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PreprintCC BY 4.0arXiv

Sparsely connected rank-inspired neural network

  • Yunqing Huang
  • Wu Su
  • Nianyu Yi
  • Peimeng Yin
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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.

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Cite

BibTeXRIS
BibTeX
@misc{huang2026sparsely,
  title = {{Sparsely connected rank-inspired neural network}},
  author = {Yunqing Huang and Wu Su and Nianyu Yi and Peimeng Yin},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.30750},
  eprint = {2609.30750},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.30750},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Sparsely connected rank-inspired neural network
AU  - Yunqing Huang
AU  - Wu Su
AU  - Nianyu Yi
AU  - Peimeng Yin
PY  - 2026
DA  - 2026/09/25
PB  - arXiv
DO  - 10.48550/arxiv.2609.30750
UR  - https://arxiv.org/abs/2609.30750
AB  - 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.
ER  -