9 citations · 13 across the 5 of their papers we have counts for
7 papers
Hierarchical rank-evolving representation for physics-informed neural networks
Ruoyang Su, Xi-Le Zhao, Kun Li +1
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…
Optimal Stirring Strategies for Passive Scalars in a Domain with a General Shape and No-Flux Boundary Condition
Sirui Zhu, Zhi Lin, Liang Li +1
Multiscale metrics such as negative Sobolev norms are effective for quantifying the degree of mixedness of a passive scalar field advected by an incompressible flow in the absence…
Minimum Width of Leaky-ReLU Neural Networks for Uniform Universal Approximation
Li'ang Li, Yifei Duan, Guanghua Ji +1
The study of universal approximation properties (UAP) for neural networks (NN) has a long history. When the network width is unlimited, only a single hidden layer is sufficient for…
Model order reduction for parameterized electromagnetic problems using matrix decomposition and deep neural networks
Xiao-Feng He, Liang Li, Stephane Lanteri +1
A non-intrusive model order reduction (MOR) method for solving parameterized electromagnetic scattering problems is proposed in this paper. A database collecting snapshots of high-…
Thick-Net: Parallel Network Structure for Sequential Modeling
Yu-Xuan Li, Jin-Yuan Liu, Liang Li +1
Recurrent neural networks have been widely used in sequence learning tasks. In previous studies, the performance of the model has always been improved by either wider or deeper str…
Machine Discovery of Partial Differential Equations from Spatiotemporal Data
Ye Yuan, Junlin Li, Liang Li +9
The study presents a general framework for discovering underlying Partial Differential Equations (PDEs) using measured spatiotemporal data. The method, called Sparse Spatiotemporal…
Fast OBDD Reordering using Neural Message Passing on Hypergraph
Feifan Xu, Fei He, Enze Xie +1
Ordered binary decision diagrams (OBDDs) are an efficient data structure for representing and manipulating Boolean formulas. With respect to different variable orders, the OBDDs' s…