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Finding discrete symmetry groups via machine learning.

Pablo Calvo-Barlés1,2, Sergio G Rodrigo1,3, Eduardo Sánchez-Burillo4

  • 1<a href="https://ror.org/031n2c920">Instituto de Nanociencia y Materiales de Aragón (INMA)</a>, CSIC-<a href="https://ror.org/012a91z28">Universidad de Zaragoza</a>, Zaragoza 50009, Spain.

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This summary is machine-generated.

We developed a machine learning method to automatically find discrete symmetries in physical systems. This approach identifies parameter changes that keep system properties the same without needing prior symmetry knowledge.

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Area of Science:

  • Physics
  • Computer Science
  • Materials Science

Background:

  • Discovering symmetries in physical systems is crucial for understanding their behavior.
  • Traditional methods often require prior knowledge of the system's mathematical structure.
  • Automating symmetry discovery can accelerate scientific research across various domains.

Purpose of the Study:

  • To introduce a novel machine learning approach for automatic discovery of discrete symmetry groups.
  • To demonstrate the method's ability to identify symmetries without prior system information.
  • To showcase the versatility of the approach across different scientific fields.

Main Methods:

  • Developed a machine learning model named the symmetry seeker neural network.
  • The model learns to identify parameter transformations that leave physical properties invariant.
  • Tested the method on diverse systems from mathematics, nanophotonics, and quantum chemistry.

Main Results:

  • Successfully automated the discovery of discrete symmetry groups in physical systems.
  • The method identified symmetries without requiring pre-existing knowledge of the system or its properties.
  • Demonstrated applicability across mathematics, nanophotonics, and quantum chemistry examples.

Conclusions:

  • The symmetry seeker neural network offers a powerful, automated tool for uncovering fundamental symmetries.
  • This machine learning approach broadens the scope of systems amenable to symmetry analysis.
  • The method holds significant potential for advancing research in physics, chemistry, and materials science.