16 citations · 34 across the 7 of their papers we have counts for
5 papers · 1 filter
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…
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…