Foundation Model Approach Enables In-Context Learning for Temporal Point Process Inference
Researchers have introduced FIM-SDE, a pretrained neural network model capable of estimating the drift and diffusion functions of stochastic differential equations directly from noisy time series data, without requiring prior knowledge of the underlying dynamics. The work, accepted at NeurIPS 2025, frames the problem as in-context (zero-shot) inference using amortized inference and neural operator concepts. This approach could accelerate scientific modeling across fields such as finance, climatology, and physics by removing the need for bespoke, dataset-specific training procedures.
Stochastic differential equations (SDEs) are a foundational mathematical tool for modeling systems that combine deterministic trends with random fluctuations, with applications spanning finance, ecology, and the physical sciences. Estimating the two core components of an SDE — the drift function and the diffusion function — from observed data has historically required either strong prior knowledge of the system or computationally intensive, problem-specific training. FIM-SDE addresses this by pretraining a transformer-based recognition model on a large, diverse set of synthetic SDE trajectories, enabling it to map noisy, discretely observed time series directly onto drift and diffusion function estimates in a zero-shot fashion. The model was benchmarked against symbolic regression, Gaussian process, and Neural SDE baselines across both canonical systems (such as double-well potentials and weakly perturbed Lorenz attractors) and real-world datasets including stock prices, oil prices, and wind-speed recordings. In zero-shot mode, FIM-SDE matched the performance of these baselines, which were each trained specifically on the target datasets. When finetuned to a target process, FIM-SDE consistently outperformed all baselines, suggesting that the pretrained representations provide a strong initialization. The paper was accepted at the 39th Conference on Neural Information Processing Systems (NeurIPS 2025).
What's missing
The study focuses on low-dimensional SDEs; the authors do not extensively address scalability to high-dimensional systems, which is a known challenge for SDE inference methods. The scope of the pretraining distribution and how out-of-distribution dynamics affect zero-shot performance are important open questions not fully resolved in the abstract. Computational cost of pretraining relative to training individual baselines is not discussed.
What different sources said
- arXiv cs.LGCenter
In-Context Learning of Stochastic Differential Equations with Foundation Inference Models
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