Related papers: Nonlinear Schr\"odinger Kernel for hardware accele…

Nonlinear systems are capable of displaying complex behavior even if this is the result of a small number of interacting time scales. A widely studied case is when complex dynamics emerges out of a nonlinear system being forced by a simple…

In this paper, we show that the presence of nonlinear coupling between time series may be detected employing kernel feature space representations alone dispensing with the need to go back to solve the pre-image problem to gauge model…

Artificial intelligence (AI) has rapidly evolved into a critical technology; however, electrical hardware struggles to keep pace with the exponential growth of AI models. Free space optical hardware provides alternative approaches for…

Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations.…

Optical fibers have been enabling numerous distinguished applications involving the operation and generation of light, such as soliton transmission, light amplification, all-optical switching and supercontinuum generation. The active…

Advances in machine learning have revolutionized capabilities in applications ranging from natural language processing to marketing to health care. Here, we demonstrate the efficacy of machine learning in predicting chaotic behavior in…

The recent rapid increase in demand for data processing has resulted in the need for novel machine learning concepts and hardware. Physical reservoir computing and an extreme learning machine are novel computing paradigms based on physical…

We propose a technique for reformulation of state and parameter estimation problems as that of matching explicitly computable definite integrals with known kernels to data. The technique applies for a class of systems of nonlinear ordinary…

Fractional nonlinear differential equations present an interplay between two common and important effective descriptions used to simplify high dimensional or more complicated theories: nonlinearity and fractional derivatives. These…

Time-dependent nonlinear media, such as rapidly generated plasmas produced via laser ionization of gases, can increase the energy of individual laser photons and generate tunable high-order harmonic pulses. This phenomenon, known as photon…

Advances in the amplification and manipulation of ultrashort laser pulses has led to revolutions in several areas. Examples include chirped pulse amplification for generating high peak-power lasers, power-scalable amplification techniques,…

Machine-intelligence has become a driving factor in modern society. However, its demand outpaces the underlying electronic technology due to limitations given by fundamental physics such as capacitive charging of wires, but also by system…

Electromagnetically induced transparency in an optically thick, cold medium creates a unique system where pulse-propagation velocities may be orders of magnitude less than $c$ and optical nonlinearities become exceedingly large. As a…

Nonlinear and dispersive transmission impairments in coherent fiber-optic communication systems are often compensated by reverting the nonlinear Schr\"odinger equation, which describes the evolution of the signal in the link, numerically.…

Regression on medical image sequences can capture temporal image pattern changes and predict images at missing or future time points. However, existing geodesic regression methods limit their regression performance by a strong underlying…

Kernel methods are fundamental tools in machine learning that allow detection of non-linear dependencies between data without explicitly constructing feature vectors in high dimensional spaces. A major disadvantage of kernel methods is…

There has been a recent surge of interest in the implementation of linear operations such as matrix multipications using photonic integrated circuit technology. However, these approaches require an efficient and flexible way to perform…

Research in modern data-driven dynamical systems is typically focused on the three key challenges of high dimensionality, unknown dynamics, and nonlinearity. The dynamic mode decomposition (DMD) has emerged as a cornerstone for modeling…

Kernel approximation via nonlinear random feature maps is widely used in speeding up kernel machines. There are two main challenges for the conventional kernel approximation methods. First, before performing kernel approximation, a good…

A body of recent work in modeling neural activity focuses on recovering low-dimensional latent features that capture the statistical structure of large-scale neural populations. Most such approaches have focused on linear generative models,…