arXiv Machine Learning June 9, 2026 By Maximilian Mauel, Johannes R. H\"ubers, David Berghaus, Patrick Seifner, Ramses J. Sanchez

Foundation Inference Models for Ordinary Differential Equations

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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.

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fine-tuning

arXiv Machine Learning

Jun 5

Function-Space Priors for Bayesian Neural ODEs with Application to Vessel Trajectory Prediction

arXiv:2606. 06351v1 Announce Type: cross Abstract: Vessel trajectory prediction from Automatic Identification System (AIS) data is essential for maritime situational awareness, yet it remains challenging due to irregular sampling, missing reports, and complex dynamics.

By Jaeyeong Lee, Wonmo Koo, Heeyoung Kim

arXiv Machine Learning

Jun 9

In-Context Learning of Stochastic Differential Equations with Foundation Inference Models

arXiv:2502. 19049v3 Announce Type: replace Abstract: Stochastic differential equations (SDEs) describe dynamical systems where deterministic flows, governed by a drift function, are superimposed with random fluctuations, dictated by a diffusion function.

By Patrick Seifner, Kostadin Cvejoski, David Berghaus, Cesar Ojeda, Ramses J. Sanchez

llms diffusion fine-tuning

arXiv Machine Learning

Jun 9

Learning to Solve Generative ODEs Beyond the Linear Span

arXiv:2606. 08672v1 Announce Type: cross Abstract: Diffusion and flow generative models sample by integrating a learned ODE, but high quality still requires many sequential model evaluations.

By Sihyeon Kim, Seunghun Lee, Vikas Singh, Hyunwoo J. Kim

diffusion benchmarks

arXiv Statistics ML

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Symbolic Neural ODEs: Learning interpretable models from time-series data

arXiv:2608.22112v1 Announce Type: cross Abstract: We present a machine learning framework for identifying sparse, interpretable models of dynamical systems directly from time-series data. Our approac...

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efficiency

arXiv Machine Learning

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Flow Map Learning via Nongradient Vector Flow

arXiv:2607. 26398v1 Announce Type: new Abstract: Diffusion and flow-based models benefit from simple regression losses, but inference incurs significant overhead because sampling requires integration.

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diffusion benchmarks

arXiv Machine Learning

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MPINeuralODE: Multiple-Initial-Condition Physics-Informed Neural ODEs for Globally Consistent Dynamical System Learning

arXiv:2605. 13305v2 Announce Type: replace Abstract: Neural ordinary differential equations (Neural ODEs) often fit training trajectories while generalizing poorly to unseen initial conditions and long horizons.

By Lake Yang, Antonio Malpica-Morales, Frank Ioannis Papadakis Wood, Serafim Kalliadasis

benchmarks

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