On Computing the Hyperparameter of Extreme Learning Machines: Algorithm and Application to Computational PDEs, and Comparison with Classical and High-Order Finite Elements

@article{Dong2021OnCT,
  title={On Computing the Hyperparameter of Extreme Learning Machines: Algorithm and Application to Computational PDEs, and Comparison with Classical and High-Order Finite Elements},
  author={Suchuan Dong and Jielin Yang},
  journal={ArXiv},
  year={2021},
  volume={abs/2110.14121}
}
We consider the use of extreme learning machines (ELM) for computational partial differential equations (PDE). In ELM the hidden-layer coefficients in the neural network are assigned to random values generated on [−Rm, Rm] and fixed, where Rm is a user-provided constant, and the output-layer coefficients are trained by a linear or nonlinear least squares computation. We present a method for computing the optimal or near-optimal value of Rm based on the differential evolution algorithm. This… 
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