5 papers
Modeling Unknown Nonlocal PDE Systems via Flow Map Learning
Zhongshu Xu, Ying Li, Yanzhi Zhang +1
Nonlocal partial differential equations arise in many applications but are often difficult to model and learn because of the presence of nonlocal operators. We present a flow-map l…
Targeted Digital Twin via Flow Map Learning and Its Application to Fluid Dynamics
Qifan Chen, Zhongshu Xu, Jinjin Zhang +1
We present a numerical framework for constructing a targeted digital twin (tDT) that directly models the dynamics of quantities of interest (QoIs) in a full digital twin (DT). The…
Chebyshev Feature Neural Network for Accurate Function Approximation
Zhongshu Xu, Yuan Chen, Dongbin Xiu
We present a new Deep Neural Network (DNN) architecture capable of approximating functions up to machine accuracy. Termed Chebyshev Feature Neural Network (CFNN), the new structure…
Modeling Unknown Stochastic Dynamical System via Autoencoder
Zhongshu Xu, Yuan Chen, Qifan Chen +1
We present a numerical method to learn an accurate predictive model for an unknown stochastic dynamical system from its trajectory data. The method seeks to approximate the unknown…
Butterfly-Net2: Simplified Butterfly-Net and Fourier Transform Initialization
Zhongshu Xu, Yingzhou Li, Xiuyuan Cheng
Structured CNN designed using the prior information of problems potentially improves efficiency over conventional CNNs in various tasks in solving PDEs and inverse problems in sign…