ASP-Assisted Symbolic Regression: Uncovering Hidden Physics in Fluid Mechanics

TL;DR

This paper applies symbolic regression to fluid mechanics data to derive interpretable physical models and introduces a hybrid SR/ASP framework to ensure physical plausibility.

Contribution

It presents a novel hybrid SR/ASP approach that combines data-driven symbolic regression with domain knowledge constraints for fluid mechanics modeling.

Findings

Derived symbolic equations accurately model 3D laminar flow.

The hybrid SR/ASP framework ensures physical plausibility of models.

Models show excellent agreement with analytical solutions.

Abstract

Symbolic Regression (SR) offers an interpretable alternative to conventional Machine-Learning (ML) approaches, which are often criticized as ``black boxes''. In contrast to standard regression models that require a prescribed functional form, SR constructs expressions from a user-defined set of mathematical primitives, enabling the automated discovery of compact formulas that fit the data and reveal underlying physical relationships. In fluid mechanics, where understanding the underlying physics is as crucial as predictive accuracy, this study applies SR to model three-dimensional (3D) laminar flow in a rectangular channel, focusing on the axial velocity and pressure fields. Compact symbolic equations were derived from numerical simulation data, accurately reproducing the expected parabolic velocity profile and linear pressure drop, and showing excellent agreement with analytical solutions from the literature. To address the limitation that purely data-driven SR models may overlook domain-specific constraints, an innovative hybrid framework that integrates SR with Answer Set Programming (ASP) is also introduced. This integration combines the generative power of SR with the declarative reasoning capabilities of ASP, ensuring that derived equations remain both statistically accurate and physically plausible. The proposed SR/ASP methodology demonstrates the potential of combining data-driven and knowledge-representation approaches to enhance interpretability, reliability, and alignment with physical principles in fluid dynamics and related domains.