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Data-driven kernel selection in Smoothed Particle Hydrodynamics using machine learning: automated hyperparameter optimization for heat conduction problems
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DOI：10.1007/s00366-026-02354-w.png)
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Abstract
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The selection of smoothing kernel functions and support parameters remains a critical challenge in Smoothed Particle Hydrodynamics (SPH), directly affecting the accuracy, stability, and computational efficiency of simulations. Despite its importance, this process is still largely based on empirical tuning or exhaustive parameter sweeps, limiting reproducibility and scalability. In this work, a comprehensive data-driven framework for automated SPH configuration was proposed, integrating machine learning techniques for hyperparameter selection in steady-state and transient diffusion problems. One- and two-dimensional SPH formulations are implemented to solve the Poisson and heat conduction equations under Dirichlet and Neumann boundary conditions, considering multiple kernel functions. To identify optimal configurations, supervised learning models including Extreme Learning Machine (ELM), Multilayer Perceptron (MLP), Random Forest (RF), and Extreme Gradient Boosting (XGBoost), are trained on a large dataset generated from 8,028 SPH simulations. These models predict the most suitable kernel function for a given physical scenario. The results show that ensemble-based models (Random Forest and XGBoost) achieve prediction accuracies above 93% across all scenarios, exceeding 97% in two-dimensional cases, and reaching up to 99.4%, while neural network baselines (ELM and MLP) reach up to 96.6%. Cohen’s Kappa coefficients above 0.92 for the ensemble-based models confirm strong agreement beyond chance. SHAP-based feature importance analysis further demonstrates that the models learned physically grounded decision boundaries consistent with the SPH formulation. The proposed framework reduces computational time by up to five orders of magnitude in transient two-dimensional cases, eliminating the need for exhaustive parameter exploration while maintaining high numerical accuracy. The framework provides a robust, scalable, and generalizable strategy for automated SPH configuration, establishing a foundation for future extension to more complex problems, including multiphase flows, fluid–structure interaction, and coupled thermo-mechanical systems, subject to dedicated retraining and validation.
Keywords:
Smoothed Particle Hydrodynamics
Machine learning
Kernel selection
Heat conduction
Hyperparameter optimization
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