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Data-driven inference of coupling functions in oscillatory systems via physics-informed neural networks

Gyuyoung Hwang1, Hyeontae Jo1,2,*, and Jae Kyoung Kim1,3,4,†

  • 1Biomedical Mathematics Group, Institute for Basic Science, Daejeon 34126, Republic of Korea
  • 2Department of Mathematics, Ajou University, Suwon 16499, Republic of Korea
  • 3Department of Mathematics, KAIST, Daejeon 34141, Republic of Korea
  • 4Department of Medicine, College of Medicine, Korea University, Seoul 02841, Republic of Korea

  • *Contact author: ajouhtj@ajou.ac.kr
  • †Contact author: jaekkim@kaist.ac.kr
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Phys. Rev. Research 8, 013259 – Published 9 March, 2026

DOI: https://doi.org/10.1103/t8g2-n22v

Abstract

Coupling of oscillators is a universal phenomenon observed across diverse fields, from power grids in engineering to neuronal oscillators and circadian rhythms in biology. Understanding their dynamics requires identifying how individual oscillators interact. Traditionally, inferring the coupling mechanism from observable time series data involves estimating the coupling function—describing the interaction mechanism—using preassigned basis functions such as trigonometric polynomials. However, this approach is limited by the lack of a definitive rule for selecting the optimal number of basis functions, relying instead on subjective user choices. Here, we found that no single optimal number of basis functions exists: While using more basis functions helps capture complex coupling mechanisms, it tends to overfit and degrade performance with sparse or noisy data. To overcome these limitations, we developed Inference of Coupling using physics-informed neural networks (IC-PINN). Unlike conventional approaches, IC-PINN can infer diverse coupling functions from sparse and noisy data without requiring manual tuning, making it broadly applicable to various real-world systems of coupled oscillators. IC-PINN successfully identified that the segmentation clock operates via a “Winner-Take-All” synchronization mechanism and accurately inferred the coupling function in the self-assembly of optically interacting nanorotors. By offering a powerful tool for studying coupled oscillators, IC-PINN can provide deeper insights into complex interacting systems across biology, physics, and beyond.

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Phys. Rev. Research 8, 013259– Published 9 March, 2026
  • Received 1 April 2025
  • Accepted 10 February 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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