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Area of Science:

  • Numerical Computation
  • Deep Learning
  • Scientific Computing

Background:

  • Solving large-scale linear equations is computationally intensive.
  • Existing iterative methods face challenges with problem size and efficiency.

Purpose of the Study:

  • To introduce an innovative deep neural network (DNN) method for solving linear equations.
  • To demonstrate the accuracy and efficiency of the DNN-based approach for large-scale problems.

Main Methods:

  • Utilizing a residual network architecture.
  • Incorporating correction iteration inspired by classic methods.
  • Applying the method to 1D Burgers and 2D heat-conduction equations.

Main Results:

  • Achieved high accuracy with errors below 10-7.
  • Demonstrated the method's effectiveness on benchmark equations.
  • Showcased reduced sensitivity of computation time to problem size.

Conclusions:

  • The DNN-based method provides a precise and effective solution for linear equations.
  • This technique offers a significant efficiency advantage for large-scale numerical computations.
  • The proposed method represents a promising advancement in scientific computing.