###### Abstract  
Traditional femtosecond laser modeling relies on the iterative solution of the Nonlinear Schrodinger Equation (NLSE) using the Split-Step Fourier Method (SSFM). However, SSFM's high computational complexity leads to significant time consumption, particularly in automatic control and system optimization, thus limiting control model responsiveness. Recent studies have suggested using neural networks to simulate fiber dynamics, offering faster computation and lower costs. In this study, we introduce a novel fiber propagation method utilizing the DeepONet architecture for the first time. By separately managing fiber parameters and input-output pulses in the branch and trunk networks, this method can simulate various fiber configurations with high accuracy and without altering the architecture. Additionally, while SSFM generation time increases linearly with fiber length, the GPU-accelerated AI generation time remains consistent at around 0.0014 s, regardless of length. Notably, in high-order soliton (HOS) compression over a 12 m distance, the AI method is approximately 56,865 times faster than SSFM. DeepONet; fiber pulse propagation; nonlinear dynamics; neural networks; femtosecond laser; Split-Step Fourier Method +
Footnote †: journal: Applied  
_Applied_  
_Acticle_  
A Fast Prediction Framework for Multi-Variable Dynamic Modeling of Fiber Pulse Propagation Using DeepONet  
[PERSON], [PERSON], [PERSON], N. A Fast Prediction Framework for Multi-Variable Nonlinear Dynamic Modeling of Fiber Pulse Propagation Using DeepONet. _Applied_  
A Fast Prediction Framework for Multi-Variable Dynamic Modeling of Fiber Pulse Propagation Using DeepONet  
A Fast Prediction Framework for Multi-Variable Nonlinear Dynamic Modeling of Fiber Pulse Propagation Using  
idea combines traditional neural networks with operator learning, thereby enabling the handling of highly complex dynamic systems. Both operator learning and Physics-Informed Neural Networks (PINNs) leverage neural networks to approximate a mapping [13]. According to the universal approximation theorem, a feedforward neural network with a single hidden layer, with sufficient width and nonlinear activation functions, can approximate a mapping to any desired accuracy [11]. The main difference between the two is that PINNs approximate the solution of the differential equation themselves, while operator learning approximates the mapping from the input function of the differential equation to the solution function. In this context, the independent variable in the mapping is the input function of the differential equation, while the dependent variable is the output function. The advantage of operator learning over traditional PINNs is that when the input function, initial conditions, or boundary conditions of the differential equation change, the neural network does not need retraining [14]. Regular neural networks approximate the solution of the differential equation itself, causing any slight change in initial conditions to result in a different solution. Conversely, the DeepONet neural network learns the mapping from the input function to the solution, allowing it to manage input functions not included in the training set and derive the corresponding solutions [14]. As a result, a trained DeepONet exhibits stronger generalization capabilities, theoretically achieving similar results with less data, and does not require retraining when switching to a new simulation object as long as the type of differential equation remains the same. This represents a significant advancement given the high costs associated with training neural networks [11; 12]. Although studies have shown that various data-driven neural networks, such as Recurrent Neural Networks (RNNs) [15], Convolutional Neural Networks (CNNs) [16], and Long Short-Term Memory networks (LSTMs) [17], perform well in simulating optical systems, they also have drawbacks.