The initial state of a nonlinear optical fiber system plays a vital role in the ultrafast pulse evolution dynamic. In this work, a data-driven compressed convolutional neural network, named inverse network, is proposed to predict initial pulse distribution through a series of discrete power profiles at different propagation distances. The inverse network is trained and tested based on two typical nonlinear dynamics: (1) the pulse evolution in a fiber optical parametric amplifier system and (2) soliton pair evolution in high-nonlinear fibers. Great prediction accuracy is reached when the epoch grows to 5000 in both cases, with the normalized root mean square errors below 0.01 on the entire testing set. Meanwhile, the lightweight network is highly effective. In this work, it takes approximately 30 seconds for 5,000 epochs training with a dataset size of 900. The inverse network is further tested and analyzed on the dataset with different signal-to-noise ratios and input sizes. The results show fair stability at the deviation on the testing set. The proposed inverse network demonstrates a promising approach to optimizing the initial pulse of fiber optics systems.

A physics-based deep learning (DL) method termed Phynet is proposed for modeling the nonlinear pulse propagation in optical fibers totally independent of the ground truth. The presented Phynet is a combination of a handcrafted neural network and the nonlinear Schrödinger physics model. In particular, Phynet is optimized through physics loss generated by the interaction between the network and the physical model rather than the supervised loss. The inverse pulse propagation problem is leveraged to exemplify the performance of Phynet when in comparison to the typical DL method under the same structure and datasets. The results demonstrate that Phynet is able to precisely restore the initial pulse profiles with varied initial widths and powers, while revealing a similar prediction accuracy compared with the typical DL method. The proposed Phynet method can be expected to break the severe bottleneck of the traditional DL method in terms of relying on abundant labeled data during the training phase, which thus brings new insight for modeling and predicting the nonlinear dynamics of the fibers.

The nonlinear evolution of ultrashort pulses in optical fiber has broad applications, but the computational burden of convolutional numerical solutions necessitates rapid modeling methods. Here, a lightweight convolutional neural network is designed to characterize nonlinear multi-pulse propagation in highly nonlinear fiber. With the proposed network, we achieve the forward mapping of multi-pulse propagation using the initial multi-pulse temporal profile as well as the inverse mapping of the initial multi-pulse based on the propagated multi-pulse with the coexistence of group velocity dispersion and self-phase modulation. A multi-pulse comprising various Gaussian pulses in 4-level pulse amplitude modulation is utilized to simulate the evolution of a complex random multi-pulse and investigate the prediction precision of two tasks. The results obtained from the unlearned testing sets demonstrate excellent generalization and prediction performance, with a maximum absolute error of 0.026 and 0.01 in the forward and inverse mapping, respectively. The approach provides considerable potential for modeling and predicting the evolution of an arbitrary complex multi-pulse.

Brillouin optical time-domain analyzer (BOTDA) is used to monitor the temperature and strain along a fiber. So far, neural network and machine learning methods have been successfully applied for temperature extraction. But for different frequency scanning steps, different networks should be designed and trained. Here, a BOTDA assisted by kernel extreme learning machine (K-ELM) with high generalization is proposed and experimentally demonstrated. By utilizing K-ELM, the raw Brillouin gain spectra measured from BOTDA system are classified into different temperature classes. The performance of K-ELM is investigated both in simulation and experiment under different cases of signal-to-noise ratios, pump pulse widths, and frequency scanning steps. Compared with curve fitting methods, the K-ELM algorithm has better measurement accuracy of 0.3 and it realizes great improvement of the processing speed over 120 times. The ultrafast processing speed, high accuracy and universality make K-ELM become a highly competitive candidate for the high-speed BOTDA sensing system.

Ocean temperature prediction plays crucial roles in the ocean-related fields. The graph neural networks (GNNs) show advantages for modeling complex environmental issues. However, the prior methods typically focus on node features to predict ocean temperature. Note that the edge features are essential, especially for 3-D ocean temperature prediction. In this letter, a GNN with optimized attention mechanisms (GNN-OAMs) model is proposed to predict 3-D ocean temperature. The GNN-OAM introduces a random forest (RF) module to capture the nonstationary temporal dependencies. Especially, the OAMs, via combination of multiple adjacency matrices construct edge features, are presented to capture the dynamic spatial dependencies. The prediction performance of GNN-OAM model is evaluated in the 3-D ocean temperature experimental dataset, and the results show that the GNN-OAM achieves ocean temperature prediction with high accuracy, and the MAEs are 0.146 and 0.26, when predicting temperatures in next one day and five days.