7 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…
Fast Reconstruction of Exact Maxwell Dynamics from Sparse Data
Dan DeGenaro, Xin Li, Obed Amo +4
We introduce FLASH-MAX, a shallow, exact-by-construction neural network architecture for predicting homogeneous electromagnetic fields from sparse pointwise observations. Each hidd…
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…
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…
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…
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…