Cluster-Weighted Training of Deep Surrogate Models for Subgrid Turbulent Transport

Abstract

Turbulence in the solar interior and atmosphere plays a crucial role in energy transport, yet modeling its subgrid-scale effects remains a major challenge. This study leverages machine learning (ML) models to predict components of the Reynolds stress tensor using high-resolution StellarBox simulations of the quiet Sun. Previously, we have compared a Multi-Layer Perceptron (MLP) and a 3D Convolutional Neural Network (CNN) against physics-based baselines to achieve a lower Mean Squared Error (MSE) and better generalization across various heights and depths in the solar atmosphere. To enhance learning, in this work, we investigate cluster-weighted training using K-Means and Hierarchical Agglomerative Clustering (HAC). By weighing the loss function based on cluster-specific prediction errors, we direct the model's attention to high-error regions. It significantly improves CNN performance, achieving 34% lower MSE and a significantly higher R2 score indicating that integrating deterministic clustering with ML is a promising technique for modeling subgrid turbulence, in particular, and regression in diverse environments, in general.