物理定律生态学：将多机制生态的映射作为数据驱动科学发现的第零步

中文摘要 AI 辅助

每种数据驱动的方程发现方法都（隐含地且未经验证地）假设目标系统遵循单一支配定律（$K{=}1$）。在此，我们表明这一假设是限制多机制系统中科学发现的主要瓶颈，并引入物理定律生态学（Physical Law Ecology）框架，该框架将$K^*$（共存独立机制的数量）本身作为首个需要从数据中确定的量。该框架自动挖掘一组拓扑上不同的候选方程池，在参数空间上构建连续的支配权重场，并发现支配机制演替的解析演化定律——可选单调性约束用于编码不可逆物理过程。在四个不相关的系统（弹性体力学、池沸腾、星系动力学和液滴蒸发）中，BIC一致地识别出$K^*{=}3$个独立的支配拓扑。应用于163个SPARC星系（3269个空间分辨测量），该框架自主恢复出三个引力定律，其共存为反对MOND的单一普适加速度假说提供了证据（$p<10^{-34}$）。在工程应用中，多定律加权预测相比单方程基线将误差降低了67-72%，同时保持完全可解释性。通过将$K^*$的确定确立为科学发现的第零步——先于且独立于方程搜索——这项工作开辟了一个与现有符号回归正交的方向：不是寻找更好的方程，而是映射支配复杂系统的机制生态。

英文摘要

Every data-driven equation discovery method assumes (implicitly and without verification) that the target system obeys a single governing law ($K{=}1$). Here we show that this assumption is the primary bottleneck limiting scientific discovery in multi-mechanism systems, and introduce Physical Law Ecology, a framework that makes $K^*$ (the number of coexisting independent mechanisms) itself the first quantity to be determined from data. The framework automatically mines a pool of topologically distinct candidate equations, constructs a continuous dominance weight field across parameter space, and discovers analytic evolution laws governing mechanism succession---with optional monotonicity constraints encoding irreversible physics. Across four unrelated systems (elastomer mechanics, pool boiling, galactic dynamics, and droplet evaporation), BIC consistently identifies $K^*{=}3$ independent governing topologies. Applied to 163 SPARC galaxies (3,269 spatially resolved measurements), the framework autonomously recovers three gravitational laws whose coexistence provides evidence against the single-universal-acceleration hypothesis of MOND ($p<10^{-34}$). In engineering applications, multi-law weighted prediction reduces error by 67-72\% over single-equation baselines while retaining full interpretability. By establishing the determination of $K^*$ as the zeroth step of scientific discovery-prior to and independent of equation search---this work opens a direction orthogonal to existing symbolic regression: not finding better equations, but mapping the ecology of mechanisms that govern complex systems.

发表机构

• School of Information Science and Technology, Nantong University（南通大学信息科学与技术学院）
• School of Artificial Intelligence and Computer Science, Nantong University（南通大学人工智能与计算机学院）

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