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12/07/2022
On the Convergence of the Multi-scale Deep Neural Network (MscaleDNN) in Approximating Oscillatory Functions
In this paper, we derive diffusion models for the error evolution for a ...
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09/17/2022
A Causality-DeepONet for Causal Responses of Linear Dynamical Systems
In this paper, we propose a DeepONet structure with causality to represe...
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02/27/2022
DeepPropNet – A Recursive Deep Propagator Neural Network for Learning Evolution PDE Operators
In this paper, we propose a deep neural network approximation to the evo...
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11/08/2021
Multiscale DeepONet for Nonlinear Operators in Oscillatory Function Spaces for Building Seismic Wave Responses
In this paper, we propose a multiscale DeepONet to represent nonlinear o...
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02/05/2021
A Linearized Learning with Multiscale Deep Neural Network for Stationary Navier-Stokes Equations with Oscillatory Solutions
In this paper, we combine a linearized iterative method with multi-scale...
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09/23/2019
A Phase Shift Deep Neural Network for High Frequency Wave Equations in Inhomogeneous Media
In this paper, we propose a phase shift deep neural network (PhaseDNN) w...
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05/03/2019