Cover Image

Functional tensor train neural network for solving high-dimensional PDEs

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Feng, Yani, Ng, Michael K., Tang, Kejun, Zhang, Zhiwen
Format:	Preprint
Published:	2025
Subjects:	Numerical Analysis
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

A DeepLagrangian method for learning and generating aggregation patterns in multi-dimensional Keller-Segel chemotaxis systems
by: Feng, Yani, et al.
Published: (2025)

On understanding and overcoming spectral biases of deep neural network learning methods for solving PDEs
by: Xu, Zhi-Qin John, et al.
Published: (2025)

Gauss Newton method for solving variational problems of PDEs with neural network discretizaitons
by: Hao, Wenrui, et al.
Published: (2023)

APTT: An accuracy-preserved tensor-train method for the Boltzmann-BGK equation
by: Zhu, Zhitao, et al.
Published: (2024)

Combining physics-informed graph neural network and finite difference for solving forward and inverse spatiotemporal PDEs
by: Zhang, Hao, et al.
Published: (2024)

Tensor train methods for high-dimensional nonlinear filtering problems with correlated noise
by: Meng, Yuhua, et al.
Published: (2026)

Weak TransNet: A Petrov-Galerkin based neural network method for solving elliptic PDEs
by: Xu, Zhihang, et al.
Published: (2025)

Adaptive quadratures for nonlinear approximation of low-dimensional PDEs using smooth neural networks
by: Magueresse, Alexandre, et al.
Published: (2023)

VS-PINN: A fast and efficient training of physics-informed neural networks using variable-scaling methods for solving PDEs with stiff behavior
by: Ko, Seungchan, et al.
Published: (2024)

Tensor neural networks for high-dimensional Fokker-Planck equations
by: Wang, Taorui, et al.
Published: (2024)

Moving sample method for solving time-dependent partial differential equations
by: Xu, Beining, et al.
Published: (2026)

A novel model reduction method to solve inverse problems of parabolic type
by: Zhang, Wenlong, et al.
Published: (2024)

Towards optimal hierarchical training of neural networks
by: Feischl, Michael, et al.
Published: (2024)

Adversarial Adaptive Sampling: Unify PINN and Optimal Transport for the Approximation of PDEs
by: Tang, Kejun, et al.
Published: (2023)

Deep neural network approximation theory for high-dimensional functions
by: Beneventano, Pierfrancesco, et al.
Published: (2021)

HANN: Homotopy auxiliary neural network for solving nonlinear algebraic equations
by: Zai, Ling-Zhe, et al.
Published: (2025)

Deep Neural networks for solving high-dimensional parabolic partial differential equations
by: Zhang, Wenzhong, et al.
Published: (2026)

Data-integrated neural networks for solving partial differential equations
by: Zheng, Jiachun, et al.
Published: (2025)

Deep collocation method: A framework for solving PDEs using neural networks with error control
by: Weng, Mingxing, et al.
Published: (2025)

Solving high-dimensional Hamilton-Jacobi-Bellman equation with functional hierarchical tensor
by: Tang, Xun, et al.
Published: (2024)

The discrete inverse conductivity problem solved by the weights of an interpretable neural network
by: Beretta, Elena, et al.
Published: (2024)

Subspace method based on neural networks for solving the partial differential equation
by: Xu, Zhaodong, et al.
Published: (2024)

Physics-informed neural networks for solving two-phase flow problems with moving interfaces
by: Zhai, Qijia, et al.
Published: (2026)

A tensor Alternating Anderson-Richardson method for solving multilinear systems with M-tensors
by: Niu, Jing, et al.
Published: (2024)

Error estimates of a training-free diffusion model for high-dimensional sampling
by: Wang, Pengjun, et al.
Published: (2026)

Improved randomized neural network methods with boundary processing for solving elliptic equations
by: Zhou, Huifang, et al.
Published: (2024)

Deep neural network approximation for high-dimensional parabolic partial integro-differential equations
by: Baranek, Marcin
Published: (2025)

Multiscale interpolative construction of quantized tensor trains
by: Lindsey, Michael
Published: (2023)

Subspace method based on neural networks for solving the partial differential equation in weak form
by: Liu, Pengyuan, et al.
Published: (2024)

General transformation neural networks: A class of parametrized functions for high-dimensional function approximation
by: Wang, Xiaoyang, et al.
Published: (2025)

Cell-induced densification and tether formation in fibrous extracellular matrices with biomimetic physics-informed neural networks
by: Lin, Anci, et al.
Published: (2026)

Annealed adaptive importance sampling method in PINNs for solving high dimensional partial differential equations
by: Zhang, Zhengqi, et al.
Published: (2024)

Variational inference and density estimation with non-negative tensor train
by: Tang, Xun, et al.
Published: (2025)

Efficient iterative techniques for solving tensor problems with the T-product
by: Kooshkghazi, Malihe Nobakht, et al.
Published: (2025)

Fredholm integral equations for function approximation and the training of neural networks
by: Gelß, Patrick, et al.
Published: (2023)

IG-PINNs: Interface-gated physics-informed neural networks for solving elliptic interface problems
by: Zheng, Jiachun, et al.
Published: (2025)

Group-invariant tensor train networks for supervised learning
by: Sprangers, Brent, et al.
Published: (2022)

The low-rank tensor-train finite difference method for three-dimensional parabolic equations
by: Manzini, Gianmarco, et al.
Published: (2025)

An efficient stochastic particle method for high-dimensional nonlinear PDEs
by: Lei, Zhengyang, et al.
Published: (2023)

AMFR-W numerical methods for solving high dimensional SABR/LIBOR PDE models
by: López-Salas, J. G., et al.
Published: (2024)