Synapse
⌘+K
Synapse
PulseExploreClubsResearchersJournals
Instagram
HomeClubsExplore
May 6, 2026Science Discovery Physics

Physics-informed Neural Networks for Solving Second-order Boundary Value Problems Comparison with FEM, FD Methods

View Full Paper
Ask AI
Bookmark
Share

Authors

UMUjjal MandalIndian Institute of Information Technology Allahabad

Discussion

Loading...

Member takes

Implication

Comparison of PINNs, FEM, and FD methods shows similar accuracy in boundary value problems, indicating PINNs could solve more complex cases effectively.

Key Points

  • This research aims to evaluate the effectiveness of physics-informed neural networks (PINNs) in solving boundary value problems compared to traditional numerical methods.
  • Detailed comparison of PINNs with finite element method (FEM) and finite difference (FD) methods.
  • Utilization of feedforward neural network framework to incorporate boundary conditions.
  • Implementation of automatic differentiation for derivative calculations without numerical approximations.
  • PINNs demonstrate comparable accuracy to classical methods in boundary value problems.
  • Mesh-free nature of PINNs allows for flexibility in complicated domains.
  • Results highlight that while FEM and FD are efficient in low-dimensional cases, PINNs can handle higher dimensions better.

Cite This Study

Ujjal Mandal (2026) studied this question.

synapsesocial.com/papers/69faa22704f884e66b532dc5https://doi.org/10.11648/j.sdp.20260102.14
View Full Paper
Ask AI
Bookmark
Share

Also Consider

Synapse has enriched one closely related paper. Consider it for comparative context:

  1. 1Physics-Informed Neural Networks for Heat Transfer Problems2021 · 1,322 citations