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

Unlike conventional Machine-Learning (ML) approaches, often criticized as "black boxes", Symbolic Regression (SR) stands out as a powerful tool for revealing interpretable mathematical relationships in complex physical systems, requiring no a priori assumptions about models' structures. Motivated by the recognition that, in fluid mechanics, an understanding of the underlying flow physics is as crucial as accurate prediction, this study applies SR to model a fundamental three-dimensional (3D) incompressible flow in a rectangular channel, focusing on the (axial) velocity and pressure fields under laminar conditions. By employing the PySR library, compact symbolic equations were derived directly from numerical simulation data, revealing key characteristics of the flow dynamics. These equations not only approximate the parabolic velocity profile and pressure drop observed in the studied fluid flow, but also perfectly coincide with analytical solutions from the literature. Furthermore, we propose an innovative approach that integrates SR with the knowledge-representation framework of Answer Set Programming (ASP), combining the generative power of SR with the declarative reasoning strengths of ASP. The proposed hybrid SR/ASP framework ensures that the SR-generated symbolic expressions are not only statistically accurate, but also physically plausible, adhering to domain-specific principles. Overall, the study highlights two key contributions: SR's ability to simplify complex flow behaviours into concise, interpretable equations, and the potential of knowledge-representation approaches to improve the reliability and alignment of data-driven SR models with domain principles. Insights from the examined 3D channel flow pave the way for integrating such hybrid approaches into efficient frameworks, [...] where explainable predictions and real-time data analysis are crucial.