Physics-informed machine learning for optical fiber channel modeling

Introduction
Optical fiber communication systems form the backbone of modern digital infrastructure, enabling global Internet connectivity with ultra-high bandwidth and low latency. An accurate fiber channel model plays a critical role in optimizing transmission performance, as it enables the development of advanced receivers, analysis of signal distortions, signal shaping and coding design, and reliable system performance prediction.  

The nonlinear Schrödinger equation (NLSE) serves as the fundamental mathematical model for describing optical signal propagation in fibers. However, the NLSE is a nonlinear partial differential equation that lacks an analytical solution except for a few specific cases. Traditional numerical methods such as the split-step Fourier method (SSFM), have been widely used to obtain approximate solutions. While these methods are physically accurate, they are computationally expensive and limited in scalability for real-time applications.  

Recent advances in physics-informed machine learning offer new opportunities for efficient and physically consistent optical fiber modeling. By embedding physical laws (such as the NLSE) directly into the learning process through a customized loss, models such as physics-informed neural networks (PINNs) or physics-informed neural operators (PINO) can learn to approximate fiber channel behavior and perform fast inference without requiring large datasets [1,2].  

In this project, we will explore how recent physics-informed machine learning methods can be utilized for fiber channel modeling together and evaluate their performance. 

Objective
The goal of this project is to investigate and compare physics-informed machine learning methods for optical fiber channel modeling. Starting from the classical SSFM and progressing toward advanced AI-based approaches, you will explore various neural network architectures and learn how physics knowledge can be incorporated into the training process.  

Contents:

1. Baseline modeling: Implement a reference optical fiber propagation model using the SSFM. This will serve as a benchmark for evaluating the performance of subsequent machine learning approaches.  

2. Physics-informed machine learning methods:  Develop and train physics-informed neural models to learn fiber channel dynamics. Begin by implementing PINNs and PINO to understand how physical priors can be incorporated into the training process. Subsequently, explore more advanced architectures such as physics-informed Fourier neural operators [3], physics-informed Kolmogorov-Arnold networks [4], or physics-informed diffusion model [5] to investigate their potential for fiber channel modeling. You are encouraged to experiment with different methods and system configurations according to your research interests. 

3. Performance evaluation: Assess the benefits of physics-informed machine learning methods in comparison with the SSFM by evaluating their accuracy and inference speed against SSFM results. Further, analyze the strengths, weaknesses, and trade-offs among different physics-informed approaches developed in Step 2.  

Expected Contributions

1. A novel, ML-based fiber modeling method for single-span systems.

Prerequisites: Interest in optical fiber communications and exploring.  Basic knowledge of machine learning and Python.  

Level: Bachelor thesis project.

Number of students: Between 3–6 students.

Contact: Zicong Jiang, zicongj@chalmers.se

References: 

[1] Zang, Yubin, et al. "Principle-driven fiber transmission model based on PINN neural network." Journal of Lightwave Technology 40.2 (2021): 404-414.  

[2] Song, Yuchen, et al. "Physics-informed neural operator for fast and scalable optical fiber channel modelling in multi-span transmission." 2022 European Conference on Optical Communication (ECOC). IEEE, 2022.  

[3] He, Xingchen, et al. "Fourier neural operator for accurate optical fiber modeling with low complexity." Journal of Lightwave Technology 41.8 (2022): 2301-2311.  

[4] Jiang, Xiaotian, et al. "FiberKAN: Kolmogorov-Arnold Networks for Nonlinear Fiber Optics." Journal of Lightwave Technology (2025).  

[5] Wang, Sifan, et al. "Fundiff: Diffusion models over function spaces for physics-informed generative modeling." arXiv preprint arXiv:2506.07902 (2025).