Parameter-Aware Ensemble SINDy for Interpretable Symbolic SGS Closure

Abstract

This work designs a scalable, parameter-aware sparse regression framework for discovering interpretable partial differential equations and subgrid-scale closures from multi-parameter simulation data. Building on SINDy (Sparse Identification of Nonlinear Dynamics), the approach addresses key limitations through four enhancements. First, symbolic parameterisation enables physical parameters to vary within unified regression. Second, the Dimensional Similarity Filter enforces unit consistency while reducing candidate libraries. Third, memory-efficient Gram-matrix accumulation enables batch processing of large datasets. Fourth, ensemble consensus with coefficient stability analysis ensures robust model identification. Validation on canonical one-dimensional benchmarks demonstrates consistent discovery of governing equations across parameter ranges. Applied to filtered Burgers datasets, the framework autonomously discovers the SGS closure $τ_{\mathrm{SGS}} = 0.1604\cdotΔ^2\left(\frac{\partial \bar{u}}{\partial x}\right)^2$ with the SINDy-discovered Smagorinsky constant $C_s^{\text{SINDy}} \approx 0.4005$ without predefined closure assumptions, recovering Smagorinsky-type structure directly from data. The discovered model achieves $R^2 = 0.885$ across filter scales and demonstrates improved prediction accuracy compared to classical SGS closures. The ability of the framework to identify physically meaningful SGS forms and calibrate coefficients offers a complementary approach to existing turbulence modelling methods, contributing to the broader field of data-driven turbulence closure discovery.