A Unified Data-Driven Framework for Efficient Scientific Discovery

2025-09-08

AI Summary

Addressing the prohibitively large search space and high computational cost in automated discovery of physical laws, this paper proposes a data-driven scientific discovery framework integrating dimensional analysis with Taylor series expansion. The method introduces latent-variable modeling and a two-stage symbolic regression strategy to construct a unified formula representation, reducing the search space from hundreds of millions to merely dozens of candidates. By embedding constraints from the Buckingham Π theorem, simplicity priors, and gradient-assisted parameter optimization, it significantly enhances physical consistency and convergence efficiency. Evaluated on 11 cross-disciplinary datasets spanning astronomy, physics, and chemistry, the framework successfully recovers and discovers key dimensionless numbers, partial differential equations, and critical parameters. Results demonstrate its high efficiency, broad applicability across domains, and strong generalization capability.

Technology Category

• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Web Mining and Content Analysis: Interdisciplinary science discovery with web data mining
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

Scientific discovery drives progress across disciplines, from fundamental physics to industrial applications. However, identifying physical laws automatically from gathered datasets requires identifying the structure and parameters of the formula underlying the data, which involves navigating a vast search space and consuming substantial computational resources. To address these issues, we build on the Buckingham $Π$ theorem and Taylor's theorem to create a unified representation of diverse formulas, which introduces latent variables to form a two-stage structure. To minimize the search space, we initially focus on determining the structure of the latent formula, including the relevant contributing inputs, the count of latent variables, and their interconnections. Following this, the process of parameter identification is expedited by enforcing dimensional constraints for physical relevance, favoring simplicity in the formulas, and employing strategic optimization techniques. Any overly complex outcomes are refined using symbolic regression for a compact form. These general strategic techniques drastically reduce search iterations from hundreds of millions to just tens, significantly enhancing the efficiency of data-driven formula discovery. We performed comprehensive validation to demonstrate FIND's effectiveness in discovering physical laws, dimensionless numbers, partial differential equations, and uniform critical system parameters across various fields, including astronomy, physics, chemistry, and electronics. The excellent performances across 11 distinct datasets position FIND as a powerful and versatile tool for advancing data-driven scientific discovery in multiple domains.

Problem

• Automatically identifying physical laws from datasets
• Reducing vast search space and computational resources
• Discovering formulas across multiple scientific disciplines

Innovation

• Unified representation using Buckingham and Taylor theorems
• Two-stage structure with latent variables for efficiency
• Dimensional constraints and symbolic regression for simplification