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

arXiv: https://arxiv.org/abs/2507.17777 · HTML: https://mlsanity.com/paper/2507.17777/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 47 references that are in the map.
- First posted on arXiv 22 Jul 2025.

## Builds on (most cited first, 6 of 6)

- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Interpretable Scientific Discovery with Symbolic Regression: A Review](https://mlsanity.com/paper/2211.10873/) (2022)
- [Integration of Neural Network-Based Symbolic Regression in Deep Learning for Scientific Discovery](https://mlsanity.com/paper/1912.04825/) (2019)
- [Can Large Language Models Transform Natural Language Intent into Formal Method Postconditions?](https://mlsanity.com/paper/2310.01831/) (2023)
- [Symbolic regression based genetic approximations of the Colebrook equation for flow friction](https://mlsanity.com/paper/1808.10394/) (2018)

## Built on by (most cited first, 1 of 1)

- [Aligning Perception, Reasoning, Modeling and Interaction: A Survey on Physical AI](https://mlsanity.com/paper/2510.04978/) (2025)

## Abstract (arXiv)

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.