Temporal Lifting as Latent-Space Regularization for Continuous-Time Flow Models in AI Systems

2025/10/10 by Camlin, Jeffrey
#03D45 #35Q30 #65M70 #68T07 #68T27 #76D05 #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #I.2.0 #Machine Learning (cs.LG)

paper · doi:10.48550/arxiv.2510.09805

Abstract

We present a latent-space formulation of adaptive temporal reparametrization for continuous-time dynamical systems. The method, called *temporal lifting*, introduces a smooth monotone mapping t ↦ τ(t) that regularizes near-singular behavior of the underlying flow while preserving its conservation laws. In the lifted coordinate, trajectories such as those of the incompressible Navier-Stokes equations on the torus \mathbbT³ become globally smooth. From the standpoint of machine-learning dynamics, temporal lifting acts as a continuous-time normalization or time-warping operator that can stabilize physics-informed neural networks and other latent-flow architectures used in AI systems. The framework links analytic regularity theory with representation-learning methods for stiff or turbulent processes.

Citations

• Physics-informed machine learning
• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Neural Ordinary Differential Equations
• Sur le mouvement d'un liquide visqueux emplissant l'espace

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