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Related Experiment Videos

A High-Efficient Hybrid Physics-Informed Neural Networks Based on Convolutional Neural Network.

Zhiwei Fang

    IEEE Transactions on Neural Networks and Learning Systems
    |April 13, 2021
    PubMed
    Summary

    This study introduces a hybrid physics-informed neural network (hybrid PINN) that approximates differential operators for solving partial differential equations (PDEs). This novel machine learning approach offers a proven convergent rate, enhancing prediction accuracy and efficiency.

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    Area of Science:

    • Computational mathematics
    • Machine learning
    • Numerical analysis

    Background:

    • Partial differential equations (PDEs) are fundamental in science and engineering.
    • Existing physics-informed neural networks (PINNs) often rely on automatic differentiation, which can lead to prediction inaccuracies.
    • There is a need for robust and convergent machine learning solvers for PDEs.

    Purpose of the Study:

    • To develop a novel hybrid physics-informed neural network (hybrid PINN) for solving PDEs.
    • To introduce a new method that approximates differential operators using local fitting instead of automatic differentiation.
    • To establish a convergent rate for machine learning-based PDE solvers.

    Main Methods:

    • A hybrid physics-informed neural network (hybrid PINN) framework is developed.

    Related Experiment Videos

  • The method integrates concepts from convolutional neural networks (CNNs) and finite volume methods.
  • Differential operators are approximated using a local fitting method, diverging from automatic differentiation (AD).

    • Main Results:

    • The proposed hybrid PINN method demonstrates a proven convergent rate.
    • This approach mitigates issues of inaccurate predictions sometimes observed with traditional PINNs.
    • Numerical experiments confirm the algorithm's correctness and efficiency.

    Conclusions:

    • The developed hybrid PINN offers a convergent and reliable machine learning approach for solving PDEs.
    • This work represents a significant advancement, being the first to achieve a proven convergent rate for a machine learning PDE solver.
    • The method shows potential for application in inverse problems and surface PDEs.