Data-driven Progressive Discovery of Physical Laws
Mingkun Xia, Weiwei Zhang

TL;DR
This paper introduces CoSR, a hierarchical symbolic regression framework that models the scientific discovery process as a progressive chain, improving interpretability and accuracy in discovering physical laws from data.
Contribution
It proposes a novel knowledge chain approach for symbolic regression that mimics scientific discovery, enabling hierarchical and interpretable physical law extraction.
Findings
Successfully recapitulates classical physical laws from data.
Improves scaling theories in fluid dynamics and laser-metal interactions.
Discovers new engineering knowledge in aircraft aerodynamics.
Abstract
Symbolic regression is a powerful tool for knowledge discovery, enabling the extraction of interpretable mathematical expressions directly from data. However, conventional symbolic discovery typically follows an end-to-end, "one-step" process, which often generates lengthy and physically meaningless expressions when dealing with real physical systems, leading to poor model generalization. This limitation fundamentally stems from its deviation from the basic path of scientific discovery: physical laws do not exist in a single form but follow a hierarchical and progressive pattern from simplicity to complexity. Motivated by this principle, we propose Chain of Symbolic Regression (CoSR), a novel framework that models the discovery of physical laws as a chain of symbolic knowledge. This knowledge chain is formed by progressively combining multiple knowledge units with clear physical…
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Taxonomy
TopicsModel Reduction and Neural Networks · Machine Learning in Materials Science · Evolutionary Algorithms and Applications
