相关论文: Low-complexity full-field ultrafast nonlinear dyna…

The propagation of ultrashort pulses in optical fibre displays complex nonlinear dynamics that find important applications in fields such as high power pulse compression and broadband supercontinuum generation. Such nonlinear evolution…

The modeling of optical wave propagation in optical fiber is a task of fast and accurate solving the nonlinear Schr\"odinger equation (NLSE), and can enable the optical system design, digital signal processing verification and fast waveform…

The nonlinear propagation of ultrashort pulses in optical fiber depends sensitively on both input pulse and fiber parameters. As a result, optimizing propagation for specific applications generally requires time-consuming simulations based…

The ever-increasing demand for processing data with larger machine learning models requires more efficient hardware solutions due to limitations such as power dissipation and scalability. Optics is a promising contender for providing lower…

With the rapid development of deep learning, a variety of change detection methods based on deep learning have emerged in recent years. However, these methods usually require a large number of training samples to train the network model, so…

Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited…

The use of deep neural network (DNN) models as surrogates for linear and nonlinear structural dynamical systems is explored. The goal is to develop DNN based surrogates to predict structural response, i.e., displacements and accelerations,…

Nonlinear dynamic models are widely used for characterizing functional forms of processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data…

Transition prediction is an important aspect of aerodynamic design because of its impact on skin friction and potential coupling with flow separation characteristics. Traditionally, the modeling of transition has relied on correlation-based…

Design and analysis of inelastic materials requires prediction of physical responses that evolve under loading. Numerical simulation of such behavior using finite element (FE) approaches can call for significant time and computational…

We study the fundamental problem of learning a marginally stable unknown nonlinear dynamical system. We describe an algorithm for this problem, based on the technique of spectral filtering, which learns a mapping from past observations to…

Image restoration is a long-standing problem in low-level computer vision with many interesting applications. We describe a flexible learning framework based on the concept of nonlinear reaction diffusion models for various image…

The nonlinear Schr\"odinger equation (NLSE) is a fundamental model for wave dynamics in nonlinear media ranging from optical fibers to Bose-Einstein condensates. Accurately estimating its parameters, which are often strongly correlated,…

Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…

This paper focuses on developing a method to obtain an uncertain linear fractional transformation (LFT) system that adequately captures the dynamics of a nonlinear time-invariant system over some desired envelope. First, the nonlinear…

We utilize the Feature Decoupling Distributed (FDD) method to enhance the capability of deep learning to fit the Nonlinear Schrodinger Equation (NLSE), significantly reducing the NLSE loss compared to non decoupling model.

Modeling nonlinear pulse propagation in multimode fibers is challenging due to the large number of interacting modes and the resulting spatiotemporal complexity. Traditional optimization methods often become intractable, while…

Recently developed reduced-order modeling techniques aim to approximate nonlinear dynamical systems on low-dimensional manifolds learned from data. This is an effective approach for modeling dynamics in a post-transient regime where the…

This paper establishes a nonlinear separation principle based on contraction theory and derives sharp stability conditions for recurrent neural networks (RNNs). First, we introduce a nonlinear separation principle that guarantees global…

Feature propagation in Deep Neural Networks (DNNs) can be associated to nonlinear discrete dynamical systems. The novelty, in this paper, lies in letting the discretization parameter (time step-size) vary from layer to layer, which needs to…