16 citations · 42 across the 9 of their papers we have counts for
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math.NA2022★ 1 cited
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…
math.NA2022★ 8 cited
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…
math.NA2022★ 3 cited
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…