Foundation Inference Models for Ordinary Differential Equations
This addresses the problem of simplifying ODE inference for scientific modeling by reducing the need for complex training pipelines or system-specific prior knowledge, though it is incremental as it builds on existing pretrained and neural operator approaches.
The paper tackles the challenge of inferring vector fields from noisy trajectories in ordinary differential equations (ODEs) by proposing FIM-ODE, a pretrained foundation model that predicts vector fields directly from data in a single forward pass, achieving strong zero-shot performance that matches or improves upon ODEFormer and enabling fast finetuning that outperforms neural and GP baselines.
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.