{"ID":2855829,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.12650","arxiv_id":"2510.12650","title":"Towards Foundation Inference Models that Learn ODEs In-Context","abstract":"Ordinary differential equations (ODEs) describe dynamical systems evolving deterministically in continuous time. Accurate data-driven modeling of systems as ODEs, a central problem across the natural sciences, remains challenging, especially if the data is sparse or noisy. We introduce FIM-ODE (Foundation Inference Model for ODEs), a pretrained neural model designed to estimate ODEs zero-shot (i.e., in context) from sparse and noisy observations. Trained on synthetic data, the model utilizes a flexible neural operator for robust ODE inference, even from corrupted data. We empirically verify that FIM-ODE provides accurate estimates, on par with a neural state-of-the-art method, and qualitatively compare the structure of their estimated vector fields.","short_abstract":"Ordinary differential equations (ODEs) describe dynamical systems evolving deterministically in continuous time. Accurate data-driven modeling of systems as ODEs, a central problem across the natural sciences, remains challenging, especially if the data is sparse or noisy. We introduce FIM-ODE (Foundation Inference Mod...","url_abs":"https://arxiv.org/abs/2510.12650","url_pdf":"https://arxiv.org/pdf/2510.12650v1","authors":"[\"Maximilian Mauel\",\"Manuel Hinz\",\"Patrick Seifner\",\"David Berghaus\",\"Ramses J. Sanchez\"]","published":"2025-10-14T15:44:54Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[]","has_code":false}