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
  • [21] Optimization for problem classes -: Neural networks that learn to learn
    Hüsken, M
    Gayko, JE
    Sendhoff, B
    2000 IEEE SYMPOSIUM ON COMBINATIONS OF EVOLUTIONARY COMPUTATION AND NEURAL NETWORKS, 2000, : 98 - 109
  • [22] Best kinematics for shell finite elements using convolutional neural networks
    Petrolo, M.
    Iannotti, P.
    MECHANICS OF ADVANCED MATERIALS AND STRUCTURES, 2023, 30 (05) : 1106 - 1116
  • [23] Neural Networks to Solve Partial Differential Equations: A Comparison With Finite Elements
    Sacchetti, Andrea
    Bachmann, Benjamin
    Loffel, Kaspar
    Kunzi, Urs-Martin
    Paoli, Beatrice
    IEEE ACCESS, 2022, 10 : 32271 - 32279
  • [24] Hierarchical deep-learning neural networks: finite elements and beyond
    Lei Zhang
    Lin Cheng
    Hengyang Li
    Jiaying Gao
    Cheng Yu
    Reno Domel
    Yang Yang
    Shaoqiang Tang
    Wing Kam Liu
    Computational Mechanics, 2021, 67 : 207 - 230
  • [25] Hierarchical deep-learning neural networks: finite elements and beyond
    Zhang, Lei
    Cheng, Lin
    Li, Hengyang
    Gao, Jiaying
    Yu, Cheng
    Domel, Reno
    Yang, Yang
    Tang, Shaoqiang
    Liu, Wing Kam
    COMPUTATIONAL MECHANICS, 2021, 67 (01) : 207 - 230
  • [26] Artificial neural networks can learn to estimate extinction rates from molecular phylogenies
    Bokma, Folmer
    JOURNAL OF THEORETICAL BIOLOGY, 2006, 243 (03) : 449 - 454
  • [27] Can Deep Neural Networks Learn Process Model Structure? An Assessment Framework and Analysis
    Peeperkorn, Jari
    vanden Broucke, Seppe
    De Weerdt, Jochen
    PROCESS MINING WORKSHOPS, ICPM 2021, 2022, 433 : 127 - 139
  • [28] Silicon neural networks learn as they compute
    Paillet, G
    LASER FOCUS WORLD, 1996, 32 (08): : S17 - S19
  • [29] Can neural networks with arbitrary delays be finite-timely synchronized?
    Yang, Xinsong
    NEUROCOMPUTING, 2014, 143 : 275 - 281
  • [30] MICROCONTROLLERS LEARN TO EMBRACE NEURAL NETWORKS
    Edwards, Chris
    New Electronics, 2022, 55 (11): : 34 - 35
12345