Physical Law Ecology: mapping multi-mechanism ecologies as the zeroth step of data-driven scientific discovery
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.
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BibTeX
@misc{bian2026physical,
title = {{Physical Law Ecology: mapping multi-mechanism ecologies as the zeroth step of data-driven scientific discovery}},
author = {Xiongheng Bian and Xiangyu Cui and Ma Feng and Xiaoyan Shen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08536},
eprint = {2609.08536},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08536},
}
RIS
TY - UNPB
TI - Physical Law Ecology: mapping multi-mechanism ecologies as the zeroth step of data-driven scientific discovery
AU - Xiongheng Bian
AU - Xiangyu Cui
AU - Ma Feng
AU - Xiaoyan Shen
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08536
UR - https://arxiv.org/abs/2609.08536
AB - 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.
ER -