Hierarchical rank-evolving representation for physics-informed neural networks
Recently, tensor-based physics-informed neural networks (T-PINNs) have received increasing attention. However, existing T-PINNs still face a fundamental challenge: they mainly rely on pre-specified low-rank tensor decompositions with manually tuned ranks, which limits their ability to capture the underlying structures of multivariate solution functions and hinders their practical deployment. To address this challenge, we propose a hierarchical rank-evolving (abbreviated as HRE) representation for multivariate functions, which endows us to faithfully capture the underlying structure of the targeted multivariate function accompanying with automatic rank determination. Concretely, in the hie...
| Authors | Ruoyang Su, Xi-Le Zhao, Kun Li et al. |
|---|---|
| Primary category | cs.LG |
| Published | 10 August 2026 |
| Last updated at source | 10 August 2026 |
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