Related papers: NHDS: The New Hampshire Dispersion Relation Solver
Artificial Neural Network (ANN) is used as numerical methode in solving modified Nonlinear Schroedinger (NLS) equation with Dispersion Managed System (DMS) for jitter analysis. We take the optical axis z and the time t as input, and then…
The design of accurate helium-solute interaction potentials for the simulation of chemically complex molecules solvated in superfluid helium has long been a cumbersome task due to the rather weak but strongly anisotropic nature of the…
Neural routing solvers (NRSs) that leverage deep learning to tackle vehicle routing problems have demonstrated notable potential for practical applications. By learning implicit heuristic rules from data, NRSs replace the handcrafted…
Recently, a lot of papers proposed to use neural networks to approximately solve partial differential equations (PDEs). Yet, there has been a lack of flexible framework for convenient experimentation. In an attempt to fill the gap, we…
In this paper, we investigate the convergence performance of a cooperative diffusion Gauss-Newton (GN) method, which is widely used to solve the nonlinear least squares problems (NLLS) due to the low computation cost compared with Newton's…
Tensor networks (TNs) and neural networks (NNs) are two fundamental data modeling approaches. TNs were introduced to solve the curse of dimensionality in large-scale tensors by converting an exponential number of dimensions to polynomial…
Tensor network methods provide a scalable solution to represent high-dimensional data. However, their efficacy is often limited by static, expert-defined structures that fail to adapt to evolving data correlations. We address this…
Hamiltonian neural networks (HNNs) are state-of-the-art models that regress the vector field of a dynamical system under the learning bias of Hamilton's equations. A recent observation is that embedding a bias regarding the additive…
Neural networks have been identified as powerful tools for the study of complex systems. A noteworthy example is the neural network differential equation (NN DE) solver, which can provide functional approximations to the solutions of a wide…
In this paper, we propose Neumann Series Neural Operator (NSNO) to learn the solution operator of Helmholtz equation from inhomogeneity coefficients and source terms to solutions. Helmholtz equation is a crucial partial differential…
Nearest Neighbor Search (NNS) over generalized weighted distances is fundamental to a wide range of applications. The problem of NNS over the generalized weighted square Euclidean distance has been studied in previous work. However,…
Partial diffusion-based recursive least squares (PDRLS) is an effective method for reducing computational load and power consumption in adaptive network implementation. In this method, each node shares a part of its intermediate estimate…
Nearest neighbors search is a fundamental problem in various research fields like machine learning, data mining and pattern recognition. Recently, hashing-based approaches, e.g., Locality Sensitive Hashing (LSH), are proved to be effective…
Diffuse correlation spectroscopy (DCS) is a powerful tool for assessing microvascular hemodynamic in deep tissues. Recent advances in sensors, lasers, and deep learning have further boosted the development of new DCS methods. However,…
Geometric deep learning (GDL) has gained significant attention in scientific fields, for its proficiency in modeling data with intricate geometric structures. However, very few works have delved into its capability of tackling the…
Online availability and diffusion of New Psychoactive Substances (NPS) represent an emerging threat to healthcare systems. In this work, we analyse drugs forums, online shops, and Twitter. By mining the data from these sources, it is…
Near MDS (NMDS) codes are closely related to interesting objects in finite geometry and have nice applications in combinatorics and cryptography. But there are many unsolved problems about construction of NMDS codes. In this paper, by using…
In this paper, we present a general review of the status of numerical modelling applied to the design of high temperature superconductor (HTS) devices. The importance of this tool is emphasized at the beginning of the paper, followed by…
In this work, we consider the challenges of developing a distributed solver for models based on nonlocal interactions. In nonlocal models, in contrast to the local model, such as the wave and heat partial differential equation, the material…
Adaptive methods for derivation of analytical and numerical solutions of heat diffusion in one dimensional thin rod have investigated. Comperhensive comparsion analysis based on the homotopy perturbation method (HPM) and finite difference…