Symbolic Regression for Learning Scale Transition Equations in Synthetic Fractal Surface Roughness

Aneesh Chatrathi, Zayan Hasan

Track: Short paper

Keywords: Symbolic Regression, Surface Roughness, Fractal Geometry, Coarse Graining, Multiscale Modeling, Machine Learning, Uncertainty Quantification

TL;DR: We use symbolic regression to derive interpretable scale-transition equations from synthetic fractal surface roughness data, enabling accurate and explainable multiscale modeling.

Abstract: Modeling surface roughness in materials science is a challenging multiscale problem, as surface textures often exhibit hierarchical (fractal-like) structure across multiple scales. In this work, we present a synthetic data-driven approach to studying scale transitions in surface roughness using fractal data generation and symbolic regression. We construct coarse-grained representations of synthetic fractal surfaces and apply symbolic regression to derive interpretable mathematical expressions that map fine-scale features to coarse-scale behavior. On controlled synthetic data, our approach achieves high predictive accuracy (R² near 1, low MSE), serving as a baseline validation. While the data is idealized, these results suggest that symbolic regression can capture scale-transition relationships in hierarchical surface structures and may also be able to support future efforts in data-driven multiscale modeling. This work highlights the potential of symbolic learning in accelerating modeling workflows for complex physical systems.

Supplementary: https://constructor.app/platform/research/public/project/mlmp-v3mg

Submission Number: 31