Work

An Intelligent SPH Framework Based on Machine-Learned Residual Correction for Elliptic PDEs

Year: 2025

Type: article

Abstract: We present an intelligent, non-intrusive framework to enhance the performance of Symmetric Smoothed Particle Hydrodynamics (SSPH) for elliptic partial differential equations, focusing on the linear and nonlinear Poisson equations. Classical Smoothed Particle Hydrodynamics methods, while meshfree, suffer from discretization errors due to kernel truncation and irregular particle distributions. To address this, we employ a machine-learning-based residual correction, where a neural network learns the difference between the SSPH solution and a reference solution. The predicted residuals are added to the SSPH solution, yielding a corrected approximation with significantly reduced errors. The method preserves numerical stability and consistency while systematically reducing errors. Numerical results demonstrate that the proposed approach outperforms standard SSPH.

Source: Algorithms

DOI: 10.3390/a18120803

Authors: Ammar Qarariyah, Tianhui Yang, Fang Deng

Institutions: Bethlehem University, Xi’an University of Posts and Telecommunications, North China University of Water Resources and Electric Power

Language: English

Topic: Fluid Dynamics Simulations and Interactions

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,930

Funders: National Natural Science Foundation of China, Natural Science Foundation of Shandong Province