61 citations · 113 across the 7 of their papers we have counts for
5 papers · 1 filter
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…
FBSDE based Neural Network Algorithms for High-Dimensional Quasilinear Parabolic PDEs
Wenzhong Zhang, Wei Cai
In this paper, we propose forward and backward stochastic differential equations (FBSDEs) based deep neural network (DNN) learning algorithms for the solution of high dimensional q…
Multi-scale Deep Neural Network (MscaleDNN) Methods for Oscillatory Stokes Flows in Complex Domains
Bo Wang, Wenzhong Zhang, Wei Cai
In this paper, we study a multi-scale deep neural network (MscaleDNN) as a meshless numerical method for computing oscillatory Stokes flows in complex domains. The MscaleDNN employ…