Temporal Lifting as Latent-Space Regularization for Continuous-Time Flow Models in AI Systems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915757250576384 |
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| author | Camlin, Jeffrey |
| author_facet | Camlin, Jeffrey |
| contents | We present a latent-space formulation of adaptive temporal lifting for continuous-time dynamical systems. The method 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 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_09805 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Temporal Lifting as Latent-Space Regularization for Continuous-Time Flow Models in AI Systems Camlin, Jeffrey Machine Learning Artificial Intelligence 35Q30, 76D05, 65M70, 68T07, 68T27, 03D45 I.2.0 We present a latent-space formulation of adaptive temporal lifting for continuous-time dynamical systems. The method 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 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. |
| title | Temporal Lifting as Latent-Space Regularization for Continuous-Time Flow Models in AI Systems |
| topic | Machine Learning Artificial Intelligence 35Q30, 76D05, 65M70, 68T07, 68T27, 03D45 I.2.0 |
| url | https://arxiv.org/abs/2510.09805 |