Discovering like a scientist: Literature-informed dimensionless learning for physical closure of data-driven equations
Abstract
Data-driven methods can recover compact equations, yet the physical dependence of their coefficients across operating conditions often remains unresolved. Dimensionless groups can explain this variation, but selecting relevant groups from the many dimensionally admissible combinations remains challenging. Here, we introduce a knowledge-guided framework for dimensionless learning, called π-former. It learns patterns of variable association and exponent assignment from a corpus of 1,288 established dimensionless groups. Under exact dimensional constraints, the model proposes interpretable basic groups whose combinations are optimized against observations. Across seven physical problems, the framework identifies predictive dimensionless coordinates within seconds. Integration with equation discovery further expresses condition-dependent coefficients through these coordinates, recovering established physical scalings in multi-condition simulations. Applied to experimental measurements of evaporation-driven wetting, the framework discovers dimensionless coordinates and uses them to construct a unified trajectory equation. The resulting model generalizes to held-out conditions across liquids and initial volumes, outperforming existing empirical models. These results establish dimensionless learning as a transferable bridge between accumulated scientific knowledge and data-driven equation discovery, enabling artificial intelligence to uncover physically meaningful laws from observations.
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BibTeX
@misc{xu2026discovering,
title = {{Discovering like a scientist: Literature-informed dimensionless learning for physical closure of data-driven equations}},
author = {Hao Xu and Tianhao Wu and Dongxiao Zhang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05780},
eprint = {2611.05780},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05780},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Discovering like a scientist: Literature-informed dimensionless learning for physical closure of data-driven equations
AU - Hao Xu
AU - Tianhao Wu
AU - Dongxiao Zhang
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.05780
UR - https://arxiv.org/abs/2611.05780
AB - Data-driven methods can recover compact equations, yet the physical dependence of their coefficients across operating conditions often remains unresolved. Dimensionless groups can explain this variation, but selecting relevant groups from the many dimensionally admissible combinations remains challenging. Here, we introduce a knowledge-guided framework for dimensionless learning, called π-former. It learns patterns of variable association and exponent assignment from a corpus of 1,288 established dimensionless groups. Under exact dimensional constraints, the model proposes interpretable basic groups whose combinations are optimized against observations. Across seven physical problems, the framework identifies predictive dimensionless coordinates within seconds. Integration with equation discovery further expresses condition-dependent coefficients through these coordinates, recovering established physical scalings in multi-condition simulations. Applied to experimental measurements of evaporation-driven wetting, the framework discovers dimensionless coordinates and uses them to construct a unified trajectory equation. The resulting model generalizes to held-out conditions across liquids and initial volumes, outperforming existing empirical models. These results establish dimensionless learning as a transferable bridge between accumulated scientific knowledge and data-driven equation discovery, enabling artificial intelligence to uncover physically meaningful laws from observations.
ER -