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PreprintCC BY 4.0arXiv

Automated discovery of dimensional reductions in coupled oscillators

  • Dishant Sisodia
  • Sarika Jalan
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Abstract

There have been persistent efforts to uncover low-dimensional macroscopic dynamics in large systems of interacting microscopic units, in which underlying physical principles govern their collapse onto low-dimensional manifolds. Here, focusing on interacting phase oscillator systems, we show that an unsupervised autoencoder framework can determine their intrinsic dimensionality, in agreement with the predictions of Watanabe-Strogatz theory. Systematic sweeps over the latent dimensions identify the analytically predicted reduced dimensions, while supervised regression confirms that the learned latent variables capture the full information contained in the theoretical Watanabe-Strogatz coordinates. We demonstrate this capability for two prototype systems: Kuramoto oscillators and resistively loaded Josephson junctions. We further establish the diagnostic specificity of the framework by showing that systems lacking such reducible dynamics do not exhibit a sharp dimensional reduction.

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Cite

BibTeXRIS
BibTeX
@misc{sisodia2026automated,
  title = {{Automated discovery of dimensional reductions in coupled oscillators}},
  author = {Dishant Sisodia and Sarika Jalan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.03784},
  eprint = {2610.03784},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.03784},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Automated discovery of dimensional reductions in coupled oscillators
AU  - Dishant Sisodia
AU  - Sarika Jalan
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.03784
UR  - https://arxiv.org/abs/2610.03784
AB  - There have been persistent efforts to uncover low-dimensional macroscopic dynamics in large systems of interacting microscopic units, in which underlying physical principles govern their collapse onto low-dimensional manifolds. Here, focusing on interacting phase oscillator systems, we show that an unsupervised autoencoder framework can determine their intrinsic dimensionality, in agreement with the predictions of Watanabe-Strogatz theory. Systematic sweeps over the latent dimensions identify the analytically predicted reduced dimensions, while supervised regression confirms that the learned latent variables capture the full information contained in the theoretical Watanabe-Strogatz coordinates. We demonstrate this capability for two prototype systems: Kuramoto oscillators and resistively loaded Josephson junctions. We further establish the diagnostic specificity of the framework by showing that systems lacking such reducible dynamics do not exhibit a sharp dimensional reduction.
ER  -