Can neural networks learn finite elements?

被引：0
|
作者：
Novo, Julia [1 ]
Terres, Eduardo [1 ]
机构：
[1] Univ Autonoma Madrid, Dept Matemat, Madrid, Spain
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2025年 / 453卷
关键词：
Neural networks; Finite elements; Partial differential equations; GALERKIN;
D O I：
10.1016/j.cam.2024.116168
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The aim of this note is to construct a neural network for which the linear finite element approximation of a simple one dimensional boundary value problem is a minimum of the cost function to find out if the neural network is able to reproduce the finite element approximation. The deepest goal is to shed some light on the problems one encounters when trying to use neural networks to approximate partial differential equations.
引用
收藏
页数：8
相关论文
共 50 条
  • [1] How easily can neural networks learn relativity?
    Chitturi, Kartik
    Onyisi, Peter
    18TH INTERNATIONAL WORKSHOP ON ADVANCED COMPUTING AND ANALYSIS TECHNIQUES IN PHYSICS RESEARCH (ACAT2017), 2018, 1085
  • [2] Neural networks can learn to approximate autonomous flows
    Rodriguez, Jose M.
    Garzon, Max H.
    FLUIDS AND WAVES: RECENT TRENDS IN APPLIED ANALYSIS, 2007, 440 : 197 - 206
  • [3] Neural Networks can Learn Representations with Gradient Descent
    Damian, Alex
    Lee, Jason D.
    Soltanolkotabi, Mahdi
    CONFERENCE ON LEARNING THEORY, VOL 178, 2022, 178
  • [4] Convolutional Neural Networks Are Not Invariant to Translation, but They Can Learn to Be
    Biscione, Valerio
    Bowers, Jeffrey S.
    JOURNAL OF MACHINE LEARNING RESEARCH, 2021, 22
  • [5] Convolutional neural networks are not invariant to translation, but they can learn to be
    Biscione, Valerio
    Bowers, Jeffrey S.
    Journal of Machine Learning Research, 2021, 22
  • [6] Can recurrent neural networks learn natural language grammars?
    Lawrence, S
    Giles, CL
    Fong, S
    ICNN - 1996 IEEE INTERNATIONAL CONFERENCE ON NEURAL NETWORKS, VOLS. 1-4, 1996, : 1853 - 1858
  • [7] Can SGD Learn Recurrent Neural Networks with Provable Generalization?
    Allen-Zhu, Zeyuan
    Li, Yuanzhi
    ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 32 (NIPS 2019), 2019, 32
  • [8] Can recurrent neural networks learn process model structure?
    Jari Peeperkorn
    Seppe vanden Broucke
    Jochen De Weerdt
    Journal of Intelligent Information Systems, 2023, 61 : 27 - 51
  • [9] Can recurrent neural networks learn process model structure?
    Peeperkorn, Jari
    Broucke, Seppe vanden
    De Weerdt, Jochen
    JOURNAL OF INTELLIGENT INFORMATION SYSTEMS, 2023, 61 (01) : 27 - 51
  • [10] Neural networks can learn to utilize correlated auxiliary noise
    Aida Ahmadzadegan
    Petar Simidzija
    Ming Li
    Achim Kempf
    Scientific Reports, 11
12345