Towards Foundation Inference Models that Learn ODEs In-Context
This addresses a central challenge in the natural sciences for modeling dynamical systems, but it appears incremental as it builds on existing neural methods.
The paper tackles the problem of data-driven modeling of dynamical systems as ordinary differential equations (ODEs) from sparse and noisy observations, introducing FIM-ODE, a pretrained neural model that estimates ODEs zero-shot and achieves accuracy on par with a neural state-of-the-art method.
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.