Journal of Computational and Applied Mathematics最新文献

英文中文

Random forest regression feature importance for climate impact pathway detection

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2025-01-15 DOI: 10.1016/j.cam.2024.116479

Meredith G.L. Brown , Matt G. Peterson , Irina K. Tezaur , Kara J .Peterson , Diana L. Bull

Disturbances to the climate system, both natural and anthropogenic, have far reaching impacts that are not always easy to identify or quantify using traditional climate science analyses or causal modeling techniques. In this paper, we develop a novel technique for discovering and ranking the chain of spatio-temporal downstream impacts of a climate source, referred to herein as a source-impact pathway, using Random Forest Regression (RFR) and SHapley Additive exPlanation (SHAP) feature importances. Rather than utilizing RFR for classification or regression tasks (the most common use case for RFR), we propose a fundamentally new workflow in which we: (i) train random forest (RF) regressors on a set of spatio-temporal features of interest, (ii) calculate their pair-wise feature importances using the SHAP weights associated with those features, and (iii) translate these feature importances into a weighted pathway network (i.e., a weighted directed graph), which can be used to trace out and rank interdependencies between climate features and/or modalities. Importantly, while herein we employ RFR and SHAP feature importance in steps (i) and (ii) of our algorithm, our novel workflow is in no way tied to these approaches, which could be replaced with any regression and sensitivity method, respectively. We adopt a tiered verification approach to verify our new pathway identification methodology. In this approach, we apply our method to ensembles of data generated by running two increasingly complex benchmarks: (i) a set of synthetic coupled equations, and (ii) a fully coupled simulation of the 1991 eruption of Mount Pinatubo in the Philippines performed using a modified version 2 of the U.S. Department of Energy’s Energy Exascale Earth System Model (E3SMv2). We find that our RFR feature importance-based approach can accurately detect known pathways of impact for both test cases.

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引用次数: 0

Numerical methods for solving a class of matrix equations arising from inference for ranked set sampling on imperfect ranking

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2025-01-14 DOI: 10.1016/j.cam.2025.116519

Qiang Niu , Binrui Shen , Yenan Wang

In this paper, we investigate some numerical methods for a class of matrix equations with constraints arising from inference for ranked set sampling on imperfect ranking. Based on the structure of the matrix equation, two classes of numerical methods are studied to solve the problem. The first idea is to treat the problem as a simplified Riccati equation, then a Schur method and a square-root method are derived. The second idea is entirely novel, which is based on an extended Krylov subspace originated from the doubly stochastic property of the related matrices. The performance and efficiency of all the numerical solvers are verified by numerical examples.

引用次数: 0

D-bar reconstructions with nonsmooth learned spatial priors in 2D electrical impedance tomography

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2025-01-14 DOI: 10.1016/j.cam.2025.116512

Melody Alsaker , Benjamin Bladow , Scott E. Campbell , Nicholas Linthacum , Thomas M. McKenzie , Jennifer L. Mueller , Talles Batista Rattis Santos

The use of 2D Electrical Impedance Tomography (EIT) for imaging in clinical settings has gained increasing attention from the medical community in recent years. This is due in part to state-of-the-art reconstruction algorithms which have led to enhanced EIT image quality. Advances in direct D-bar reconstruction methods, for example, have allowed the inclusion of spatial priors which provide improved image sharpness and robustness. As a first step, these techniques require polygonal estimates of boundaries of regions of interest in the 2D spatial domain. In the literature, the methodology for choosing such boundaries has involved extracting this spatial information from previous medical scans, which may not exist in practice, or from an anatomical atlas, which may not be representative of individual patient physiology and pathology. Manual extraction from previous scans also leads to labor-intensive procedures and the introduction of human bias. Furthermore, in previous works, some of the sharpness provided by the introduction of priors was lost due to a mathematical need for smoothing of the a priori conductivity distribution, which also introduced computational overhead. In this work, we address these problems via (1) a method for the automated selection of boundaries via trained convolutional neural networks, and (2) use of an alternative mathematical formulation which eliminates the need for smoothing of the conductivity prior. We present a scenario where the network is trained and validated using simulated thoracic phantoms on circular domains.

{"title":"D-bar reconstructions with nonsmooth learned spatial priors in 2D electrical impedance tomography","authors":"Melody Alsaker , Benjamin Bladow , Scott E. Campbell , Nicholas Linthacum , Thomas M. McKenzie , Jennifer L. Mueller , Talles Batista Rattis Santos","doi":"10.1016/j.cam.2025.116512","DOIUrl":"10.1016/j.cam.2025.116512","url":null,"abstract":"<div><div>The use of 2D Electrical Impedance Tomography (EIT) for imaging in clinical settings has gained increasing attention from the medical community in recent years. This is due in part to state-of-the-art reconstruction algorithms which have led to enhanced EIT image quality. Advances in direct D-bar reconstruction methods, for example, have allowed the inclusion of spatial priors which provide improved image sharpness and robustness. As a first step, these techniques require polygonal estimates of boundaries of regions of interest in the 2D spatial domain. In the literature, the methodology for choosing such boundaries has involved extracting this spatial information from previous medical scans, which may not exist in practice, or from an anatomical atlas, which may not be representative of individual patient physiology and pathology. Manual extraction from previous scans also leads to labor-intensive procedures and the introduction of human bias. Furthermore, in previous works, some of the sharpness provided by the introduction of priors was lost due to a mathematical need for smoothing of the <em>a priori</em> conductivity distribution, which also introduced computational overhead. In this work, we address these problems via (1) a method for the automated selection of boundaries via trained convolutional neural networks, and (2) use of an alternative mathematical formulation which eliminates the need for smoothing of the conductivity prior. We present a scenario where the network is trained and validated using simulated thoracic phantoms on circular domains.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"463 ","pages":"Article 116512"},"PeriodicalIF":2.1,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143155981","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An inner–outer iterative method for inverse Sturm–Liouville problems

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2025-01-14 DOI: 10.1016/j.cam.2025.116514

Qin Gao , Minhong Chen

In this paper, we present an inner–outer iterative method for two inverse Sturm–Liouville problems known as the symmetric and the two-spectra problems, aimed to achieve a continuous approximation of the unknown potential belonging to a suitable function space from the prescribed spectra data. To reduce the discrepancy between the matrix and differential eigenvalues, we use the optimal grid for a general reference potential and update it at each outer iteration. By discretizing the Sturm–Liouville problem over these grids, we get a series of matrix inverse eigenvalue problems. Then, a sequence of approximations of the unknown potential is obtained by employing a third-order Newton-type method as the inner iterations at each step of the outer iteration. Convergence of our method is established. Numerical experiments confirm its effectiveness.

引用次数: 0

Reproducing kernel function-based formulation for highly oscillatory integrals

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2025-01-13 DOI: 10.1016/j.cam.2025.116507

Sakhi Zaman , Siraj-ul-Islam

Reproducing-kernel functions are effective approximating tools for interpolation of various types of functions regardless of the troublesome sensitivity to shape parameters like that of Radial Basis Functions (RBFs). In the current work, a stable algorithm based on reproducing-kernel functions is proposed for numerical evaluation of oscillatory integrals with or without stationary phase. Reproducing-kernel functions, defined on a real Hilbert space, serve as basis functions in the Levin formulation. The proposed algorithm provides accurate approximation on both uniformly distributed and scattered data points in similar pattern to that of RBFs. High-resolution integration techniques based on wavelets are combined with reproducing kernel functions to evaluate oscillatory integrals with stationary phase. Theoretical error bounds of the new algorithm are derived. Several test cases are included to demonstrate accuracy and efficiency of the proposed algorithm.

引用次数: 0

Tetrahedral quadratic finite volume method schemes for the Stokes equation

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2025-01-13 DOI: 10.1016/j.cam.2024.116472

Jiehua Zhang

A family of quadratic finite volume methods is proposed in this paper for solving the Stokes equation over three-dimensional tetrahedral meshes, where the velocity is approximated by continuous piecewise Lagrange quadratic polynomials while the pressure is approximated by continuous piecewise linear polynomials on the same meshes. By introducing a map with a non-zero coefficient, who connects the trial space with the test space of the finite volume methods, an equivalence relationship is founded between the traditional finite volume method schemes, the classical finite volume method schemes, and the particular finite volume method schemes. By analyzing the affine matrix induced by tetrahedral meshes and establishing the equivalent discrete norms over tetrahedral meshes, it is discovered that the stability of the finite volume method schemes relies on the geometric shape conditions of tetrahedra. Under certain constraints on the geometric shape requirements, the stability of the finite volume method schemes is certificated by the Lax Milgram theorem of Babuska’s generalization. Based on the stability, when selecting the dual partitions of tetrahedrons that satisfies the so-called orthogonal conditions, the Aubin–Nitsche technique is applied to derive the error estimates of the optimal L²-norm with regard to the velocity. Finally, some numerical tests are presented to demonstrate the accuracy and efficiency for the proposed methods.

{"title":"Tetrahedral quadratic finite volume method schemes for the Stokes equation","authors":"Jiehua Zhang","doi":"10.1016/j.cam.2024.116472","DOIUrl":"10.1016/j.cam.2024.116472","url":null,"abstract":"<div><div>A family of quadratic finite volume methods is proposed in this paper for solving the Stokes equation over three-dimensional tetrahedral meshes, where the velocity is approximated by continuous piecewise Lagrange quadratic polynomials while the pressure is approximated by continuous piecewise linear polynomials on the same meshes. By introducing a map with a non-zero coefficient, who connects the trial space with the test space of the finite volume methods, an equivalence relationship is founded between the <em>traditional finite volume method</em> schemes, the <em>classical finite volume method</em> schemes, and the <em>particular finite volume method</em> schemes. By analyzing the affine matrix induced by tetrahedral meshes and establishing the equivalent discrete norms over tetrahedral meshes, it is discovered that the stability of the finite volume method schemes relies on the geometric shape conditions of tetrahedra. Under certain constraints on the geometric shape requirements, the stability of the finite volume method schemes is certificated by the Lax Milgram theorem of Babuska’s generalization. Based on the stability, when selecting the dual partitions of tetrahedrons that satisfies the so-called orthogonal conditions, the Aubin–Nitsche technique is applied to derive the error estimates of the optimal <strong>L<sup>2</sup></strong>-norm with regard to the velocity. Finally, some numerical tests are presented to demonstrate the accuracy and efficiency for the proposed methods.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"463 ","pages":"Article 116472"},"PeriodicalIF":2.1,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143155983","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

FastAGMGar: An aggregation-based algebraic multigrid method

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2025-01-13 DOI: 10.1016/j.cam.2025.116515

Rong-Fang Pu , Liang Li , Qin Wang , Zhao-Yu Lu , Li-Hong Liao

In this paper, we solve large sparse symmetric positive definite linear systems with the Krylov subspace method preconditioned by an aggregation-based algebraic multigrid (AGMG) scheme. We study the AGMGar (stands for AGMG with guaranteed convergence rate) method and present a new method called FastAGMGar. This method is developed by relaxing the aggregation requirement employed in AGMGar. Additionally, an integral correction method is introduced to improve the Jacobi smoother. The applicability of AGMGar and FastAGMGar methods to non-M-matrices is investigated, and their limitations are also examined and mitigated. To improve the performance of solving linear systems with non-M-matrices as coefficient matrices, the original aggregation algorithm is modified by only accepting the aggregate that contains nodes corresponding to negative couplings. Moreover, to reduce the high setup cost of AGMGar caused by the low coarsening ratio, different approaches are considered to compute the coarse-grid matrices based on the coarsening ratio. The numerical results demonstrate the effectiveness of these improvements. Furthermore, compared with classical AGMG and AGMGar, the newly proposed FastAGMGar not only features a shorter setup time but also maintains competitive efficiency in the solution phase. Consequently, this method showcases superior performance, with the shortest total CPU time for all test problems.

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引用次数: 0

Comparision of Conformable and Caputo fractional grey models

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2025-01-11 DOI: 10.1016/j.cam.2025.116500

Halis Bilgil , Simge Yüksel

In recent years, fractional order derivatives have been encountered in various fields of science, particularly in applied mathematics. Although there are many fractional derivative definitions in the literature, there are very few studies on which derivative definition works better in a mathematical model. In applications, it is seen that calculations are easier with the model using the Conformable derivative operator due to the simplicity of the derivative definition. However, the Caputo derivative operator, which is considered to be more effective in models related to time series due to its memory property, leads to more complex calculations. In this article, two fractional grey models were created in the same structure with Conformable and Caputo derivative operators and their applications were implemented on the same data sets to a performance comparison of the fractional operators. The working mechanisms of fractional grey models constructed with both Caputo and Conformable derivative operators were demonstrated in detail. Solution of the whitening differential equation in the Caputo fractional grey model was obtained using Laplace transforms. Here, Conformable and Caputo fractional grey models were applied to the forecast of three real time series and their forecast performances were compared. Data on China’s annual domestic energy consumption, annual wind energy consumption, and areas affected by drought disasters were utilized as real-time series. It has been observed that Conformable fractional grey models provide more accurate predictions with lower errors for certain datasets, while Caputo fractional grey models demonstrate better performance for others. This study is the first study in the literature that compared the Conformable and Caputo derivative operators on a grey model.

{"title":"Comparision of Conformable and Caputo fractional grey models","authors":"Halis Bilgil , Simge Yüksel","doi":"10.1016/j.cam.2025.116500","DOIUrl":"10.1016/j.cam.2025.116500","url":null,"abstract":"<div><div>In recent years, fractional order derivatives have been encountered in various fields of science, particularly in applied mathematics. Although there are many fractional derivative definitions in the literature, there are very few studies on which derivative definition works better in a mathematical model. In applications, it is seen that calculations are easier with the model using the Conformable derivative operator due to the simplicity of the derivative definition. However, the Caputo derivative operator, which is considered to be more effective in models related to time series due to its memory property, leads to more complex calculations. In this article, two fractional grey models were created in the same structure with Conformable and Caputo derivative operators and their applications were implemented on the same data sets to a performance comparison of the fractional operators. The working mechanisms of fractional grey models constructed with both Caputo and Conformable derivative operators were demonstrated in detail. Solution of the whitening differential equation in the Caputo fractional grey model was obtained using Laplace transforms. Here, Conformable and Caputo fractional grey models were applied to the forecast of three real time series and their forecast performances were compared. Data on China’s annual domestic energy consumption, annual wind energy consumption, and areas affected by drought disasters were utilized as real-time series. It has been observed that Conformable fractional grey models provide more accurate predictions with lower errors for certain datasets, while Caputo fractional grey models demonstrate better performance for others. This study is the first study in the literature that compared the Conformable and Caputo derivative operators on a grey model.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"463 ","pages":"Article 116500"},"PeriodicalIF":2.1,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143155728","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Robust inference for linear regression models with possibly skewed error distribution

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2025-01-11 DOI: 10.1016/j.cam.2025.116502

Amarnath Nandy, Ayanendranath Basu, Abhik Ghosh

Traditional methods for linear regression generally assume that the underlying error distribution, equivalently the distribution of the responses, is normal. Yet, sometimes real life response data may exhibit a skewed pattern, and assuming normality would not give reliable results in such cases. This is often observed in cases of some biomedical, behavioral, socio-economic and other variables. In this paper, we propose to use the class of skew normal (SN) distributions, which also includes the ordinary normal distribution as its special case, as the model for the errors in a linear regression setup and perform subsequent statistical inference using the popular and robust minimum density power divergence approach to get stable insights in the presence of possible data contamination (e.g., outliers). We provide the asymptotic distribution of the proposed estimator of the regression parameters and also propose robust Wald-type tests of significance for these parameters. We provide an influence function analysis of these estimators and test statistics, and also provide level and power influence functions. Numerical verification including simulation studies and real data analysis is provided to substantiate the theory developed.

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引用次数: 0

Existence of solution for a coupled diffusion PDE system for various noise reduction

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics

Pub Date : 2025-01-11 DOI: 10.1016/j.cam.2025.116521

A. Mohssine , L. Afraites , A. Hadri , A. Laghrib

In this work, we introduce a new model based on a high-order, non-linear PDE system for image denoising, which is controlled by a function

h

that detects the type of noise. The proposed model generalizes and improves upon the coupled PDE system of Jain et al. (2019), allowing for the handling of various noise types, such as Gaussian, Speckle, and Salt & Pepper’s noise. Our model is based on a diffusion tensor that corrects the anisotropic, coherent diffusion property of the Weickert operator near tiny edges with a high diffusion order. This configuration exhibits flexibility in the diffusion speed, allowing for efficient smoothing near flat areas without changing directions along the edges or across them. We perform a rigorous analysis of the existence and uniqueness of the weak solution of the proposed coupled PDE system in a suitable functional framework, using the Schauder fixed-point theorem. Finally, we present representative numerical results to demonstrate the effectiveness of our model against various noise types, by comparing the obtained results with those of some competitive models.

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引用次数: 0

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Journal of Computational and Applied Mathematics

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