提出复杂性度量的统一框架，揭示数据驱动方法如何逼近经典理论理想。
Compression, Regularity, Randomness and Emergent Structure: Rethinking Physical Complexity in the Data-Driven Era
- 从规律、随机、复杂三维度构建统一框架，整合统计、算法与动力学测度。
- 发现不可计算性是核心挑战，现代方法如自编码器是实用近似。
- 适合关注物理信息人工智能与复杂系统建模的研究者阅读。
复杂性科学提供了多种量化不可预测性、结构与信息的度量方法，但尚未形成系统的概念组织。本文提出一个统一框架，将统计、算法与动力学度量置于规律性、随机性与复杂性三个轴上，置于同一概念空间中。我们分析了这些度量的计算可及性与近似性，揭示了不可计算性的深层挑战，并指出自编码器、潜在动力学模型、符号回归与物理信息神经网络等现代数据驱动方法，是经典复杂性理想的务实近似。潜在空间成为规律提取、噪声管理与结构化压缩交汇的操作场域，连接理论基础与高维系统中的实际建模。最后，文章展望了其对物理信息人工智能与复杂物理系统中AI引导发现的影响，强调经典复杂性问题仍是下一代科学建模的核心。
原文摘要 · Abstract (English)
Complexity science offers a wide range of measures for quantifying unpredictability, structure, and information. Yet, a systematic conceptual organization of these measures is still missing. We present a unified framework that locates statistical, algorithmic, and dynamical measures along three axes (regularity, randomness, and complexity) and situates them in a common conceptual space. We map statistical, algorithmic, and dynamical measures into this conceptual space, discussing their computational accessibility and approximability. This taxonomy reveals the deep challenges posed by uncomputability and highlights the emergence of modern data-driven methods (including autoencoders, latent dynamical models, symbolic regression, and physics-informed neural networks) as pragmatic approximations to classical complexity ideals. Latent spaces emerge as operational arenas where regularity extraction, noise management, and structured compression converge, bridging theoretical foundations with practical modeling in high-dimensional systems. We close by outlining implications for physics-informed AI and AI-guided discovery in complex physical systems, arguing that classical questions of complexity remain central to next-generation scientific modeling.
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