PhaseDNN - A Parallel Phase Shift Deep Neural Network for Adaptive Wideband Learning. - Wei Cai; Xiaoguang Li; Lizuo Liu (CoRR, 2019)

A Phase Shift Deep Neural Network for High Frequency Wave Equations in Inhomogeneous Media. - Wei Cai; Xiaoguang Li; Lizuo Liu (CoRR, 2019)

A Phase Shift Deep Neural Network for High Frequency Approximation and Wave Problems. - Wei Cai; Xiaoguang Li; Lizuo Liu (SIAM J. Sci. Comput., 2020)

A Linearized Learning with Multiscale Deep Neural Network for Stationary Navier-Stokes Equations with Oscillatory Solutions. - Lizuo Liu; Bo Wang; Wei Cai 003 (CoRR, 2021)

Multiscale DeepONet for Nonlinear Operators in Oscillatory Function Spaces for Building Seismic Wave Responses. - Lizuo Liu; Wei Cai (CoRR, 2021)

DeepPropNet - A Recursive Deep Propagator Neural Network for Learning Evolution PDE Operators. - Lizuo Liu; Wei Cai (CoRR, 2022)

A Causality-DeepONet for Causal Responses of Linear Dynamical Systems. - Lizuo Liu; Kamaljyoti Nath; Wei Cai (CoRR, 2022)

On the Convergence of the Multi-scale Deep Neural Network (MscaleDNN) in Approximating Oscillatory Functions. - Bo Wang; Heng Yuan; Lizuo Liu; Wenzhong Zhang; Wei Cai 003 (CoRR, 2022)

Entropy stable conservative flux form neural networks. - Lizuo Liu; Tongtong Li; Anne Gelb; Yoonsang Lee 002 (CoRR, 2024)

On spectral bias reduction of multi-scale neural networks for regression problems. - Bo Wang; Heng Yuan; Lizuo Liu; Wenzhong Zhang; Wei Cai 003 (Neural Networks, 2025)

Multi-scale DeepOnet (Mscale-DeepOnet) for Mitigating Spectral Bias in Learning High Frequency Operators of Oscillatory Functions. - Bo Wang; Lizuo Liu; Wei Cai (CoRR, 2025)

Invariant Representations via Wasserstein Correlation Maximization. - Keenan Eikenberry; Lizuo Liu; Yoonsang Lee 002 (CoRR, 2025)

Neural Entropy-stable conservative flux form neural networks for learning hyperbolic conservation laws. - Lizuo Liu; Lu Zhang; Anne Gelb (CoRR, 2025)