Year: 2026
Type: preprint
Abstract: We propose a Sparsely Connected Rank-Inspired Neural Network (SCRINN) for function approximation and the numerical solution of partial differential equations (PDEs). By introducing a structured sparse connectivity architecture and an orthogonality- and normalization-guided loss function, SCRINN constructs an approximately orthonormal neural basis while promoting progressive rank growth of its evaluation matrix and reducing the number of trainable parameters. A two-stage framework is developed, in which an approximately orthonormal neural basis is first constructed, and the output weights are subsequently determined using least-squares methods. Numerical experiments on function approximation and a variety of steady-state, time-dependent, and nonlinear PDEs demonstrate that SCRINN consistently achieves high approximation accuracy with substantially lower training costs. The code is publicly available on GitHub.
Source: arXiv (Cornell University)
Authors: Huang, Yunqing, Su, Wu, Yi, Nianyu, Yin, Peimeng
Institutions: Xiangtan University, The University of Texas at El Paso
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Award: G4534188866
OpenAlex ID: W7214674399