A Novel Tensor Product-Based Neural Network for Solving Partial Differential Equations

arXiv:2605.29688v1 Announce Type: new Abstract: 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 com

Source: arXiv cs.LG — read the full report at the original publisher.

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