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Summary

This summary is machine-generated.

A new neural network method, Encoder-X, improves polynomial fitting stability and speed. This approach accurately represents curves and surfaces for various modeling tasks.

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Area of Science:

Computational mathematics
Machine learning
Data representation

Background:

Polynomial functions are crucial for representing curves and surfaces in modeling.
Existing neural network methods for polynomial fitting lack stability and convergence speed.

Purpose of the Study:

To introduce Encoder-X, a novel neural network-based method for robust polynomial fitting.
To address limitations of current neural network approaches in terms of stability and convergence.

Main Methods:

Developed Encoder-X, a special autoencoder model comprising a neural network encoder and a polynomial decoder.
Treated polynomial coefficients as feature values, enabling fitting through the autoencoder structure.
Trained the encoder by minimizing the error between predicted and true function values.

Main Results:

Encoder-X demonstrated superior stability, convergence, and accuracy compared to existing methods.
The method successfully performed both explicit and implicit polynomial fitting.
Validated Encoder-X's effectiveness in enhancing polynomial representation for modeling tasks.

Conclusions:

Encoder-X offers a stable and efficient solution for polynomial fitting.
The proposed method advances neural network applications in mathematical modeling.
Encoder-X shows potential for broader applications beyond polynomial fitting.