Resonant optical systems can behave like exquisitely sensitive instruments, but extracting the physical information hidden in their spectral signals has long been a difficult computational problem. Now, researchers in China have developed a physics-data co-driven deep neural network that combines the predictive power of machine learning with the governing principles of coupled mode theory. The approach could make it dramatically faster and more reliable to decode complex optical resonators—and may enable nanoscale displacement sensing with a level of speed and precision difficult to achieve using conventional methods.
The work addresses a central challenge in the study of coupled resonant systems. When two or more optical cavities interact, their resonances can shift, broaden, split, or interfere with one another. These changes produce complicated transmission spectra that contain information about the system’s intrinsic resonant frequencies, losses, coupling strengths, and transmission phases. In principle, researchers can recover these parameters by fitting measured spectra to theoretical formulas. In practice, however, the process can be slow, computationally demanding, and vulnerable to multiple solutions.
The problem arises because different combinations of physical parameters can generate spectral responses that look remarkably similar. A fitting algorithm may therefore identify several plausible answers, making it difficult to determine which set of parameters accurately represents the real optical system. This ambiguity is particularly serious in advanced resonant platforms associated with exceptional points, topological photonics, bound states in the continuum, high-sensitivity sensing, optical signal processing, and low-threshold lasers.
To overcome these limitations, a team led by Da-Quan Yang of Beijing University of Posts and Telecommunications, Yi Xu of Guangdong University of Technology, and Hua-Shun Wen of Nankai University designed a neural network trained with data generated by coupled mode theory. Rather than relying only on large collections of experimental measurements, the system learns from low-cost theoretical datasets produced by a physical model. This gives the network access to many possible combinations of resonant-system parameters without requiring researchers to measure every case in the laboratory.
The network also incorporates physical constraints based on the eigenvalues of the coupled system directly into its loss function. In a conventional deep-learning model, the loss function measures how far a prediction is from a target answer. Here, the loss function additionally penalizes predictions that violate the physical behavior expected from the resonator. This physics-guided design helps the network distinguish between mathematically possible solutions and solutions that are consistent with the underlying dynamics of coupled optical modes.
In simulations and experiments, the method retrieved four important parameters in complex coupled resonant systems: intrinsic resonant frequency, intrinsic loss, coupling strength, and transmission phase. According to the researchers, the average computation time was reduced by three orders of magnitude compared with traditional fitting methods, while predicted performance improved by more than two orders of magnitude. Relative to a conventional data-driven neural network without the same physical constraints, the prediction error for physical parameters fell by as much as 81.59 percent.
The result is significant because it shows how machine learning can be used not simply as a fast pattern-recognition tool, but as a way to preserve and exploit the physical structure of a problem. In optical systems, where a small change in geometry, material properties, or cavity spacing can produce a large and highly nonlinear spectral response, this combination may be especially valuable. A model that understands both the measured signal and the equations behind it can be more robust when data are limited, noisy, or affected by multiple interacting resonances.
The researchers next tested the framework in a displacement-sensing experiment involving two coupled microcavities. As the displacement changed, it modified the system’s underlying physical parameters, producing spectral signatures that included resonance shifts, linewidth broadening, and mode splitting. The researchers fed the measured transmission spectra into the pre-trained network, then used the predicted parameter changes to infer displacement. The system maintained strong performance across different displacement conditions, with reported coefficients of determination, or R² values, above 0.979.
This approach could have applications beyond the particular microcavity platform tested in the study. Fast retrieval of hidden physical parameters could help researchers characterize integrated photonic circuits, tune coupled-resonator devices, monitor microscopic mechanical motion, and develop intelligent sensors for nanoscale particles. The framework may also support non-invasive morphological measurements of on-chip optical systems, where extracting information from spectral changes without physically disturbing the device is highly desirable.
The researchers say the method’s broader potential lies in its scalability. By combining physics-based simulation, experimental data, and neural-network inference, the framework could be adapted to increasingly complicated systems containing multiple cavities or several sensing modalities. Future integration with optoelectronic chips and multimodal sensing technologies may create compact platforms capable of analyzing several physical properties at once. For a field in which interpreting every spectral feature can be computationally expensive, a neural network that learns the language of coupled light could turn complex resonances into rapid, actionable measurements.
Subject of Research: Physics-data co-driven deep neural networks for analyzing coupled optical resonant systems and nanoscale displacement sensing
Article Title: Deciphering optical coupled resonant systems with physics-data co-driven deep neural networks
Web References: https://doi.org/10.1038/s41377-026-02389-0
References: Light: Science & Applications, DOI: 10.1038/s41377-026-02389-0
Image Credits: Hua-Shun Wen et al.
Keywords
Optical resonators, coupled mode theory, deep neural networks, physics-informed machine learning, photonics, microcavities, resonant sensing, nanoscale displacement detection, coupled resonant systems, optical spectroscopy
Tags: artificial intelligence in photonic device characterizationcomplex optical transmission spectra interpretationcomputational methods for optical cavity analysiscoupled optical resonator spectral analysisdeep learning for coupled mode theorymachine learning in nanophotonicsnanoscale displacement sensing techniquesneural network-based spectral fittingoptical resonator parameter extractionphysics-data driven neural networks for optical sensingresonant optical system sensitivity enhancementspectral signal decoding in optical systems
