Neural-Integrated Meshfree (NIM) Method: A differentiable programming-based hybrid solver for computational mechanics

• DOI: 10.48550/arxiv.2311.12915
• Publication Date: 2023-01-01
• Authors: Honghui Du; Qizhi He
• Keywords: Solver; Meshfree methods

We present the neural-integrated meshfree (NIM) method, a differentiable programming-based hybrid approach within field of computational mechanics. NIM seamlessly integrates traditional physics-based discretization techniques with deep learning architectures. It employs approximation scheme, NeuroPU, to effectively represent solution by combining continuous DNN representations partition unity (PU) basis functions associated underlying spatial discretization. This neural-numerical hybridization not only enhances representation through functional space decomposition but also reduces both size model and need for gradient computations based on automatic differentiation, leading significant improvement in training efficiency. Under framework, we propose two truly solvers: strong form-based (S-NIM) local variational (V-NIM). In S-NIM solver, strong-form governing equation is directly considered loss function, while V-NIM solver Petrov-Galerkin that allows construction residuals arbitrary overlapping subdomains. ensures satisfaction physics preservation property. perform extensive numerical experiments stationary transient benchmark problems assess effectiveness proposed methods terms accuracy, scalability, generalizability, convergence properties. Moreover, comparative analysis other physics-informed machine demonstrates NIM, especially V-NIM, significantly accuracy efficiency end-to-end predictive capabilities.