5 citations · 8 across the 9 of their papers we have counts for
9 papers
LRX-PINN: A Layer-Resolving XNet Physics-Informed Neural Network with Integrated Cauchy Activations for Convection-Dominated Problems
Zihao Guo, Xin Li, Zhihong Xia
Convection-dominated convection-diffusion problems often develop thin layers, where the solution has sharp transition profiles and its derivatives are highly localized. This create…
CauchyNet: Compact and Data-Efficient Learning using Holomorphic Activation Functions
Hong-Kun Zhang, Xin Li, Sikun Yang +1
A novel neural network inspired by Cauchy's integral formula, is proposed for function approximation tasks that include time series forecasting, missing data imputation, etc. Hence…
Enhancing Neural Function Approximation: The XNet Outperforming KAN
Xin Li, Xiaotao Zheng, Zhihong Xia
XNet is a single-layer neural network architecture that leverages Cauchy integral-based activation functions for high-order function approximation. Through theoretical analysis, we…
XNet-Enhanced Deep BSDE Method and Numerical Analysis
Xiaotao Zheng, Xingye Yue, Zhihong Xia +1
Semilinear parabolic partial differential equations (PDEs) are fundamental to modeling complex dynamical systems across scientific domains. The Deep Backward Stochastic Differentia…
Complex Physics-Informed Neural Network
Chenhao Si, Ming Yan, Xin Li +1
We propose compleX-PINN, a novel physics-informed neural network (PINN) architecture incorporating a learnable activation function inspired by the Cauchy integral theorem. By optim…
Model Comparisons: XNet Outperforms KAN
Xin Li, Zhihong Jeff Xia, Xiaotao Zheng
In the fields of computational mathematics and artificial intelligence, the need for precise data modeling is crucial, especially for predictive machine learning tasks. This paper…
Resonant amplitude distribution of the Hilda asteroids and the free-floating planet flyby scenario
Jian Li, Zhihong Jeff Xia, Hanlun Lei +3
In some recent work, we provided a quantitative explanation for the number asymmetry of Jupiter Trojans by hypothesizing a free-floating planet (FFP) flyby into the Solar System. I…
Cauchy activation function and XNet
Xin Li, Zhihong Xia, Hongkun Zhang
We have developed a novel activation function, named the Cauchy Activation Function. This function is derived from the Cauchy Integral Theorem in complex analysis and is specifical…
The invasion of a free floating planet and the number asymmetry of Jupiter Trojans
Jian Li, Zhihong Jeff Xia, Nikolaos Georgakarakos +1
This paper extends our previous study (Li et al. 2023) of the early evolution of Jupiter and its two Trojan swarms by introducing the possible perturbations of a free floating plan…