5 citations · 5 across the 8 of their papers we have counts for
9 papers
Optimal Neural Network Approximation via Empirical Least Squares with Deterministic Samples
Xinliang Liu, Tong Mao, Jinchao Xu
We develop a rigorous theory of discrete residual least-squares approximation for elliptic spectral equations using linearized ReLU neural networks on the sp…
McMg: A Learned Phase-Space Multi-channel Multigrid Preconditioner for Helmholtz Equation
Jiwei Jia, Xinliang Liu, Juntao Wang +1
Solving heterogeneous Helmholtz equations at high wavenumbers remains challenging because the discretized operator is indefinite, pollution degrades phase accuracy, and scalar coar…
Condition Numbers and Eigenvalue Spectra of Shallow Networks on Spheres
Xinliang Liu, Tong Mao, Jinchao Xu
We present an estimation of the condition numbers of the \emph{mass} and \emph{stiffness} matrices arising from shallow ReLU neural networks defined on the unit sphere~$\mathbb…
Self-composing neural operators for high-frequency and multiscale PDE surrogates
Juncai He, Xinliang Liu, Jinchao Xu
Addressing the computational challenges of high-frequency and multiscale partial differential equations (PDEs), this work introduces a self-composing neural operator (SC-NO) framew…
OpenBreastUS: Benchmarking Neural Operators for Wave Imaging Using Breast Ultrasound Computed Tomography
Zhijun Zeng, Youjia Zheng, Hao Hu +8
Accurate and efficient simulation of wave equations is crucial in computational wave imaging applications, such as ultrasound computed tomography (USCT), which reconstructs tissue…
Integral Representations of Sobolev Spaces via ReLU Activation Function and Optimal Error Estimates for Linearized Networks
Xinliang Liu, Tong Mao, Jinchao Xu
This paper presents two main theoretical results concerning shallow neural networks with ReLU activation functions. We establish a novel integral representation for Sobolev spa…
Advanced Long-term Earth System Forecasting
Hao Wu, Yuan Gao, Ruijian Gou +30
Reliable long-term forecasting of Earth system dynamics is fundamentally limited by instabilities in current artificial intelligence (AI) models during extended autoregressive simu…
A MgNO Method for Multiphase Flow in Porous Media
Xinliang Liu, Xia Yang, Chen-Song Zhang +2
This research investigates the application of Multigrid Neural Operator (MgNO), a neural operator architecture inspired by multigrid methods, in the simulation for multiphase flow…
MgNO: Efficient Parameterization of Linear Operators via Multigrid
Juncai He, Xinliang Liu, Jinchao Xu
In this work, we propose a concise neural operator architecture for operator learning. Drawing an analogy with a conventional fully connected neural network, we define the neural o…