vector-field magnitude on the enlarged support created by MIC, leading to recovery of the underlying dynamics.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"MPINeuralODE combines soft physics residuals with multiple-initial-condition training to reduce out-of-sample and long-horizon errors in dynamical system learning.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Combining a soft physics residual with multiple-initial-condition shooting lets Neural ODEs recover the true vector field from few trajectories.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"bffe54b45e1eae1124c7ced9ff9648a51d7358350384a1bd761bb86de1e278d0"},"source":{"id":"2605.13305","kind":"arxiv","version":1},"verdict":{"id":"77b44840-a5ec-4c2a-86cf-470b50f01957","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T19:18:09.541352Z","strongest_claim":"On Lotka-Volterra, MPINeuralODE achieves the lowest out-of-sample and long-horizon MSE among data-driven methods, with a 26% reduction over the baseline Neural ODE, while essentially matching the PINN ablation on Hamiltonian drift.","one_line_summary":"MPINeuralODE combines soft physics residuals with multiple-initial-condition training to reduce out-of-sample and long-horizon errors in dynamical system learning.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the soft physics-informed residual and MIC multiple-shooting curriculum are structurally complementary such that the physics term anchors the vector-field magnitude on the enlarged support created by MIC, leading to recovery of the underlying dynamics.","pith_extraction_headline":"Combining a soft physics residual with multiple-initial-condition shooting lets Neural ODEs recover the true vector field from few trajectories."},"references":{"count":30,"sample":[{"doi":"","year":null,"title":"Lotka , title =","work_id":"9652ed9f-695f-41ac-a0f4-06d13f9807e9","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Nature , volume =","work_id":"7cba183d-b56c-4878-b8e0-cec1643e89de","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"L. S. Pontryagin and V. G. Boltyanskii and R. V. Gamkrelidze and E. F. Mishchenko , title =","work_id":"9d5007b2-b239-4392-af35-c975710265c1","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Murray , title =","work_id":"1d7bcfeb-a27d-4b6d-80da-10b1df453edd","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Strogatz , title =","work_id":"4f1ec077-4514-4489-a094-f864b1104bf1","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":30,"snapshot_sha256":"b19d29a2fc8114ee819490c4d89ac97326bac4d9749ee287c8ac3c6f353821cb","internal_anchors":2},"formal_canon":{"evidence_count":1,"snapshot_sha256":"6d1e60945350f2fa7a2238c7000f0942b5e35bdcf9ee60c16cf1a4a9939bab78"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}