Technology Category
Constraint Satisfaction and Optimization: Satisfiability Modulo TheoriesCognitive Modeling & Cognitive Systems: Symbolic RepresentationsComputer Vision: Visual Reasoning & Symbolic Representations
ASP-Assisted Symbolic Regression: Uncovering Hidden Physics in Fluid Mechanics
🤖 AI Summary
This work addresses the interpretable modeling of axial velocity and pressure fields in three-dimensional incompressible rectangular channel flow. We propose a novel framework integrating symbolic regression (SR) with answer set programming (ASP): PySR serves as the data-driven symbolic discovery engine, while ASP explicitly encodes physical constraints—namely, mass conservation and momentum balance—to verify and prune candidate expressions. Compared to purely data-driven SR, our approach substantially improves physical consistency and interpretability. Experiments demonstrate that the discovered symbolic expressions exactly recover the theoretical solutions: parabolic axial velocity distribution and linear pressure gradient decay, all in compact, dimensionally consistent forms. To our knowledge, this is the first systematic integration of ASP into the SR pipeline to enforce physical plausibility of fluid-dynamic equations, establishing a new paradigm for interpretable modeling of complex physical systems.
Technology Category
Application Category
📝 Abstract
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.
Problem
Research questions and friction points this paper is trying to address.
Discover interpretable equations for fluid flow dynamics
Combine symbolic regression with domain-specific physical principles
Enhance reliability of data-driven models in fluid mechanics
Innovation
Methods, ideas, or system contributions that make the work stand out.
Symbolic Regression for interpretable fluid dynamics equations
Hybrid SR/ASP framework ensures physical plausibility
PySR library derives equations from simulation data
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