Solutions to elliptic and parabolic problems via finite difference based unsupervised small linear convolutional neural networks

DOI10.1016/J.CAMWA.2024.08.013MaRDI QIDQ6647580

Béatrice Rivière, David Fuentes, Keegan L. A. Kirk, Adrian Celaya

Publication date: 3 December 2024

Published in: Computers & Mathematics with Applications (Search for Journal in Brave)

zbMATH Keywords

finite differencepartial differential equationsunsupervised learningconvolutional neural networks

Mathematics Subject Classification ID

Biology and other natural sciences (92-XX) Numerical analysis (65-XX)

Cites Work

• Multilayer feedforward networks are universal approximators
• The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
• A posteriori error estimates for a discontinuous Galerkin method applied to elliptic problems
• DGM: a deep learning algorithm for solving partial differential equations
• Optimal control of PDEs using physics-informed neural networks
• CAN-PINN: a fast physics-informed neural network based on coupled-automatic-numerical differentiation method
• Scientific machine learning through physics-informed neural networks: where we are and what's next
• DAS-PINNs: a deep adaptive sampling method for solving high-dimensional partial differential equations
• Neural‐network‐based approximations for solving partial differential equations
• Approximation by superpositions of a sigmoidal function

This page was built for publication: Solutions to elliptic and parabolic problems via finite difference based unsupervised small linear convolutional neural networks

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6647580)