稀疏连接秩启发神经网络
Sparsely connected rank-inspired neural network
- Xiangtan University（湘潭大学）
- University of Texas at El Paso（埃尔帕索得克萨斯大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出稀疏连接秩启发神经网络（SCRINN），通过结构化稀疏连接和正交归一化损失构建近似正交基，结合两阶段最小二乘输出权重，高效求解函数逼近及多种PDE，精度高且训练成本低。
AI中文摘要：
我们提出了一种稀疏连接秩启发神经网络（SCRINN），用于函数逼近和偏微分方程（PDE）的数值求解。通过引入结构化稀疏连接架构以及由正交性和归一化指导的损失函数，SCRINN构建了近似正交的神经基，同时促进其评估矩阵的秩逐步增长，并减少了可训练参数的数量。我们开发了一个两阶段框架，首先构建近似正交的神经基，随后使用最小二乘法确定输出权重。针对函数逼近以及多种稳态、时间依赖和非线性PDE的数值实验表明，SCRINN在显著降低训练成本的同时，持续实现了高逼近精度。代码已在GitHub上公开提供。
英文摘要：
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.
