A Physics-Informed Machine Learning Framework for Solid Boundary Treatment in Meshfree Particle Methods
Nariman Mehranfar, Ahmad Shakibaeinia
TL;DR
The paper tackles the boundary-treatment challenge in meshfree particle methods by introducing a physics-informed ML framework that learns boundary correction terms from ghost-particle data using a hybrid CNN–MLP architecture. This approach uses physics-inspired features to predict boundary contributions for multiple operators, ensuring consistency across number density, gradients, divergences, and Laplacians while reducing the computational burden associated with ghost particles. Demonstrations on predefined fields, diffusion, and incompressible Navier–Stokes flows show accuracy comparable to ghost-particle methods with improved efficiency and generalization to unseen geometries and dynamic domains. The proposed paradigm offers a scalable, flexible boundary-treatment strategy for particle-based PDE solvers and can be extended to SPH and 3D problems, enhancing accuracy and performance across meshfree 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.