Related papers: Wave Computing based on Dynamical Networks: Applic…
In order to better accommodate the dramatically increasing demand for data caching and computing services, storage and computation capabilities should be endowed to some of the intermediate nodes within the network. In this paper, we design…
We revisit the problem of solving the one-dimensional wave equation on a domain with moving boundary. In J. Math. Phys. 11, 2679 (1970), Moore introduced an interesting method to do so. As only in rare cases, a closed analytical solution is…
We perform full-scale numerical simulation of instability of weakly nonlinear waves on the surface of deep fluid. We show that the instability development leads to chaotization and formation of wave turbulence. We study instability both of…
Wave equations are fundamental to describing a vast array of physical phenomena, yet their simulation in inhomogeneous media poses a computational challenge due to the highly oscillatory nature of the solutions. To overcome the high costs…
Nonlinear waves have played a historical role in laying the foundations of the science of complexity. Recently, they have also allowed the development of a new reservoir computing paradigm: neuromorphic computing by waves. In these systems,…
Next generation (5G) wireless networks are expected to support the massive data and accommodate a wide range of services/use cases with distinct requirements in a cost-effective, flexible, and agile manner. As a promising solution, wireless…
Similar to algorithms, which consume time and memory to run, hardware requires resources to function. For devices processing physical waves, implementing operations needs sufficient "space," as dictated by wave physics. How much space is…
Quantum computers are ideally set up to solve linear systems which are of a form similar to the Schrodinger/Dirac equation of quantum mechanics. In the framework of linear response theory, the propagation and scattering of electromagnetic…
Quantum computing promises the possibility of studying the real-time dynamics of nonperturbative quantum field theories while avoiding the sign problem that obstructs conventional lattice approaches. Current and near-future quantum devices…
Neuromorphic computing seeks to replicate the remarkable efficiency, flexibility, and adaptability of the human brain in artificial systems. Unlike conventional digital approaches, which suffer from the Von Neumann bottleneck and depend on…
In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…
The Massive Parallel Computing (MPC) model gained popularity during the last decade and it is now seen as the standard model for processing large scale data. One significant shortcoming of the model is that it assumes to work on static…
Decentralized optimization strategies are helpful for various applications, from networked estimation to distributed machine learning. This paper studies finite-sum minimization problems described over a network of nodes and proposes a…
We study dispersion properties of linear surface gravity waves propagating in an arbitrary direction atop a current profile of depth-varying magnitude using a piecewise linear approximation, and develop a robust numerical framework for…
With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing techniques that incorporate known physical constraints into the learned…
Dynamical systems can be modelled by partial differential equations and numerical computations are used everywhere in science and engineering. In this work, we investigate the performance of recurrent and convolutional deep neural network…
A dynamical neural network consists of a set of interconnected neurons that interact over time continuously. It can exhibit computational properties in the sense that the dynamical system's evolution and/or limit points in the associated…
The demands of proliferating big data and massive deep learning models, against a backdrop of a mounting climate emergency and the abating of Moore's law, push technologists to develop high-speed, high-throughput, low energy and…
As it is getting increasingly difficult to achieve gains in the density and power efficiency of microelectronic computing devices because of lithographic techniques reaching fundamental physical limits, new approaches are required to…
Real world networks are often subject to severe uncertainties which need to be addressed by any reliable prescriptive model. In the context of the maximum flow problem subject to arc failure, robust models have gained particular attention.…