A machine learning-based solid boundary treatment for meshfree particle methods

Meshfree particle methods, such as Moving Particle Semi-Implicit (MPS) and Smoothed Particle Hydrodynamics (SPH), face difficulties in treating solid boundaries, where kernel truncation can lead to errors and instabilities. Traditional boundary treatments, such as the ghost particle method, restore kernel completeness but can add to computational cost and complexity, especially for irregular geometries. We propose a physics-guided machine learning (ML) framework that directly predicts boundary correction terms for particle approximations, eliminating the need for ghost particles or analytical corrections. The framework is based on a hybrid convolutional neural network–multilayer perceptron (CNN–MLP) trained on physics-guided features that capture local geometry, particle states, and kernel properties. Once trained, it provides boundary contributions across all spatial differential operators, including gradients, divergences, and Laplacians. The approach is demonstrated with MPS but is readily extensible to other particle methods. Tests with predefined fields, unsteady diffusion, and incompressible Navier–Stokes flows demonstrate an accuracy comparable to that of ghost-particle methods with the potential to reduce computational overhead. The model generalizes well to unseen geometries, flow conditions, and particle distributions, including dynamically evolving domains. This work establishes a flexible, physics-guided ML paradigm for boundary treatment in particle-based PDE solvers.