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arXiv · 2510.12650

Towards Foundation Inference Models that Learn ODEs In-Context

Maximilian Mauel·Manuel Hinz·Patrick Seifner·David Berghaus·Ramses J. Sanchez
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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.

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Maximilian Mauel, Manuel Hinz, Patrick Seifner, David Berghaus, Ramses J. Sanchez. 2025-10-14. Towards Foundation Inference Models that Learn ODEs In-Context. https://arxiv.org/abs/2510.12650

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