In our paper, we present a sparse quasi-Newton method, called the sparse direct Broyden method, for solving sparse nonlinear equations. The method can be seen as a Broyden-like method and is a least change update satisfying the sparsity condition and...
Numerical simulation of elastic waves in anisotropic media is a fundamental technique for seismic exploration and the characterization of subsurface geological structures. Compared with the conventional finite-difference method, the compact finite-di...
In this short communication, an algorithm for efficiently solving a sparse matrix equation, which arises frequently in the field of distributed control and estimation theory, is proposed. The efficient algorithm stems from the fact that the sparse eq...
Many text mining methods use statistical information as a text- and language-independent approach for sentiment analysis. However, text mining methods based on stochastic patterns and rules require many samples for training. On the other hand, determ...
In this paper, we consider a sparse program with symmetric cone constrained parameterized generalized equations (SPSCC). Such a problem is a symmetric cone analogue with vector optimization, and we aim to provide a smoothing framework for dealing wit...
Land cover dynamics play a critical role in understanding environmental changes, but accurately modeling these dynamics remains a challenge due to the complex interactions between temporal and spatial factors. In this study, we propose a novel tempor...
Solving polynomial equations inevitably faces many severe challenges, such as easily occupying storage space and demanding prohibitively expensive computation resources. There has been considerable interest in exploiting the sparsity to improve compu...
We propose a construction of a Hermite cubic spline-wavelet basis on the interval and hypercube. The basis is adapted to homogeneous Dirichlet boundary conditions. The wavelets are orthogonal to piecewise polynomials of degree at most seven on a unif...
Sparse ergodic control provides a natural framework for long-run stochastic decision-making under resource constraints. Existing formulations, however, are typically restricted to control-affine systems with control-independent diffusion. When the di...
In this paper, a localized boundary knot method is proposed, based on the local concept in the localized method of fundamental solutions. The localized boundary knot method is formed by combining the classical boundary knot method and the localizatio...
We present a finite difference method working on sparse grids to solve higher dimensional heterogeneous agent models. If one wants to solve the arising Hamilton–Jacobi–Bellman equation on a standard full grid, one faces the problem that t...
This work aims to supplement the realization and validation of a higher-order well-balanced unstructured finite volume (FV) scheme, that has been relatively recently presented, for numerically simulating weakly non-linear weakly dispersive water wave...
The Kaczmarz algorithm is an iterative method for solving systems of linear equations. We introduce a randomized Kaczmarz algorithm for solving systems of linear equations in a distributed environment, i.e., the equations within the system are distri...
Accurately modeling the degradation of food antioxidants in oils is essential for understanding oxidative stability and improving food shelf life. This study presents an innovative machine learning approach integrating neural differential equations a...
Physics-informed neural networks (PINNs) provide mesh-free approximation and rapid inference for dam-break flood simulations. However, the effectiveness and underlying mechanisms of different enhancement strategies for engineering-representative shoc...
Applying bionic airfoils is essential in enlightening the design of rotating machinery and flow control. Dynamic mode decomposition was used to reveal the low dimensional flow structure of Riblets, Seagull, and Teal bionic airfoils at low Reynolds nu...
We consider parameter estimation for linear stochastic differential equations with independent experiments observed at infrequent and irregularly spaced follow-up times. The maximum likelihood method is used to obtain an asymptotically consistent est...
This paper presents a numerical method for solving transient one-dimensional heat conduction problems in multilayer slabs with temperature-dependent thermal conductivities. The governing nonlinear partial differential equations are formulated separat...
Partial differential equations are common models in biology for predicting and explaining complex behaviors. Nevertheless, deriving the equations and estimating the corresponding parameters remains challenging from data. In particular, the fine descr...
Injection molding is an efficient and precise manufacturing technology that is widely used in the production of plastic products. In recent years, injection molding technology has made significant progress, especially with the combination of in-mold...
Sparse regularization methods play an important role in inverse problems for extracting key features of underlying parameters and have attracted increasing attention in meteorological data assimilation. However, when the condition number of the backg...
The paper is concerned with the issues of modeling dynamic systems with interval parameters. In previous works, the authors proposed an adaptive interpolation algorithm for solving interval problems; the essence of the algorithm is the dynamic constr...
Problems with interval uncertainties arise in many applied fields. The authors have earlier developed, tested, and proved an adaptive interpolation algorithm for solving this class of problems. The algorithm’s idea consists of constructing a pi...
First-order approximations have been used with some success for criticality analysis; sensitivity analysis of physical networks, such as water distribution systems; and uncertainty propagation of model parameters. Certain limitations have been report...
Currently, many of the leading supercomputers are equipped with GPUs from manufacturers such as NVIDIA, AMD, or Intel, which provide substantial parallelism and high throughput. It is common for a single compute node to host multiple GPUs (typically...
This paper presents an efficient numerical method for the fractional-order generalization of the stochastic Stokes–Darcy model, which finds application in various engineering, biomedical and environmental problems involving interaction between...
Topology identification and signal inference are cornerstone tasks in graph signal processing (GSP). Structural Equation Modeling (SEM) is particularly effective for network inference as it explicitly captures causal dependencies. However, a major bo...
Autonomous navigation of underwater vehicles in infrastructure-limited environments presents persistent challenges due to the constraints of traditional acoustic positioning systems. Sparse long baseline (sparse LBL) navigation, which relies on a min...
Estimating evapotranspiration at the field scale is a major component of sustainable water management. Due to the difficulty to assess some major unknowns of the water cycle at that scale, including irrigation amounts, evapotranspiration is often com...
Acid stimulation is a widely used technique for enhancing hydrocarbon recovery from carbonate reservoir formations. In this study, a mathematical model is developed to describe acidizing-induced pressure behavior in carbonate rocks, based on fluid dy...
Estimating governing equations from observed time-series data is crucial for understanding dynamical systems. From the perspective of system comprehension, the demand for accurate estimation and interpretable results has been particularly emphasized....
The miniaturization of spectrometer can broaden the application area of spectrometry, which has huge academic and industrial value. Among various miniaturization approaches, filter-based miniaturization is a promising implementation by utilizing broa...
Comprehending complex systems by simplifying and highlighting important dynamical patterns requires modeling and mapping higher-order network flows. However, complex systems come in many forms and demand a range of representations, including memory a...
With their constantly increasing peak performance and memory capacity, modern supercomputers offer new perspectives on numerical studies of open many-body quantum systems. These systems are often modeled by using Markovian quantum master equations de...
In this paper, a novel two-dimensional direction of arrival (2D-DOA) estimation method with total variation regularization is proposed to deal with the problem of sparse DOA estimation for spatially extended sources. In a general sparse framework, th...
In this article, we propose a modified self-adaptive conjugate gradient algorithm for handling nonlinear monotone equations with the constraints being convex. Under some nice conditions, the global convergence of the method was established. Numerical...
A robust sparse least-mean mixture-norm (LMMN) algorithm is proposed, and its performance is appraised in the context of estimating a broadband multi-path wireless channel. The proposed algorithm is implemented via integrating a correntropy-induced m...
Solving shallow water equations is crucial in science and engineering for understanding and predicting natural phenomena. To address the limitations of Physics-Informed Neural Network (PINN) in solving shallow water equations, we propose an improved...
At the heart of many computations in science and engineering lies the need to efficiently and accurately solve large sparse linear systems of equations. Direct methods are frequently the method of choice because of their robustness, accuracy and pote...
Sparse matrix-vector multiplication (SpMV) can be used to solve diverse-scaled linear systems and eigenvalue problems that exist in numerous, and varying scientific applications. One of the scientific applications that SpMV is involved in is known as...
In this article we present and discuss a two step methodology to find the closest low rank completion of a sparse large matrix. Given a large sparse matrix M, the method consists of fixing the rank to r and then looking for the closest rank-r matrix...
The Poisson equation is a fundamental equation of mathematical physics that describes the potential distribution in static fields. Solving the Poisson equation on a grid is computationally intensive and can be challenging for large grids. In recent y...
This paper proposes a distributed estimation technique utilizing the diffusion least mean-square (LMS) algorithm, specifically designed for sparse systems in which many coefficients of the system are zeros. To efficiently utilize the sparse represent...
In optical sparse projection reconstruction, the reconstruction of the tested field often requires the utilization of a priori knowledge to compensate for the lack of information due to the sparse projection angle. For situations where the radiation...
The identification of model parameters is a central challenge in the analysis of nonignorable nonresponse data. In this paper, we propose a novel penalized semiparametric likelihood method to obtain sparse estimators for a parametric nonresponse mech...
In recent years, the rapid growth of computing technology has enabled identifying mathematical models for vibration systems using measurement data instead of domain knowledge. Within this category, the method Sparse Identification of Nonlinear Dynami...
Fluid mechanics often involves complex systems characterized by a large number of physical parameters, which are usually described by experimental and numerical sparse data (temporal or spatial). The difficulty of obtaining complete spatio-temporal d...
The paper presents two effective methods for discovering process models in the form of partial differential equations based on an evolutionary algorithm and an algorithm for the best subset selection. The methods are designed to work with sparse and...
To satisfy the requirement of the modern spaceborne synthetic aperture radar (SAR) system, SAR imaging mode design makes a trade-off between resolution and swath coverage by controlling radar antenna sweeping. Existing spaceborne SAR systems can perf...
In our paper, we introduce a sparse and symmetric matrix completion quasi-Newton model using automatic differentiation, for solving unconstrained optimization problems where the sparse structure of the Hessian is available. The proposed method is a k...
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