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Buildup and switching mechanisms of solitons in complex nonlinear systems are fundamentally important dynamical regimes. Using a novel strongly nonlinear optical system,the work reveals a new buildup scenario for soliton molecules , which includes a long-duration stage dominated by the emergence of transient NLPs modes to withstand strong disturbances arising from turbulence and extreme nonlinearity in the optical cavity. Systematic simulations reveal effects of the PC rotation angle and intra-cavity nonlinearity on the periodic phase transitions between the different soliton states, and accurately reproduce the experimentally observed buildup and switching mechanisms. These findings could enhance our fundamental study and points to potential uses in designing information encoding systems., Comment: To be published in LASER & PHOTONICS REVIEWS

Soliton pulsations are ubiquitous feature of non-stationary soliton dynamics in mode-locked lasers and many other physical systems. To overcome difficulties related to huge amount of necessary computations and low efficiency of traditional numerical methods in modeling the evolution of non-stationary solitons, we propose a two-parallel bidirectional long short-term memory recurrent neural network, with the main objective to predict dynamics of vector-soliton pulsations in various complex states, whose real-time dynamics is verified by experiments. Besides, the scheme of coded information storage based on the TP-Bi_LSTM RNN, instead of actual pulse signals, is realized too. The findings offer new applications of deep learning to ultrafast optics and information storage., Comment: To be published in Laser & Photonics Reviews;https://doi.org/10.1002/lpor.202400097

The majority of current salient object detection (SOD) models are focused on designing a series of decoders based on fully convolutional networks (FCNs) or Transformer architectures and integrating them in a skillful manner. These models have achieved remarkable high performance and made significant contributions to the development of SOD. Their primary research objective is to develop novel algorithms that can outperform state-of-the-art models, a task that is extremely difficult and time-consuming. In contrast, this paper proposes a positive feedback method based on F-measure value for SOD, aiming to improve the accuracy of saliency prediction using existing methods. Specifically, our proposed method takes an image to be detected and inputs it into several existing models to obtain their respective prediction maps. These prediction maps are then fed into our positive feedback method to generate the final prediction result, without the need for careful decoder design or model training. Moreover, our method is adaptive and can be implemented based on existing models without any restrictions. Experimental results on five publicly available datasets show that our proposed positive feedback method outperforms the latest 12 methods in five evaluation metrics for saliency map prediction. Additionally, we conducted a robustness experiment, which shows that when at least one good prediction result exists in the selected existing model, our proposed approach can ensure that the prediction result is not worse. Our approach achieves a prediction speed of 20 frames per second (FPS) when evaluated on a low configuration host and after removing the prediction time overhead of inserted models. These results highlight the effectiveness, efficiency, and robustness of our proposed approach for salient object detection., Comment: 13 pages, 4 figures, 3 table

Convection-diffusion equation is used to describe particle migration process in many fields, while it is proposed based on the empirical Fick's law. In this paper, with the help of the percolation model, we theoretically investigate the particle migration law in porous media from the mesoscopic perspective, and base on the probabilistic migration characteristic of particles to strictly reformulate the convection-diffusion equation. Meanwhile the quantitative relations between the convection, diffusion coefficients and the mesoscopic parameters of particle-motion and percolation-configuration are revealed. Furthermore, via the Monte-Carlo numerical simulation, we verify the proposed mesoscopic particle migration theory and modify the expressions of convection, diffusion coefficients for global applicability. In addition, applicable qualification of the proposed mesoscopic theory is given, and relation between the blocking effect parameter and connecting probability of the percolation model is obtained.

The strongly-constrained physics-informed neural network (SCPINN) is proposed by adding the information of compound derivative embedded into the soft-constraint of physics-informed neural network(PINN). It is used to predict nonlinear dynamics and the formation process of bright and dark picosecond optical solitons, and femtosecond soliton molecule in the single-mode fiber, and reveal the variation of physical quantities including the energy, amplitude, spectrum and phase of pulses during the soliton transmission. The adaptive weight is introduced to accelerate the convergence of loss function in this new neural network. Compared with the PINN, the accuracy of SCPINN in predicting soliton dynamics is improved by 5-11 times. Therefore, the SCPINN is a forward-looking method to study the modeling and analysis of soliton dynamics in the fiber.

In the process of the deep learning, we integrate more integrable information of nonlinear wave models, such as the conservation law obtained from the integrable theory, into the neural network structure, and propose a conservation-law constrained neural network method with the flexible learning rate to predict solutions and parameters of nonlinear wave models. As some examples, we study real and complex typical nonlinear wave models, including nonlinear Schr\"odinger equation, Korteweg-de Vries and modified Korteweg-de Vries equations. Compared with the traditional physics-informed neural network method, this new method can more accurately predict solutions and parameters of some specific nonlinear wave models even when less information is needed, for example, in the absence of the boundary conditions. This provides a reference to further study solutions of nonlinear wave models by combining the deep learning and the integrable theory.

A modified physics-informed neural network is used to predict the dynamics of optical pulses including one-soliton, two-soliton, and rogue wave based on the coupled nonlinear Schr\"odinger equation in birefringent fibers. At the same time, the elastic collision process of the mixed bright-dark soliton is predicted. Compared the predicted results with the exact solution, the modified physics-informed neural network method is proven to be effective to solve the coupled nonlinear Schr\"odinger equation. Moreover, the dispersion coefficients and nonlinearity coefficients of the coupled nonlinear Schrodinger equation can be learned by modified physics-informed neural network. This provides a reference for us to use deep learning methods to study the dynamic characteristics of solitons in optical fibers.

Based on conservation laws as one of the important integrable properties of nonlinear physical models, we design a modified physics-informed neural network method based on the conservation law constraint. From a global perspective, this method imposes physical constraints on the solution of nonlinear physical models by introducing the conservation law into the mean square error of the loss function to train the neural network. Using this method, we mainly study the standard nonlinear Schr\"odinger equation and predict various data-driven optical soliton solutions, including one-soliton, soliton molecules, two-soliton interaction, and rogue wave. In addition, based on various exact solutions, we use the modified physics-informed neural network method based on the conservation law constraint to predict the dispersion and nonlinear coefficients of the standard nonlinear Schr\"odinger equation. Compared with the traditional physics-informed neural network method, the modified method can significantly improve the calculation accuracy.

We use the physics-informed neural network to solve a variety of femtosecond optical soliton solutions of the high order nonlinear Schr\"odinger equation, including one-soliton solution, two-soliton solution, rogue wave solution, W-soliton solution and M-soliton solution. The prediction error for one-soliton, W-soliton and M-soliton is smaller. As the prediction distance increases, the prediction error will gradually increase. The unknown physical parameters of the high order nonlinear Schr\"odinger equation are studied by using rogue wave solutions as data sets. The neural network is optimized from three aspects including the number of layers of the neural network, the number of neurons, and the sampling points. Compared with previous research, our error is greatly reduced. This is not a replacement for the traditional numerical method, but hopefully to open up new ideas.