[Enlarge image]Automated interpretation of soliton fission physics in temporal (left) and spectral (right) domains for the generalized nonlinear Schrödinger equation shown. Top images show propagation evolution maps as well as output temporal and spectral profiles, with the dispersive wave components (light blue) scaled as indicated. Bottom plots and accompanying color map show how the algorithm identifies different interaction regions allowing the automatic, unsupervised association with physical effects.
Machine learning has revolutionized nearly every aspect of experimental photonics. But machine learning can have just as revolutionary an impact on theory as on experiment, enabling discovery of new physical laws from data and enhancing understanding of complex nonlinear dynamics. The modeling of physical systems thus no longer relies solely on human insight and intuition; machine learning can drive entirely new directions in theoretical research.
An important initial advance in optics was the use of supervised clustering and regression to analyze instability dynamics in optical fiber.1 Ultrashort-pulse propagation in fiber is governed by the nonlinear Schrödinger equation and its extensions, involving processes such as Kerr nonlinearity, dispersion of multiple orders and inelastic Raman scattering. Understanding the interplay between these effects poses an enormous problem for researchers, yet a clear physical interpretation is vital for key applications such as pulse compression, frequency combs and supercontinuum generation.
We recently developed a fully unsupervised machine-learning technique that solves this problem algorithmically, without requiring human interpretation.2 Adapted from concepts originally used in ocean science, turbulence modeling and applied mathematics,3–5 the method can autonomously identify the dominant physics associated with specific regions of pulse propagation, revealing new insights into the physics of fiber soliton compression, optical-shock formation and soliton fission in supercontinuum generation.
The algorithm’s underlying idea is first to compute the spatiotemporal evolution of pulse propagation by numerically integrating the governing differential equation. Then, we calculate the relative magnitude of each term in the equation to determine how different combinations contribute to satisfying an equality in which the sum of terms must equal zero. This powerful concept lets us automatically detect regions of evolution where only a subset of terms possess significant magnitude, while all other terms are negligible.
To allow the procedure to run with no human input, our implementation uses statistical Gaussian mixture model clustering, followed by the application of a combinatorial metric as a threshold. This yields a robust, fully unsupervised method to determine how different regions of evolution are associated with different physical interactions. Our work is also the first application in any physical system to identify dominant-balance regimes in both temporal and spectral domains.
This algorithmic approach to interpreting complex dynamics provides, in our view, a fresh way for researchers to think about seemingly well-known phenomena. It also opens new windows into applying approximate theoretical methods, as it can automatically detect limiting asymptotic regimes. Most important, the technique is general and not limited to ultrafast fiber optics. Indeed, it can be readily extended to all systems where dynamics are described by differential equations. We thus believe it shows tremendous promise for wide application across photonics.
Researchers
A. Ermolaev and J.M. Dudley, Université de Franche-Comté, Besançon, France
C. Finot, Université de Bourgogne, Dijon, France
G. Genty, Tampere University, Tampere, Finland
References
1. A.V. Ermolaev et al. Sci. Rep. 13, 10462 (2023).
2. A.V. Ermolaev et al. Opt. Lett. 49, 4202 (2024).
3. M. Sonnewald et al. Earth Space Sci. 6, 784 (2019).
4. J.L. Callaham et al. Nat. Commun. 12, 1016 (2021).
5. B.E. Kaiser et al. Eng. Appl. Artif. Intell. 116, 105496 (2022).