Related papers: HANN: Homotopy auxiliary neural network for solvin…

This paper proposes an Adaptive-Growth Randomized Neural Network (AG-RaNN) method for computing multivalued solutions of nonlinear first-order PDEs with hyperbolic characteristics, including quasilinear hyperbolic balance laws and…

We consider polynomial systems of Prony type, appearing in many areas of mathematics. Their robust numerical solution is considered to be difficult, especially in "near-colliding" situations. We consider a case when the structure of the…

With the increasing use of nonlinear devices in both generation and consumption of power, it is essential that we develop accurate and quick control for active filters to suppress harmonics. Time delays between input and output are…

The numerical solution of partial differential equations (PDEs) is fundamental to scientific and engineering computing. In the presence of strong anisotropy, material heterogeneity, and complex geometries, however, classical iterative…

In the present work, a new approach is proposed for finding the analytical solution of population balances. This approach is relying on idea of Homotopy Perturbation Method (HPM). The HPM solves both linear and nonlinear initial and…

Hierarchical graph-based algorithms such as HNSW have achieved state-of-the-art performance for Approximate Nearest Neighbor (ANN) search in practice, yet they often lack theoretical guarantees on query time or recall due to their heavy use…

Estimating homography from an image pair is a fundamental problem in image alignment. Unsupervised learning methods have received increasing attention in this field due to their promising performance and label-free training. However,…

Partial differential equations have a wide range of applications in modeling multiple physical, biological, or social phenomena. Therefore, we need to approximate the solutions of these equations in computationally feasible terms. Nowadays,…

Feed-forward, fully-connected Artificial Neural Networks (ANNs) or the so-called Multi-Layer Perceptrons (MLPs) are well-known universal approximators. However, their learning performance varies significantly depending on the function or…

Heterogeneous information networks (HINs) can be used to model various real-world systems. As HINs consist of multiple types of nodes, edges, and node features, it is nontrivial to directly apply graph neural network (GNN) techniques in…

We explore in detail a method to solve ordinary differential equations using feedforward neural networks. We prove a specific loss function, which does not require knowledge of the exact solution, to be a suitable standard metric to…

We propose an approach based on Artificial Neural Networks (ANNs) to evaluate geometric constants relevant to the analysis and design of numerical schemes for partial differential equations. These constants play a central role,…

The paper proposes a solution based on Generative Adversarial Network (GAN) for solving jigsaw puzzles. The problem assumes that an image is divided into equal square pieces, and asks to recover the image according to information provided…

In this study, we firstly propose an auxiliary equation neural networks method (AENNM), an innovative analytical method that integrates neural networks (NNs) models with the auxiliary equation method to obtain exact solutions of nonlinear…

Quantum scientific computing is to solve engineering and science problems such as simulation and optimization on quantum computers. Solving ordinary and partial differential equations (PDEs) is essential in simulations. However, existing…

Nonlinear partial differential equations (PDEs) are crucial for modeling complex fluid dynamics and are foundational to many computational fluid dynamics (CFD) applications. However, solving these nonlinear PDEs is challenging due to the…

Neural network solvers represent an innovative and promising approach for tackling time-fractional partial differential equations by utilizing deep learning techniques. L1 interpolation approximation serves as the standard method for…

In many commercial and academic settings, numerical solvers fail to achieve their theoretical performance levels due to issues in the system definition, parameterization, and even implementation. We propose a pair of methods for detecting…

In this paper, we introduce cell-average based neural network (CANN) method to solve high-dimensional parabolic partial differential equations. The method is based on the integral or weak formulation of partial differential equations. A…

We study the problem of approximate near neighbor (ANN) search and show the following results: - An improved framework for solving the ANN problem using locality-sensitive hashing, reducing the number of evaluations of locality-sensitive…