# Physics-informed Neural Network for Nonlinear Dynamics in Fiber Optics

arXiv: https://arxiv.org/abs/2109.00526 · HTML: https://mlsanity.com/paper/2109.00526/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 40 references that are in the map.
- First posted on arXiv 1 Sep 2021.

## Builds on (most cited first, 4 of 4)

- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks](https://mlsanity.com/paper/1905.01205/) (2019)
- [A Physics-Informed Machine Learning Approach for Solving Heat Transfer Equation in Advanced Manufacturing and Engineering Applications](https://mlsanity.com/paper/2010.02011/) (2020)

## Built on by (most cited first, 7 of 7)

- [From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning](https://mlsanity.com/paper/2410.13228/) (2024)
- [A Dimension-Augmented Physics-Informed Neural Network (DaPINN) with High Level Accuracy and Efficiency](https://mlsanity.com/paper/2210.13212/) (2022)
- [Neural networks for bifurcation and linear stability analysis of steady states in partial differential equations](https://mlsanity.com/paper/2407.19707/) (2024)
- [Data assimilation and parameter identification for water waves using the nonlinear Schr"odinger equation and physics-informed neural networks](https://mlsanity.com/paper/2401.03708/) (2024)
- [Physics Informed Constrained Learning of Dynamics from Static Data](https://mlsanity.com/paper/2504.12675/) (2025)
- [Understanding the Capabilities of Molecular Graph Neural Networks in Materials Science Through Multimodal Learning and Physical Context Encoding](https://mlsanity.com/paper/2505.12137/) (2025)
- [Predicting nonlinear reshaping of periodic signals in optical fibre with a neural network](https://mlsanity.com/paper/2303.09133/) (2023)

## Abstract (arXiv)

A physics-informed neural network (PINN) that combines deep learning with physics is studied to solve the nonlinear Schr"odinger equation for learning nonlinear dynamics in fiber optics. We carry out a systematic investigation and comprehensive verification on PINN for multiple physical effects in optical fibers, including dispersion, self-phase modulation, and higher-order nonlinear effects. Moreover, both special case (soliton propagation) and general case (multi-pulse propagation) are investigated and realized with PINN. In the previous studies, the PINN was mainly effective for single scenario. To overcome this problem, the physical parameters (pulse peak power and amplitudes of sub-pulses) are hereby embedded as additional input parameter controllers, which allow PINN to learn the physical constraints of different scenarios and perform good generalizability. Furthermore, PINN exhibits better performance than the data-driven neural network using much less data, and its computational complexity (in terms of number of multiplications) is much lower than that of the split-step Fourier method. The results report here show that the PINN is not only an effective partial differential equation solver, but also a prospective technique to advance the scientific computing and automatic modeling in fiber optics.