Temporal Lifting as Latent-Space Regularization for Continuous-Time Flow Models in AI Systems
This method addresses stability issues in physics-informed neural networks and latent-flow architectures for AI systems, particularly for stiff or turbulent processes, though it appears incremental as it builds on existing regularization and representation-learning techniques.
The paper tackles the problem of near-singular behavior in continuous-time dynamical systems by introducing temporal lifting, a latent-space regularization method that smooths trajectories and preserves conservation laws, resulting in globally smooth trajectories for systems like the incompressible Navier-Stokes equations on a torus.
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 $t \mapsto τ(t)$ 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 $\mathbb{T}^3$ 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.