arXiv subjects

Mingkun Xia

Publications and source records attributed to Mingkun Xia.

3 recordsLinked to original sources

arXiv2026

Skin friction prediction for attached flows based on two-dimensional inviscid solutions

Boundary layer theory and its analytical methods for skin friction coefficients provide an important basis for aerodynamic analysis. However, classical analytical formulas are mostly limited to flat-plate flows. High-fidelity numerical simulations are not only computationally expensive but also yield predictions that are highly sensitive to physical models, numerical schemes, and grid resolution. To overcome these limitations, symbolic AI opens a new pathway to discover novel laws of complex physical systems from data. Using limited data from surface solutions of the Euler equations and the skin friction coefficient from viscous flows over airfoils, we employ symbolic regression to progressively discover a generalizable, interpretable analytical formula chain for fast skin friction prediction in subsonic and supersonic attached flows. From the perspective of physical mechanisms, the discovered analytical expression chain reveals scaling laws for skin friction at different Mach numbers: the basic form captures the logarithmic decay of skin friction along the streamwise direction in the turbulent boundary layer; the inclusion of a pressure coefficient correction term quantifies the effect of surface pressure variation; and the Mach number correction term evolves with flow regimes, transitioning from the compressibility correction term in subsonic regimes to the thermodynamic effects term in supersonic and hypersonic regimes. This knowledge chain exhibits a unified structure across different Mach numbers, and omitting the correction terms under certain conditions recovers classical theoretical forms, further demonstrating its physical consistency. Validation against typical geometries shows that this analytical formula chain achieves a low average integrated skin friction drag prediction error, with good generalization capability across different freestream conditions and geometric shapes.

physics.flu-dyn↗

arXiv2026

Data-driven Progressive Discovery of Physical Laws

Symbolic regression is a powerful tool for knowledge discovery, enabling the extraction of interpretable mathematical expressions directly from data. However, conventional symbolic discovery typically follows an end-to-end, "one-step" process, which often generates lengthy and physically meaningless expressions when dealing with real physical systems, leading to poor model generalization. This limitation fundamentally stems from its deviation from the basic path of scientific discovery: physical laws do not exist in a single form but follow a hierarchical and progressive pattern from simplicity to complexity. Motivated by this principle, we propose Chain of Symbolic Regression (CoSR), a novel framework that models the discovery of physical laws as a chain of symbolic knowledge. This knowledge chain is formed by progressively combining multiple knowledge units with clear physical meanings along a specific logic, ultimately enabling the precise discovery of the underlying physical laws from data. CoSR fully recapitulates the progressive discovery path from Kepler's third law to the law of universal gravitation in classical mechanics, and is applied to three types of problems: turbulent Rayleigh-Benard convection, viscous flows in a circular pipe, and laser-metal interaction, demonstrating its ability to improve classical scaling theories. Finally, CoSR showcases its capability to discover new knowledge in the complex engineering problem of aerodynamic coefficients scaling for different aircraft.

cs.LG↗

arXiv2025

Hierarchical Dimensionless Learning (Hi-{\pi}): A physics-data hybrid-driven approach for discovering dimensionless parameter combinations

Dimensional analysis provides a universal framework for reducing physical complexity and reveal inherent laws. However, its application to high-dimensional systems still generates redundant dimensionless parameters, making it challenging to establish physically meaningful descriptions. Here, we introduce Hierarchical Dimensionless Learning (Hi-{\pi}), a physics-data hybrid-driven method that combines dimensional analysis and symbolic regression to automatically discover key dimensionless parameter combination(s). We applied this method to classic examples in various research fields of fluid mechanics. For the Rayleigh-B\'enard convection, this method accurately extracted two intrinsic dimensionless parameters: the Rayleigh number and the Prandtl number, validating its unified representation advantage across multiscale data. For the viscous flows in a circular pipe, the method automatically discovers two optimal dimensionless parameters: the Reynolds number and relative roughness, achieving a balance between accuracy and complexity. For the compressibility correction in subsonic flow, the method effectively extracts the classic compressibility correction formulation, while demonstrating its capability to discover hierarchical structural expressions through optimal parameter transformations.

physics.flu-dyn↗