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Differential Informed Auto-Encoder

Jinrui Zhang

Abstract

In this article, an encoder was trained to obtain the inner structure of the original data by obtain a differential equations. A decoder was trained to resample the original data domain, to generate new data that obey the differential structure of the original data using the physics-informed neural network.

Differential Informed Auto-Encoder

Abstract

In this article, an encoder was trained to obtain the inner structure of the original data by obtain a differential equations. A decoder was trained to resample the original data domain, to generate new data that obey the differential structure of the original data using the physics-informed neural network.

Paper Structure

This paper contains 10 sections, 9 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Methodology
  3. first approach
  4. approach with linear assumption
  5. approach augmentation
  6. Results
  7. first approach
  8. approach with linear assumption
  9. approach augmentation
  10. Conclusion

Figures (9)

  • Figure 1: vectors $\left[{U}{U^{t}}{U^{tt}}\right]$ sit on 1-dimensional manifold
  • Figure 2: $0.5*sin(x)$
  • Figure 3: $f$ errors
  • Figure 4: $\frac{\sqrt{2}}{2}*sin(x+\frac{\pi}{4})$
  • Figure 5: $f$ errors
  • ...and 4 more figures