Towards Foundation Inference Models that Learn ODEs In-Context
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Abstract (arXiv)
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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References · 9
- 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
- 2023ODEFormer: Symbolic Regression of Dynamical Systems with Transformerscited by 58
- 2018Learning unknown ODE models with Gaussian processescited by 54
- 2019Learning interpretable continuous-time models of latent stochastic dynamical systemscited by 29
- 2024Zero-shot Imputation with Foundation Inference Models for Dynamical Systemscited by 13
- 2024Foundation Inference Models for Markov Jump Processescited by 13
- 2022The future is different: Large pre-trained language models fail in prediction taskscited by 8
- 2023Neural Dynamic Focused Topic Modelcited by 8
- 2025In-Context Learning of Stochastic Differential Equations with Foundation Inference Modelscited by 7
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