Physical Law Ecology: mapping multi-mechanism ecologies as the zeroth step of data-driven scientific discovery

2026-09-08

AI Summary

该研究针对多机制系统科学发现的瓶颈，提出物理定律生态学框架，通过数据确定共存独立机制数量，自动挖掘候选方程并构建参数空间中的主导权重场。

Abstract

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.

Problem

• data-driven equation discovery
• multi-mechanism systems
• independent mechanisms
• Physical Law Ecology
• scientific discovery

Innovation

• Physical Law Ecology
• multi-mechanism systems
• independent mechanisms
• dominance weight field
• analytic evolution laws