A Physics-Informed Machine Learning Framework for Solid Boundary Treatment in Meshfree Particle Methods

Abstract

Meshfree particle methods, such as Smoothed Particle Hydrodynamics (SPH) and the Moving Particle Semi-Implicit (MPS) method, are widely used to simulate complex free-surface and multiphase flows. A key challenge in these methods is the treatment of solid boundaries, where kernel truncation causes errors and instabilities. Traditional treatments, such as ghost particles and semi-analytical wall corrections, restore kernel completeness but add significant computational cost and complexity, especially for irregular geometries. We propose a physics-informed 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-informed features that capture local geometry, particle states, and kernel properties. Once trained, it provides consistent 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 such as SPH. Tests with predefined fields, unsteady diffusion, and incompressible Navier-Stokes flows demonstrate accuracy comparable to that of ghost-particle methods while reducing computational overhead. The model generalizes well to unseen geometries, flow conditions, and particle distributions, including dynamically evolving domains. This work establishes a flexible, physics-informed ML paradigm for boundary treatment in particle-based PDE solvers, improving both accuracy and scalability across a broad class of meshfree methods.