← 研踪 PaperTrailarXiv:2611.04642 · v1
Stabilizing Neural Emulation of Spatiotemporal Physical Dynamics through Denoising Koopman Latent Dynamics
首次提交 2026-11-03 18:32
版本更新 2026-11-03 18:32
雷达观测 2026-11-04 23:39
摘要
Koopman operator theory provides a principled framework for reduced-order modeling of nonlinear spatiotemporal dynamics through linear evolution in an observable space. In practice, however, learned finite-dimensional representations are typically approximately invariant, causing unresolved dynamics and accumulated closure errors. Recent approaches, inspired by the Mori-Zwanzig formalism, address these effects through deterministic memory or closure modeling, yet robust extrapolation beyond the training horizon remains challenging. Here, we propose KoopFlow, an efficient prediction-correction framework based on the key insight that finite-dimensional Koopman error accumulation can be reinterpreted as a progressive distributional degradation process. Accordingly, KoopFlow treats Koopman predictions as noisy intermediate estimates, which are then transported toward the target latent distribution through a generative model, thereby mitigating accumulated errors while retaining computational efficiency and temporal flexibility. Moreover, we reveal a non-monotonic relationship between Koopman spectral coherence and predictive accuracy. Experiments across diverse nonlinear dynamical systems demonstrate improved long-horizon prediction accuracy and stability over representative baselines, particularly beyond the training horizon.
作者备注：21 pages,12 figures
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v1 · 2026-11-03 18:32 · 最新观测版本
Stabilizing Neural Emulation of Spatiotemporal Physical Dynamics through Denoising Koopman Latent Dynamics
Koopman operator theory provides a principled framework for reduced-order modeling of nonlinear spatiotemporal dynamics through linear evolution in an observable space. In practice, however, learned finite-dimensional representations are typically approximately invariant, causing unresolved dynamics and accumulated closure errors. Recent approaches, inspired by the Mori-Zwanzig formalism, address these effects through deterministic memory or closure modeling, yet robust extrapolation beyond the training horizon remains challenging. Here, we propose KoopFlow, an efficient prediction-correction framework based on the key insight that finite-dimensional Koopman error accumulation can be reinterpreted as a progressive distributional degradation process. Accordingly, KoopFlow treats Koopman predictions as noisy intermediate estimates, which are then transported toward the target latent distribution through a generative model, thereby mitigating accumulated errors while retaining computational efficiency and temporal flexibility. Moreover, we reveal a non-monotonic relationship between Koopman spectral coherence and predictive accuracy. Experiments across diverse nonlinear dynamical systems demonstrate improved long-horizon prediction accuracy and stability over representative baselines, particularly beyond the training horizon.
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