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

• URL: http://arxiv.org/abs/2606.06351v1
• Date: Thu, 04 Jun 2026 16:21:08 GMT
• Title: Function-Space Priors for Bayesian Neural ODEs with Application to Vessel Trajectory Prediction
• Abstract summary: Vessel trajectory prediction from Automatic Identification System (AIS) data is essential for maritime situational awareness.<n>We propose a principled framework for continuous-time trajectory modeling with uncertainty quantification.<n>We use a kernel-based regularizer that penalizes deviations of the vector field from the structure implied by a GP prior.
• Score: 8.831954614241232
• License: http://creativecommons.org/licenses/by/4.0/
• 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. Beyond accurate point forecasts, maritime applications also demand well-calibrated uncertainty estimates for reliable decision-making. Bayesian Neural Ordinary Differential Equations (ODEs) offer a principled framework for continuous-time trajectory modeling with uncertainty quantification by placing a prior over the neural vector field parameters. However, the commonly used isotropic Gaussian weight prior fails to encode informative structural properties of vessel dynamics, such as smoothness and locality. Existing function-space Bayesian neural network methods address this limitation for static mappings, but do not transfer directly to Neural ODEs, where the primary quantity of interest is the trajectory rather than the vector field itself. In principle, one could place a Gaussian process (GP) prior directly over ODE solutions, but this requires propagating distributions through a nonlinear ODE solver, which is analytically intractable. To address this challenge, we adopt a practical approach that imposes a GP-kernel-based prior directly on the vector field evaluated at a finite set of measurement points. Specifically, we augment the standard weight-space variational objective with a kernel-based regularizer that penalizes deviations of the vector field from the structure implied by a GP prior. To handle long and irregular AIS trajectories, we further combine this function-space regularization with probabilistic multiple shooting, which decouples inference across temporal segments while maintaining global consistency.

Related papers

• Physics-informed neural particle flow for the Bayesian update step [0.8220217498103312]
  We propose a physics-informed neural particle flow, which is an amortized inference framework.<n>By embedding a governing partial differential equation (PDE) into the loss function, we train a neural network to approximate the transport velocity field.<n>We demonstrate that the neural parameterization acts as an implicit regularizer, mitigating the stiffness inherent to analytic flows.
  arXiv  Detail & Related papers  (2026-02-26T15:10:45Z)
• Foundation Inference Models for Ordinary Differential Equations [3.4253416336476246]
  We propose FIM-ODE, a pretrained Foundation Inference Model that amortises low-dimensional ODE inference.<n>We pretrain FIM-ODE on a prior distribution over ODEs with low-degree vector fields and represent the target field with neural operators.<n>Pretraining also provides a strong initialisation for finetuning, enabling fast and stable adaptation that outperforms modern neural and GP baselines.
  arXiv  Detail & Related papers  (2026-02-09T14:39:11Z)
• Is Flow Matching Just Trajectory Replay for Sequential Data? [46.770624059457724]
  Flow matching (FM) is increasingly used for time-series generation.<n>It is not well understood whether it learns a general dynamical structure or simply performs an effective "trajectory replay"<n>We show that the implied sampler is an ODE whose dynamics constitutes a nonparametric, memory-augmented continuous-time dynamical system.
  arXiv  Detail & Related papers  (2026-02-09T06:48:45Z)
• ResAD: Normalized Residual Trajectory Modeling for End-to-End Autonomous Driving [64.42138266293202]
  ResAD is a Normalized Residual Trajectory Modeling framework.<n>It reframes the learning task to predict the residual deviation from an inertial reference.<n>On the NAVSIM benchmark, ResAD achieves a state-of-the-art PDMS of 88.6 using a vanilla diffusion policy.
  arXiv  Detail & Related papers  (2025-10-09T17:59:36Z)
• Deep Neural Network-Driven Adaptive Filtering [42.10078151647835]
  This paper proposes a deep neural network (DNN)-driven framework to address the longstanding generalization challenge in adaptive filtering (AF)<n>In contrast to traditional AF frameworks that emphasize explicit cost function design, the proposed framework shifts the paradigm toward direct gradient acquisition.<n>The framework is validated by extensive numerical experiments across a spectrum of non-Gaussian scenarios.
  arXiv  Detail & Related papers  (2025-08-06T09:42:40Z)
• Efficient Transformed Gaussian Process State-Space Models for Non-Stationary High-Dimensional Dynamical Systems [49.819436680336786]
  We propose an efficient transformed Gaussian process state-space model (ETGPSSM) for scalable and flexible modeling of high-dimensional, non-stationary dynamical systems.<n>Specifically, our ETGPSSM integrates a single shared GP with input-dependent normalizing flows, yielding an expressive implicit process prior that captures complex, non-stationary transition dynamics.<n>Our ETGPSSM outperforms existing GPSSMs and neural network-based SSMs in terms of computational efficiency and accuracy.
  arXiv  Detail & Related papers  (2025-03-24T03:19:45Z)
• Bayesian Gaussian Process ODEs via Double Normalizing Flows [27.015257976208737]
  We introduce normalizing flows to re parameterize the ODE vector field, resulting in a data-driven prior distribution.<n>We also apply normalizing flows to the posterior inference of GP ODEs to resolve the issue of strong mean-field assumptions.<n>We validate the effectiveness of our approach on simulated dynamical systems and real-world human motion data.
  arXiv  Detail & Related papers  (2023-09-17T09:28:47Z)
• Linear Time GPs for Inferring Latent Trajectories from Neural Spike Trains [7.936841911281107]
  We propose cvHM, a general inference framework for latent GP models leveraging Hida-Mat'ern kernels and conjugate variational inference (CVI) We are able to perform variational inference of latent neural trajectories with linear time complexity for arbitrary likelihoods.
  arXiv  Detail & Related papers  (2023-06-01T16:31:36Z)
• Uncovering the Missing Pattern: Unified Framework Towards Trajectory Imputation and Prediction [60.60223171143206]
  Trajectory prediction is a crucial undertaking in understanding entity movement or human behavior from observed sequences. Current methods often assume that the observed sequences are complete while ignoring the potential for missing values. This paper presents a unified framework, the Graph-based Conditional Variational Recurrent Neural Network (GC-VRNN), which can perform trajectory imputation and prediction simultaneously.
  arXiv  Detail & Related papers  (2023-03-28T14:27:27Z)
• Gaussian Process-based Min-norm Stabilizing Controller for Control-Affine Systems with Uncertain Input Effects and Dynamics [90.81186513537777]
  We propose a novel compound kernel that captures the control-affine nature of the problem. We show that this resulting optimization problem is convex, and we call it Gaussian Process-based Control Lyapunov Function Second-Order Cone Program (GP-CLF-SOCP)
  arXiv  Detail & Related papers  (2020-11-14T01:27:32Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.