Neural CDEs provide a natural way to process the temporal evolution of irregular time series. The number of function evaluations (NFE) is these systems' natural analog of depth (the number of layers in traditional neural networks). It is usually regulated via solver error tolerance: lower tolerance means higher numerical precision, requiring more integration steps. However, lowering tolerances does not adequately increase the models' expressiveness. We propose a simple yet effective alternative: scaling the integration time horizon to increase NFEs and "deepen`` the model. Increasing the integration interval causes uncontrollable growth in conventional vector fields, so we also propose a way to stabilize the dynamics via Negative Feedback (NF). It ensures provable stability without constraining flexibility. It also implies robustness: we provide theoretical bounds for Neural ODE risk using Gaussian process theory. Experiments on four open datasets demonstrate that our method, DeNOTS, outperforms existing approaches~ -- ~including recent Neural RDEs and state space models,~ -- ~achieving up to $20\%$ improvement in metrics. DeNOTS combines expressiveness, stability, and robustness, enabling reliable modelling in continuous-time domains.
Stable Robot Motions on Manifolds: Learning Lyapunov-Constrained Neural Manifold ODEs
Department of Computer and Information Sciences University of Konstanz（计算机与信息科学系康斯坦茨大学）；Department of Robotics, Mohamed bin Zayed University of Artificial Intelligence（机器人学系Mohamed bin Zayed人工智能大学）；Mechanical Engineering Department, New York University Abu Dhabi（机械工程系纽约大学阿布扎克分校）
Linear Stability Analysis of Physics-Informed Random Projection Neural Networks for ODEs
Modelling Engineering Risk and Complexity, Scuola Superiore Meridionale（工程风险与复杂性建模，南方高级学院）；Dept. of Electrical and Computer Engineering, Clarkson University（电气与计算机工程系，克林顿大学）；Department of Statistics, Athens University of Economics and Business（统计学系，雅典经济与商业大学）
