发表机构
SOBIN Institute LLC（SOBIN研究所有限公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出最小一次性规范成本框架，证明预测精度可通过激活不同物理不确定性通道来选择所需精度的时域标度律，并在多尺度环面系统和Lorenz-84模型中验证了通道切换机制。
AI 中文摘要
必须分配多少精度，以及分配给哪些不确定性通道，才能满足预测要求？我们针对初始状态变量和持续强迫参数，制定了最小一次性规范成本。核心结果是，预测精度可以通过激活不同的物理不确定性通道，来选择该资源的时域标度律。在任何具有相同活跃通道的常见均匀尺度可分离体系中，改变固定容差仅需改变 $\cO(1)$ 比特的所需精度。一个可精确求解的多尺度环面系统表明，当更精细的精度激活一个扩张通道时，同一固定动力学和目标可以从 $B_N(\eps_c)=\Th(\log N)$ 切换到 $B_N(\eps_f)=\Th(N)$。随后，一个受迫的 Lorenz--84 计算在单一的双尺度诊断场中，于有限时域上数值实现了相同的通道切换机制：一个采样后的瞬态涡旋包络支持由大尺度强迫的相位速率控制的粗分支，而更精细的精度则激活指数敏感的大气自由度，并在解析窗口上产生线性化一次性成本的近似线性增加。因此，精度不仅能决定需要多少预测精度，还能决定哪个物理通道控制其随时域的增长。
英文摘要
How much precision must be allocated, and to which uncertainty channels, to meet a prediction requirement? We formulate a minimum one-shot specification cost over initial state variables and persistent forcing parameters. The central result is that prediction accuracy can select the horizon-scaling law of this resource by activating different physical uncertainty channels. Within any common uniformly scale-separable regime with the same active channels, changing a fixed tolerance changes the required precision by only $\cO(1)$ bits. An exactly solvable multiscale toral system shows that one fixed dynamics and target can nevertheless switch from $B_N(\eps_c)=\Th(\log N)$ to $B_N(\eps_f)=\Th(N)$ when finer accuracy activates an expanding channel. A forced Lorenz--84 calculation then realizes the same channel-switching mechanism numerically over finite horizons in a single two-scale diagnostic field: a sampled post-transient eddy envelope supports a coarse branch controlled by the phase rate of a large-scale forcing, whereas finer accuracy activates exponentially sensitive atmospheric degrees of freedom and produces an approximately linear increase of the linearized one-shot cost over the resolved window. Thus accuracy can determine not only how much predictive precision is required, but which physical channel controls its growth with horizon.
Comments14 pages, 6 figures
