物理学与因果约束的离散时间神经模型对湍流动力系统的研究
Physics constraints and response validation in discrete-time reduced-order modeling: from idealized turbulent systems to climate dynamics
AI总结：
本文提出了一种基于数据构建湍流动力系统物理和因果约束神经模型的框架，通过有限时间流映射和因果约束，准确捕捉了稳态统计和外部扰动响应。
摘要：
我们提出了一种框架，用于从数据构建湍流动力系统的物理和因果约束神经模型。我们首先制定了一个具有严格能量守恒非线性的有限时间流映射，以稳定地建模时间离散轨迹。然后施加因果约束以抑制跨自由度的虚假相互作用。所得到的神经模型能够准确捕捉稳态统计和对小规模和大规模外部强迫的响应。我们展示了该框架在随机Charney-DeVore方程和对称破坏的Lorenz-96系统上的应用。该框架广泛适用于从观测数据中进行湍流动力系统的降阶建模。
英文摘要：
A central challenge across science and engineering is to build data-driven reduced-order models of turbulent dynamical systems that reproduce stationary statistics, predict responses to external perturbations, and remain practical for real-world applications. To this end, we introduce an abstract discrete-time formulation of turbulent dynamical systems with exact energy-conserving nonlinearities. Parameterizing this structure with neural networks yields stable, physics-constrained reduced-order models. We then use the fluctuation-dissipation theorem (FDT) to validate the emulators' forced responses from unperturbed data alone, testing models beyond stationary statistics. The FDT also identifies candidate direct causal links, which are used as regularization terms only when they pass validation. We first test the framework on two idealized models of geophysical turbulence: the proposed emulators reproduce stationary statistics and accurately predict responses to weak and strong forcings, despite being trained solely on unperturbed data. We then move beyond idealized systems to model tropical climate dynamics from reanalysis data, where data scarcity, partial observability, and sensitivity to choices of stochastic parameterizations become central challenges. The resulting physics-constrained model reproduces key statistics of the El Niño-Southern Oscillation (ENSO) and qualitatively captures its cumulative responses to perturbations; augmenting it with a non-Markovian stochastic closure substantially improves quantitative agreement with the FDT benchmark. This response-validated model is then used to characterize long-term causal drivers of ENSO variability. The proposed methodology establishes a modular framework for stable reduced-order models capable of probing causal mechanisms in realistic, partially observed turbulent systems.
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