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02/01/2023
Experimental observation on a low-rank tensor model for eigenvalue problems
Here we utilize a low-rank tensor model (LTM) as a function approximator...
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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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02/12/2022
MIONet: Learning multiple-input operators via tensor product
As an emerging paradigm in scientific machine learning, neural operators...
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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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12/05/2020
Learning Poisson systems and trajectories of autonomous systems via Poisson neural networks
We propose the Poisson neural networks (PNNs) to learn Poisson systems a...
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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
Symplectic networks: Intrinsic structure-preserving networks for identifying Hamiltonian systems
This work presents a framework of constructing the neural networks prese...
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10/08/2019
DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators
While it is widely known that neural networks are universal approximator...
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05/27/2019