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Nonlinear photonic delay systems present interesting implementation platforms for machine learning models. They can be extremely fast, offer great degrees of parallelism and potentially consume far less power than digital processors. So far…

In this work, we propose a subsystem decomposition approach and a distributed estimation scheme for a class of implicit two-time-scale nonlinear systems. Taking the advantage of the two-time-scale separation, these processes are decomposed…

Phase retrieval, a nonlinear problem prevalent in imaging applications, has been extensively studied using random models, some of which with i.i.d. sensing matrix components. While these models offer robust reconstruction guarantees, they…

We introduce a particle-based simulation method for granular material in interactive frame rates. We divide the simulation into two decoupled steps. In the first step, a relatively small number of particles is accurately simulated with a…

This paper aims to accelerate the test-time computation of deep convolutional neural networks (CNNs). Unlike existing methods that are designed for approximating linear filters or linear responses, our method takes the nonlinear units into…

Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…

This paper addresses the problem of parallelizing computations to study non-linear dynamics in large networks of non-locally coupled oscillators using heterogeneous computing resources. The proposed approach can be applied to a variety of…

This paper presents a controller design and optimization framework for nonlinear dynamic systems to track a given reference signal in the presence of disturbances when the task is repeated over a finite-time interval. This novel framework…

We present a method based on a time domain simulation of wave propagation that allows studying the optical response of a broad range of dielectric photonic structures. This method is particularly suitable for dealing with complex biological…

An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…

In the paper, effective filtering for a type of slow-fast data assimilation systems in Hilbert spaces is considered. Firstly, the system is reduced to a system on a random invariant manifold. Secondly, nonlinear filtering of the origin…

Artificial spike-based computation, inspired by models of computations in the central nervous system, may present significant performance advantages over traditional methods for specific types of large scale problems. In this paper, we…

In this paper, we study the nonnegative matrix factorization problem under the separability assumption (that is, there exists a cone spanned by a small subset of the columns of the input nonnegative data matrix containing all columns),…

Recursive Neural Networks are non-linear adaptive models that are able to learn deep structured information. However, these models have not yet been broadly accepted. This fact is mainly due to its inherent complexity. In particular, not…

In ordinary turbulence research it has been a long standing tradition to solve the equations in spectral space giving the best possible accuracy. This is indeed a natural choice for incompressible problems with periodic boundaries, but it…

The Active Flux scheme is a finite volume scheme with additional point values distributed along the cell boundary. It is third order accurate and does not require a Riemann solver. Instead, given a reconstruction, the initial value problem…

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…

We introduce the lcm-filtration and stepwise filtration, comparing their performance across various scenarios in terms of computational complexity, efficiency, and redundancy. The lcm-filtration often involves identical steps or ideals,…

Over the last decade, both the neural network and kernel adaptive filter have successfully been used for nonlinear signal processing. However, they suffer from high computational cost caused by their complex/growing network structures. In…

We show in this paper that third- and fourth-order low storage Runge-Kutta algorithms can be built specifically for quadratic nonlinear operators, at the expense of roughly doubling the time needed for evaluating the temporal derivatives.…