A Unified Data-Driven Framework for Efficient Scientific Discovery

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 $\Pi$ 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.