Solving PDEs on Unknown Manifolds with Machine Learning
Fuente:
arXiv
Saved in:
| Main Authors: | Liang, Senwei, Jiang, Shixiao W., Harlim, John, Yang, Haizhao |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Similar Items
Finite Expression Method for Solving High-Dimensional Partial Differential Equations
by: Liang, Senwei, et al.
Published: (2022)
by: Liang, Senwei, et al.
Published: (2022)
Solving High-Dimensional Partial Integral Differential Equations: The Finite Expression Method
by: Hardwick, Gareth, et al.
Published: (2024)
by: Hardwick, Gareth, et al.
Published: (2024)
Generalized Moving Least-Squares Methods for Solving Vector-valued PDEs on Unknown Manifolds
by: Li, Rongji, et al.
Published: (2024)
by: Li, Rongji, et al.
Published: (2024)
Multi-Scale Finite Expression Method for PDEs with Oscillatory Solutions on Complex Domains
by: Hardwick, Gareth, et al.
Published: (2025)
by: Hardwick, Gareth, et al.
Published: (2025)
A Higher Order Local Mesh Method for Approximating 1-Laplacians on Unknown Manifolds
by: Peoples, John Wilson, et al.
Published: (2024)
by: Peoples, John Wilson, et al.
Published: (2024)
Learning solution operator of dynamical systems with diffusion maps kernel ridge regression
by: Song, Jiwoo, et al.
Published: (2025)
by: Song, Jiwoo, et al.
Published: (2025)
Learning Epidemiological Dynamics via the Finite Expression Method
by: Du, Jianda, et al.
Published: (2024)
by: Du, Jianda, et al.
Published: (2024)
Finite Expression Methods for Discovering Physical Laws from Data
by: Jiang, Zhongyi, et al.
Published: (2023)
by: Jiang, Zhongyi, et al.
Published: (2023)
A Finite Expression Method for Solving High-Dimensional Committor Problems
by: Song, Zezheng, et al.
Published: (2023)
by: Song, Zezheng, et al.
Published: (2023)
Beyond Expected Information Gain: Stable Bayesian Optimal Experimental Design with Integral Probability Metrics and Plug-and-Play Extensions
by: Wu, Di, et al.
Published: (2026)
by: Wu, Di, et al.
Published: (2026)
TINNs: Time-Induced Neural Networks for Solving Time-Dependent PDEs
by: Dai, Chen-Yang, et al.
Published: (2026)
by: Dai, Chen-Yang, et al.
Published: (2026)
Latent Neural Operator Pretraining for Solving Time-Dependent PDEs
by: Wang, Tian, et al.
Published: (2024)
by: Wang, Tian, et al.
Published: (2024)
Solving Nonlinear PDEs with Sparse Radial Basis Function Networks
by: Shao, Zihan, et al.
Published: (2025)
by: Shao, Zihan, et al.
Published: (2025)
Learning Coarse-Grained Dynamics on Graph
by: Yu, Yin, et al.
Published: (2024)
by: Yu, Yin, et al.
Published: (2024)
Solving Roughly Forced Nonlinear PDEs via Misspecified Kernel Methods and Neural Networks
by: Baptista, Ricardo, et al.
Published: (2025)
by: Baptista, Ricardo, et al.
Published: (2025)
Spectral Clustering via Orthogonalization-Free Methods
by: Pang, Qiyuan, et al.
Published: (2023)
by: Pang, Qiyuan, et al.
Published: (2023)
Enhanced BPINN Training Convergence in Solving General and Multi-scale Elliptic PDEs with Noise
by: Hou, Yilong, et al.
Published: (2024)
by: Hou, Yilong, et al.
Published: (2024)
RBF-Generated Finite Difference Method Coupled with Quadratic Programming for Solving PDEs on Surfaces with Derivative Boundary Conditions
by: Chen, Peng, et al.
Published: (2026)
by: Chen, Peng, et al.
Published: (2026)
FastLSQ: Solving PDEs in One Shot via Fourier Features with Exact Analytical Derivatives
by: Sulc, Antonin
Published: (2026)
by: Sulc, Antonin
Published: (2026)
TENG: Time-Evolving Natural Gradient for Solving PDEs With Deep Neural Nets Toward Machine Precision
by: Chen, Zhuo, et al.
Published: (2024)
by: Chen, Zhuo, et al.
Published: (2024)
Holistic Physics Solver: Learning PDEs in a Unified Spectral-Physical Space
by: Yue, Xihang, et al.
Published: (2024)
by: Yue, Xihang, et al.
Published: (2024)
Solving PDEs on Spheres with Physics-Informed Convolutional Neural Networks
by: Lei, Guanhang, et al.
Published: (2023)
by: Lei, Guanhang, et al.
Published: (2023)
Using Uncertainty Quantification to Characterize and Improve Out-of-Domain Learning for PDEs
by: Mouli, S. Chandra, et al.
Published: (2024)
by: Mouli, S. Chandra, et al.
Published: (2024)
AutoNumerics: An Autonomous, PDE-Agnostic Multi-Agent Pipeline for Scientific Computing
by: Du, Jianda, et al.
Published: (2026)
by: Du, Jianda, et al.
Published: (2026)
Adaptive-Distribution Randomized Neural Networks for PDEs: A Low-Dimensional Distribution-Learning Framework
by: Yang, You, et al.
Published: (2026)
by: Yang, You, et al.
Published: (2026)
Solving PDEs With Deep Neural Nets under General Boundary Conditions
by: Zhang, Chenggong
Published: (2025)
by: Zhang, Chenggong
Published: (2025)
Variational (Energy-Based) Spectral Learning: A Machine Learning Framework for Solving Partial Differential Equations
by: Hammad, M. M.
Published: (2026)
by: Hammad, M. M.
Published: (2026)
A Distributed Block Chebyshev-Davidson Algorithm for Parallel Spectral Clustering
by: Pang, Qiyuan, et al.
Published: (2022)
by: Pang, Qiyuan, et al.
Published: (2022)
One-Shot Transfer Learning for Nonlinear PDEs with Perturbative PINNs
by: Auroy, Samuel, et al.
Published: (2025)
by: Auroy, Samuel, et al.
Published: (2025)
Fourier Neural Operator with Learned Deformations for PDEs on General Geometries
by: Li, Zongyi, et al.
Published: (2022)
by: Li, Zongyi, et al.
Published: (2022)
A Physics-Informed Machine Learning Approach for Solving Distributed Order Fractional Differential Equations
by: Aghaei, Alireza Afzal
Published: (2024)
by: Aghaei, Alireza Afzal
Published: (2024)
Learning solution operators of PDEs defined on varying domains via MIONet
by: Xiao, Shanshan, et al.
Published: (2024)
by: Xiao, Shanshan, et al.
Published: (2024)
An Efficient Deep Learning Approach for Approximating Parameter-to-Solution Maps of PDEs
by: Lei, Guanhang, et al.
Published: (2024)
by: Lei, Guanhang, et al.
Published: (2024)
Deflation-PINNs: Learning Multiple Solutions for PDEs and Landau-de Gennes
by: Disarò, Sean, et al.
Published: (2026)
by: Disarò, Sean, et al.
Published: (2026)
Don't Fix the Basis -- Learn It: Spectral Representation with Adaptive Basis Learning for PDEs
by: Zhao, Xuxiang, et al.
Published: (2026)
by: Zhao, Xuxiang, et al.
Published: (2026)
DeepONet Augmented by Randomized Neural Networks for Efficient Operator Learning in PDEs
by: Jiang, Zhaoxi, et al.
Published: (2025)
by: Jiang, Zhaoxi, et al.
Published: (2025)
Adversarial Adaptive Sampling: Unify PINN and Optimal Transport for the Approximation of PDEs
by: Tang, Kejun, et al.
Published: (2023)
by: Tang, Kejun, et al.
Published: (2023)
Regularity of Second-Order Elliptic PDEs in Spectral Barron Spaces
by: Chen, Ziang, et al.
Published: (2026)
by: Chen, Ziang, et al.
Published: (2026)
Finite Element Neural Network Interpolation. Part I: Interpretable and Adaptive Discretization for Solving PDEs
by: Škardová, Kateřina, et al.
Published: (2024)
by: Škardová, Kateřina, et al.
Published: (2024)
Learning to Solve Related Linear Systems
by: Hegde, Disha, et al.
Published: (2025)
by: Hegde, Disha, et al.
Published: (2025)
Similar Items
-
Finite Expression Method for Solving High-Dimensional Partial Differential Equations
by: Liang, Senwei, et al.
Published: (2022) -
Solving High-Dimensional Partial Integral Differential Equations: The Finite Expression Method
by: Hardwick, Gareth, et al.
Published: (2024) -
Generalized Moving Least-Squares Methods for Solving Vector-valued PDEs on Unknown Manifolds
by: Li, Rongji, et al.
Published: (2024) -
Multi-Scale Finite Expression Method for PDEs with Oscillatory Solutions on Complex Domains
by: Hardwick, Gareth, et al.
Published: (2025) -
A Higher Order Local Mesh Method for Approximating 1-Laplacians on Unknown Manifolds
by: Peoples, John Wilson, et al.
Published: (2024)