提出统一框架MNCIS，用动态高通滤波稳定湍流、AI与生物系统中的不稳定性。
Multi-Scale Negative Coupled Information Systems (MNCIS): A Unified Spectral Topology Framework for Stability in Turbulence, AI, and Biology
- 引入自适应谱负耦合（ASNC），作为状态依赖的高通滤波器抑制频谱边界熵积聚。
- 在3D纳维-斯托克斯模拟中保持柯尔莫戈洛夫-5/3幂律，无超黏性且稳定无粘极限。
- 适用于超深GNN训练、拓扑形态发生等场景，无需残差连接或人工正则化。
复杂动力系统常面临谱隙坍缩导致的结构性不稳定性，趋向于低维零模吸引子（如谱堆积或过度平滑）。基于近期全局适定性估计 [Hou, arXiv:2601.00638]，本文推广了多尺度负耦合信息系统（MNCIS）框架。我们提出全局稳定需依赖主动拓扑算子——自适应谱负耦合（ASNC），其作为状态相关的高通滤波器，惩罚谱边界处的熵积累。通过三类实现验证该统一框架：(1) 流体力学：在 $N=256^3$ 的三维纳维-斯托克斯湍流中，ASNC充当全局涡度自适应亚格点模型，稳定无粘极限并保持柯尔莫戈洛夫 $-5/3$ 惯性范围，无需人工超黏性；关键是在物理不稳定性线性增长阶段，算子处于休眠状态（γ≈0），仅作为条件性拓扑约束。(2) 人工智能：解决图神经网络（GNN）的过平滑问题，将ASNC作为无参拓扑约束，实现无需残差连接的64层超深网络训练，在 ogbn-arxiv 基准上维持特征方差恒定（σ² ≡ 1.0）。(3) 生物物理：在反应-扩散形态发生中，使图灵图案在高熵环境下抵抗扩散消散。结果表明，MNCIS框架提供了不依赖基底的拓扑判据，以区分可存活复杂系统与退化至热平衡的系统。
原文摘要 · Abstract (English)
Complex dynamical systems frequently encounter a recurrent structural instability: the collapse of the spectral gap, driving the system toward a low-dimensional "Zero-Mode Attractor" (e.g., spectral pile-up or over-smoothing). Building upon recent global well-posedness estimates [Hou, arXiv:2601.00638], this work generalizes the Multi-Scale Negative Coupled Information System (MNCIS) framework. We postulate that global stability requires an active topological operator - Adaptive Spectral Negative Coupling (ASNC) - functioning as a state-dependent high-pass filter that penalizes entropy accumulation at spectral boundaries. We validate this unified framework via three implementations: (1) Hydrodynamics: In 3D Navier-Stokes turbulence ($N=256^3$), ASNC acts as a global-enstrophy adaptive sub-grid scale (SGS) model, stabilizing the inviscid limit and preserving the Kolmogorov $-5/3$ inertial range without artificial hyper-viscosity. Crucially, we verify that the operator remains dormant ($γ\approx 0$) during the linear growth phase of physical instabilities, functioning strictly as a conditional topological clamp. (2) Artificial Intelligence: Addressing Over-smoothing in Graph Neural Networks (GNNs), we implement ASNC as a parameter-free topological constraint. Unlike baselines (e.g., DeepGCNs) relying on dense residual connections, our framework enables the training of ultra-deep 64-layer networks without residual connections, maintaining perfectly stationary feature variance ($σ^2 \equiv 1.0$) on the ogbn-arxiv benchmark. (3) Biological Physics: In reaction-diffusion morphogenesis, it stabilizes Turing patterns against diffusive washout in high-entropy regimes. Our results suggest that the MNCIS framework provides a base-independent topological condition for distinguishing viable complex systems from those collapsing into thermal equilibrium.
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