# Parameter-Aware Ensemble SINDy for Interpretable Symbolic SGS Closure

arXiv: https://arxiv.org/abs/2508.14085 · HTML: https://mlsanity.com/paper/2508.14085/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 33 references that are in the map.
- First posted on arXiv 13 Aug 2025.

## Builds on (most cited first, 7 of 7)

- [Weak SINDy For Partial Differential Equations](https://mlsanity.com/paper/2007.02848/) (2020)
- [Deep symbolic regression for physics guided by units constraints: toward the automated discovery of physical laws](https://mlsanity.com/paper/2303.03192/) (2023)
- [Reduced order modeling of parametrized systems through autoencoders and SINDy approach: continuation of periodic solutions](https://mlsanity.com/paper/2211.06786/) (2022)
- [Deep Reinforcement Learning for Turbulence Modeling in Large Eddy Simulations](https://mlsanity.com/paper/2206.11038/) (2022)
- [Streaming Compression of Scientific Data via weak-SINDy](https://mlsanity.com/paper/2308.14962/) (2023)
- [Mesh-free sparse identification of nonlinear dynamics](https://mlsanity.com/paper/2505.16058/) (2025)
- [GN-SINDy: Greedy Sampling Neural Network in Sparse Identification of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/2405.08613/) (2024)

## Abstract (arXiv)

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 τSGS = 0.1604·Delta2left(fracpartial barupartial xright)2 with the SINDy-discovered Smagorinsky constant CsSINDy ≈ 0.4005 without predefined closure assumptions, recovering Smagorinsky-type structure directly from data. The discovered model achieves R2 = 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.