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Related Experiment Video

Updated: Jan 8, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

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PDE-GANet: Partial differential equation discovery powered by adversarial learning.

Bin Wang1, Yuxuan Gao1, Shenglin Guo1

  • 1School of Electronic Engineering, Xidian University, No. 2, South Taibai Road, Xi'an, Shaanxi, 710071, PR China.

Neural Networks : the Official Journal of the International Neural Network Society
|December 11, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces PDE-GANet, a novel deep learning network for discovering governing partial differential equations (PDEs) from data. PDE-GANet achieves higher accuracy in both PDE expression and numerical solution estimation compared to existing methods.

Keywords:
Deep symbolic networkGenerative adversarial networkPartial differential equationRecurrent neural network

Related Experiment Videos

Last Updated: Jan 8, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

2.1K

Area of Science:

  • Computational Mathematics
  • Artificial Intelligence
  • Scientific Computing

Background:

  • Partial differential equations (PDEs) are fundamental in describing complex systems but challenging to formulate.
  • Data-driven discovery of PDEs is a growing research area, driven by advancements in deep learning.
  • Existing methods face limitations in accurately representing and learning governing PDEs from data.

Purpose of the Study:

  • To propose a novel deep learning framework, PDE-GANet, for accurate and efficient discovery of governing PDEs from data.
  • To enhance the representation and learning strategies for PDEs using a bidirectional network architecture.
  • To improve the accuracy of both PDE expression and numerical solution estimation.

Main Methods:

  • Developed PDE-GANet, a generative adversarial network (GAN) incorporating symbolic networks and recurrent neural networks.
  • The generator (symbolic network) represents PDE expressions and estimates numerical solutions.
  • The discriminator (recurrent neural network) validates solutions against the inferred PDE from a temporal perspective.

Main Results:

  • PDE-GANet demonstrates superior performance in discovering PDEs from data.
  • Achieved higher accuracy in PDE expression compared to state-of-the-art methods.
  • Provided more precise numerical solutions for the discovered PDEs.

Conclusions:

  • PDE-GANet offers a powerful approach for data-driven PDE discovery.
  • The proposed method advances the accurate formulation and solving of PDEs for complex systems.
  • This work has the potential to broaden the application of PDEs across various scientific and engineering disciplines.