16 citations · 42 across the 9 of their papers we have counts for
9 papers
Time-Invariant Neural Operators with Applications in Solving Time-Dependent PDEs
Zihan Zhou, Wenzhong Zhang, Lizuo Liu
The deep operator network (DeepONet) is one of the basic architectures for learning nonlinear operators with neural networks. However, for operators that describe the dynamic respo…
Multi-scale DeepOnet (Mscale-DeepOnet) for Mitigating Spectral Bias in Learning High Frequency Operators of Oscillatory Functions
Bo Wang, Lizuo Liu, Wei Cai
In this paper, a multi-scale DeepOnet (Mscale-DeepOnet) is proposed to reduce the spectral bias of the DeepOnet in learning high-frequency mapping between highly oscillatory functi…
On Spectral Bias Reduction of Multi-scale Neural Networks for Regression Problems
Bo Wang, Heng Yuan, Lizuo Liu +2
In this paper, we derive diffusion equation models in the spectral domain for the evolution of training errors of two-layer multi-scale deep neural networks (MscaleDNN) \cite{caixu…
A Causality-DeepONet for Causal Responses of Linear Dynamical Systems
Lizuo Liu, Kamaljyoti Nath, Wei Cai
In this paper, we propose a DeepONet structure with causality to represent the causal linear operators between Banach spaces of time-dependent signals. The theorem of universal app…
DeepPropNet -- A Recursive Deep Propagator Neural Network for Learning Evolution PDE Operators
Lizuo Liu, Wei Cai
In this paper, we propose a deep neural network approximation to the evolution operator for time dependent PDE systems over long time period by recursively using one single neural…
Multiscale DeepONet for Nonlinear Operators in Oscillatory Function Spaces for Building Seismic Wave Responses
Lizuo Liu, Wei Cai
In this paper, we propose a multiscale DeepONet to represent nonlinear operator between Banach spaces of highly oscillatory continuous functions. The multiscale deep neural network…
Linearized Learning Methods with Multiscale Deep Neural Networks for Stationary Navier-Stokes Equations with Oscillatory Solutions
Lizuo Liu, Bo Wang, Wei Cai
In this paper, we present linearized learning methods to accelerate the convergence of training for stationary nonlinear Navier-Stokes equations. To solve the stationary nonlinear…
A Phase Shift Deep Neural Network for High Frequency Approximation and Wave Problems
Wei Cai, Xiaoguang Li, Lizuo Liu
In this paper, we propose a phase shift deep neural network (PhaseDNN), which provides a uniform wideband convergence in approximating high frequency functions and solutions of wav…
PhaseDNN - A Parallel Phase Shift Deep Neural Network for Adaptive Wideband Learning
Wei Cai, Xiaoguang Li, Lizuo Liu
In this paper, we propose a phase shift deep neural network (PhaseDNN) which provides a wideband convergence in approximating a high dimensional function during its training of the…