A Novel Tensor Product-Based Neural Network for Solving Partial Differential Equations
This paper presents the Tensor Product Network (TPNet), a novel neural architecture for efficient and accurate function approximation and PDE solving. The core of the proposal involves constructing the solution explicitly as a linear combination of basis functions integrated into the network, with coefficients determined by a direct least-squares solve, thereby bypassing traditional gradient-based training. The key methodological contribution include: (1) an efficient tensor-product scheme that generates multi-dimensional basis functions from combinations of two sets of subnetwork outputs, significantly reducing model complexity and parameter count while maintaining expressivity; (2) a bl...
| Authors | Qihong Yang, Yangtao Deng, Qiaolin He et al. |
|---|---|
| Primary category | cs.LG |
| Published | 28 May 2026 |
| Last updated at source | 28 May 2026 |
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