Pengzhan Jin

CoRR, 2024

Learning solution operators of PDEs defined on varying domains via MIONet.

[BibT_eX]

[DOI]

Shanshan Xiao

CoRR, 2024

A hybrid iterative method based on MIONet for PDEs: Theory and numerical examples.

[BibT_eX]

[DOI]

Jun Hu

CoRR, 2024

2023

Learning Poisson Systems and Trajectories of Autonomous Systems via Poisson Neural Networks.

[BibT_eX]

[DOI]

Zhen Zhang

Ioannis G. Kevrekidis

IEEE Trans. Neural Networks Learn. Syst., November, 2023

Experimental observation on a low-rank tensor model for eigenvalue problems.

[BibT_eX]

[DOI]

Jun Hu

CoRR, 2023

2022

MIONet: Learning Multiple-Input Operators via Tensor Product.

[BibT_eX]

[DOI]

Shuai Meng

Lu Lu

SIAM J. Sci. Comput., 2022

Approximation capabilities of measure-preserving neural networks.

[BibT_eX]

[DOI]

Neural Networks, 2022

Tensor Neural Network and Its Numerical Integration.

[BibT_eX]

[DOI]

Yifan Wang

Hehu Xie

CoRR, 2022

On Numerical Integration in Neural Ordinary Differential Equations.

[BibT_eX]

[DOI]

Proceedings of the International Conference on Machine Learning, 2022

2021

Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators.

[BibT_eX]

[DOI]

Nat. Mach. Intell., 2021

2020

Unit Triangular Factorization of the Matrix Symplectic Group.

[BibT_eX]

[DOI]

SIAM J. Matrix Anal. Appl., 2020

SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems.

[BibT_eX]

[DOI]

Neural Networks, 2020

Quantifying the generalization error in deep learning in terms of data distribution and neural network smoothness.

[BibT_eX]

[DOI]

Lu Lu

Neural Networks, 2020

Inverse modified differential equations for discovery of dynamics.

[BibT_eX]

[DOI]

CoRR, 2020

Deep Hamiltonian networks based on symplectic integrators.

[BibT_eX]

[DOI]

CoRR, 2020

Symplectic networks: Intrinsic structure-preserving networks for identifying Hamiltonian systems.

[BibT_eX]

[DOI]

CoRR, 2020

2019

DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators.

[BibT_eX]

[DOI]

Lu Lu