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08/28/2023
Solving parametric elliptic interface problems via interfaced operator network
Learning operator mapping between infinite-dimensional Banach spaces via...
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04/21/2023
Effective Numerical Simulations of Synchronous Generator System
Synchronous generator system is a complicated dynamical system for energ...
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03/31/2023
Implementation and (Inverse Modified) Error Analysis for implicitly-templated ODE-nets
We focus on learning unknown dynamics from data using ODE-nets templated...
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09/25/2022
Error analysis based on inverse modified differential equations for discovery of dynamics using linear multistep methods and deep learning
Along with the practical success of the discovery of dynamics using deep...
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08/08/2022
Explicit K-symplectic methods for nonseparable non-canonical Hamiltonian systems
We propose efficient numerical methods for nonseparable non-canonical Ha...
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06/15/2022
On Numerical Integration in Neural Ordinary Differential Equations
The combination of ordinary differential equations and neural networks, ...
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05/11/2022
Poisson Integrators based on splitting method for Poisson systems
We propose Poisson integrators for the numerical integration of separabl...
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04/29/2022
VPNets: Volume-preserving neural networks for learning source-free dynamics
We propose volume-preserving networks (VPNets) for learning unknown sour...
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03/07/2022
On convergence of neural network methods for solving elliptic interface problems
With the remarkable empirical success of neural networks across diverse ...
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06/21/2021
Approximation capabilities of measure-preserving neural networks
Measure-preserving neural networks are well-developed invertible models,...
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09/02/2020
Inverse modified differential equations for discovery of dynamics
We introduce inverse modified differential equations (IMDEs) to contribu...
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04/23/2020
Deep Hamiltonian networks based on symplectic integrators
HNets is a class of neural networks on grounds of physical prior for lea...
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01/11/2020