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Switched Event-Triggered Adaptive Control of Reaction-Diffusion PDE-ODE with Neural Operator Implementation
arXiv:2606.02114v1 Announce Type: cross Abstract: This paper develops a switched event-triggered adaptive boundary control for a class of reaction-diffusion PDE-ODE cascade systems, where the system and input matrices in the ODE as well as the spatially-varying reaction coefficient in the PDE are uncertain. A two-step backstepping transformation is constructed to derive the continuous-time control law. Then a novel dynamic event-triggered control strategy for the PDE-ODE cascade is proposed...
Stable and Scalable Probabilistic Numerical Solvers for Stiff and High-Dimensional ODEs
arXiv:2606.08203v1 Announce Type: new Abstract: Filtering-based probabilistic numerical solvers for ordinary differential equations (ODEs) have been established as a flexible and efficient simulation framework with built-in numerical uncertainty quantification. However, problems that are both stiff and high-dimensional remain a challenge, as current methods are either stable and have cubic cost in the ODE dimension, or scale linearly at the expense of stability. In this paper, we close this...
Control-Theoretic View of Neural ODEs: Empirical Controllability and Observability
arXiv:2606.08431v1 Announce Type: new Abstract: This paper studies neural ordinary differential equations (neural ODEs) from a control-theoretic perspective using controllability and observability concepts. The neural ODE is represented in a control-affine form to facilitate analysis using tools from nonlinear and linear time-varying (LTV) systems. Controllability is examined through trajectory linearization, where the LTV controllability Gramian provides a local, first-order measure of...
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. 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...
Input-to-State Stable Bundle Koopman Neural ODEs for Learning Controlled Dynamics under Environmental Constraints
Announce Type: new Abstract: We propose ISS-BKNO, a unified framework that integrates Koopman operator identification, Neural ordinary differential equations (ODEs), fiber bundle geometry, and input-to-state stability (ISS) certification. Unlike prior approaches that address stability, extrinsic inputs, or environmental constraints in isolation, the proposed framework simultaneously learns controlled nonlinear dynamics while guaranteeing global convergence and a computable ISS gain. The...
Learning to Solve Generative ODEs Beyond the Linear Span
Announce Type: new Abstract: Diffusion and flow generative models sample by integrating a learned ODE, but high quality still requires many sequential model evaluations. Solver learning reduces this cost by adapting scalar coefficients, timesteps, or both, while keeping the backbone model fixed. In this work, we identify a structural bottleneck in this update family: each step remains span-limited.
Mitigating the Contractivity Trap in Diffusion ODEs via Stein Stabilization
Announce Type: new Abstract: A fundamental tension exists in the large-step inference of diffusion models via their deterministic probability flow ordinary differential equation (PF-ODE) trajectories, which we identify as the contractivity trap: efficient inference favors large step sizes, while aggressive steps and highly expressive denoisers can undermine contraction-based stability certificates for error suppression. To address this, we propose SteinDiff, a step-wise inference-time...
Coordinate-wise splitting algorithms for ODE simulation via Koopman-Lie product formulas
arXiv:2506.17524v3 Announce Type: replace Abstract: We present a computational framework for simulating finite-dimensional ordinary differential equations by combining classical Koopman-Lie product formulas with coordinate-wise frozen subflows. The setting is model-known, since the vector field is assumed to be available, and no data-driven approximation of the Koopman operator is attempted. Under standard assumptions, the Koopman-Lie generator associated with the flow admits a coordinate...
Learning from Demonstrations over Riemannian Manifolds using Neural ODEs: An Extended Abstract
Announce Type: new Abstract: Learning from demonstratins (LfD) is usually performed over Euclidean spaces, while the robot state, e.g. orientation, naturally evolves over curved spaces. Therefore, to ensure natural, complex motion generation, we investigate learning from demonstrations over Riemannian manifolds that are capable of encoding both position and orientation data.
Foundation Inference Models for Ordinary Differential Equations
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...