aiqbench analysis
FIM-ODE introduces a pretrained foundation model that simplifies ODE inference by predicting vector fields directly from noisy data in a single forward pass, eliminating the need for complex training pipelines or specialized expertise. By leveraging neural operators and a simpler prior distribution, it achieves zero-shot performance that matches or exceeds recent symbolic baselines while providing robust initialization for fine-tuning. This approach offers a practical advancement for scientific modeling tasks where reducing dependency on system-specific prior knowledge is critical.
Foundation Inference Models for Ordinary Differential Equations
arXiv:2602.08733v2 Announce Type: replace Abstract: Ordinary differential equations (ODEs) are central to scientific modelling, but inferring their vector fields from noisy trajectories remains challenging. Current approaches such as symbolic regression, Gaussian process (GP) regression, and Neural ODEs often require complex training pipelines and substantial machine learning expertise, or they depend strongly on system-specific prior knowledge. We propose FIM-ODE, a pretrained Foundation Inference Model that amortises low-dimensional ODE inference by predicting the vector field directly from noisy trajectory data in a single forward pass. We pretrain FIM-ODE on a prior distribution over ODEs with low-degree polynomial vector fields and represent the target field with neural operators. FIM-ODE achieves strong zero-shot performance, matching and often improving upon ODEFormer, a recent pretrained symbolic baseline, across a range of regimes despite using a simpler pretraining prior distribution. Pretraining also provides a strong initialisation for finetuning, enabling fast and stable adaptation that outperforms modern neural and GP baselines without requiring machine learning expertise.
Abstract:Ordinary differential equations (ODEs) are central to scientific modelling, but inferring their vector fields from noisy trajectories remains challenging. Current approaches such as symbolic regression, Gaussian process (GP) regression, and Neural ODEs often require complex training pipelines and substantial machine learning expertise, or they depend strongly on system-specific prior knowledge. We propose FIM-ODE, a pretrained Foundation Inference Model that amortises low-dimensional ODE inference by predicting the vector field directly from noisy trajectory data in a single forward pass. We pretrain FIM-ODE on a prior distribution over ODEs with low-degree polynomial vector fields and represent the target field with neural operators. FIM-ODE achieves strong zero-shot performance, matching and often improving upon ODEFormer, a recent pretrained symbolic baseline, across a range of regimes despite using a simpler pretraining prior distribution. Pretraining also provides a strong initialisation for finetuning, enabling fast and stable adaptation that outperforms modern neural and GP baselines without requiring machine learning expertise.
Machine Learning (cs.LG)
arXiv:2602.08733 [cs.LG]
(or arXiv:2602.08733v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2602.08733 Focus to learn more arXiv-issued DOI via DataCite
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