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Comment on "Machine learning conservation laws from differential equations"

Michael F. Zimmer

TL;DR

The paper [1] by Liu, Madhavan, and Tegmark sought to use machine learning methods to elicit known conservation laws for several systems but made seven serious errors, causing both their method and result to be incorrect.

Abstract

The paper [1] by Liu, Madhavan, and Tegmark sought to use machine learning methods to elicit known conservation laws for several systems. However, in their example of a damped 1D harmonic oscillator they made seven serious errors, causing both their method and result to be incorrect. In this Comment, those errors are reviewed.

Comment on "Machine learning conservation laws from differential equations"

TL;DR

The paper [1] by Liu, Madhavan, and Tegmark sought to use machine learning methods to elicit known conservation laws for several systems but made seven serious errors, causing both their method and result to be incorrect.

Abstract

The paper [1] by Liu, Madhavan, and Tegmark sought to use machine learning methods to elicit known conservation laws for several systems. However, in their example of a damped 1D harmonic oscillator they made seven serious errors, causing both their method and result to be incorrect. In this Comment, those errors are reviewed.
Paper Structure (3 sections, 13 equations, 1 figure)

This paper contains 3 sections, 13 equations, 1 figure.

Table of Contents

  1. Review of Liu, et al.
  2. Summary of Errors
  3. Afterword

Figures (1)

  • Figure 1: Plots of $H_1$ and $\cos H_1$ are displayed together to illustrate how the discontinuity in $H_1$ becomes perfectly obscured when $\cos H_1$ is instead plotted. In both cases, $H_1$ was computed from Eq. \ref{['eqn:H1-last']} with $\gamma=0.1$ and with arctan computed using atan2.