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
The proliferation of foundation models in other AI domains is naturally leading to their application in scientific computing, driven by the increasing complexity of scientific data and the demand for more autonomous discovery. Advances in transformer architectures and large-scale pre-training capabilities are enabling these models to tackle previously intractable inference problems.
Foundation Inference Models (FIMs) for ODEs could significantly lower the barrier to entry for complex scientific modeling and accelerate discovery in fields relying on differential equations, from physics and biology to engineering and climate science. This abstracts away significant machine learning expertise, making advanced modeling accessible to a broader range of researchers.
Traditional bespoke model development for ODE inference, requiring deep expertise and extensive training, will be augmented or replaced by pre-trained, adaptable foundation models that streamline the process. Scientific discovery can become faster and less constrained by the availability of specialized ML engineers.
- · Scientific researchers
- · Biotech and pharmaceutical sector
- · Materials science
- · Climate modeling
- · Expert-driven symbolic regression firms
- · Niche ODE inference software requiring manual tuning
Scientific domains heavily reliant on ODEs will see accelerated hypothesis testing and model validation.
The development of highly specialized scientific AI agents becomes more feasible as core inference tasks are amortized.
A new ecosystem of 'scientific foundation models' could emerge, offering pre-trained capabilities across various scientific disciplines and potentially leading to a 'democratization' of advanced scientific AI.
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Read at arXiv cs.LG