Inverse Problems最新文献_第10页

Adaptive anisotropic Bayesian meshing for inverse problems 逆问题的自适应各向异性贝叶斯网格划分

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-02-23 DOI: 10.1088/1361-6420/ad2696

A Bocchinfuso, D Calvetti, E Somersalo

{"title":"Adaptive anisotropic Bayesian meshing for inverse problems","authors":"A Bocchinfuso, D Calvetti, E Somersalo","doi":"10.1088/1361-6420/ad2696","DOIUrl":"https://doi.org/10.1088/1361-6420/ad2696","url":null,"abstract":"We consider inverse problems estimating distributed parameters from indirect noisy observations through discretization of continuum models described by partial differential or integral equations. It is well understood that errors arising from the discretization can be detrimental for ill-posed inverse problems, as discretization error behaves as correlated noise. While this problem can be avoided with a discretization fine enough to decrease the modeling error level below that of the exogenous noise that is addressed, e.g. by regularization, the computational resources needed to deal with the additional degrees of freedom may increase so much as to require high performance computing environments. Following an earlier idea, we advocate the notion of the discretization as one of the unknowns of the inverse problem, which is updated iteratively together with the solution. In this approach, the discretization, defined in terms of an underlying metric, is refined selectively only where the representation power of the current mesh is insufficient. In this paper we allow the metrics and meshes to be anisotropic, and we show that this leads to significant reduction of memory allocation and computing time.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140004917","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

A Bayesian approach for consistent reconstruction of inclusions 用贝叶斯方法重建内含物的一致性

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-02-23 DOI: 10.1088/1361-6420/ad2531

B M Afkham, K Knudsen, A K Rasmussen, T Tarvainen

引用次数: 0

Magnetic characterisation of steel strips using transient field measurements: global sensitivity analysis and regression from a machine-learning perspective 利用瞬态场测量对钢带进行磁性表征：从机器学习角度进行全局敏感性分析和回归

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-02-16 DOI: 10.1088/1361-6420/ad2a04

A. Skarlatos, R. Miorelli, C. Reboud, Frenk van den Berg

引用次数: 0

A posterior contraction for Bayesian inverse problems in Banach spaces 巴拿赫空间中贝叶斯逆问题的后验收缩

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-02-16 DOI: 10.1088/1361-6420/ad2a03

De-Han Chen, Jingzhi Li, Ye Zhang

引用次数: 0

Imaging of nonlinear materials via the Monotonicity Principle 通过单调性原理成像非线性材料

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-02-13 DOI: 10.1088/1361-6420/ad22e9

Vincenzo Mottola, Antonio Corbo Esposito, Gianpaolo Piscitelli, Antonello Tamburrino

{"title":"Imaging of nonlinear materials via the Monotonicity Principle","authors":"Vincenzo Mottola, Antonio Corbo Esposito, Gianpaolo Piscitelli, Antonello Tamburrino","doi":"10.1088/1361-6420/ad22e9","DOIUrl":"https://doi.org/10.1088/1361-6420/ad22e9","url":null,"abstract":"Inverse problems, which are related to Maxwell’s equations, in the presence of nonlinear materials is a quite new topic in the literature. The lack of contributions in this area can be ascribed to the significant challenges that such problems pose. Retrieving the spatial behavior of some unknown physical property, from boundary measurements, is a nonlinear and highly ill-posed problem even in the presence of linear materials. Furthermore, this complexity grows exponentially in the presence of nonlinear materials. In the tomography of linear materials, the Monotonicity Principle (MP) is the foundation of a class of non-iterative algorithms able to guarantee excellent performances and compatibility with real-time applications. Recently, the MP has been extended to nonlinear materials under very general assumptions. Starting from the theoretical background for this extension, we develop a first real-time inversion method for the inverse obstacle problem in the presence of nonlinear materials. The proposed method is intendend for all problems governed by the quasilinear Laplace equation, i.e. static problems involving nonlinear materials. In this paper, we provide some preliminary results which give the foundation of our method and some extended numerical examples.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140004658","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

Multilevel dimension-independent likelihood-informed MCMC for large-scale inverse problems 用于大规模逆问题的多层次维度独立似然信息 MCMC

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-02-05 DOI: 10.1088/1361-6420/ad1e2c

Tiangang Cui, Gianluca Detommaso, Robert Scheichl

{"title":"Multilevel dimension-independent likelihood-informed MCMC for large-scale inverse problems","authors":"Tiangang Cui, Gianluca Detommaso, Robert Scheichl","doi":"10.1088/1361-6420/ad1e2c","DOIUrl":"https://doi.org/10.1088/1361-6420/ad1e2c","url":null,"abstract":"We present a non-trivial integration of dimension-independent likelihood-informed (DILI) MCMC (Cui <italic toggle=\"yes\">et al</italic> 2016) and the multilevel MCMC (Dodwell <italic toggle=\"yes\">et al</italic> 2015) to explore the hierarchy of posterior distributions. This integration offers several advantages: First, DILI-MCMC employs an intrinsic <italic toggle=\"yes\">likelihood-informed subspace</italic> (LIS) (Cui <italic toggle=\"yes\">et al</italic> 2014)—which involves a number of forward and adjoint model simulations—to design accelerated operator-weighted proposals. By exploiting the multilevel structure of the discretised parameters and discretised forward models, we design a <italic toggle=\"yes\">Rayleigh–Ritz procedure</italic> to significantly reduce the computational effort in building the LIS and operating with DILI proposals. Second, the resulting DILI-MCMC can drastically improve the sampling efficiency of MCMC at each level, and hence reduce the integration error of the multilevel algorithm for fixed CPU time. Numerical results confirm the improved computational efficiency of the multilevel DILI approach.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139762540","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

Fourier series-based approximation of time-varying parameters in ordinary differential equations 基于傅里叶级数的常微分方程时变参数近似法

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-02-01 DOI: 10.1088/1361-6420/ad1fe5

Anna Fitzpatrick, Molly Folino, Andrea Arnold

{"title":"Fourier series-based approximation of time-varying parameters in ordinary differential equations","authors":"Anna Fitzpatrick, Molly Folino, Andrea Arnold","doi":"10.1088/1361-6420/ad1fe5","DOIUrl":"https://doi.org/10.1088/1361-6420/ad1fe5","url":null,"abstract":"Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some unobservable system parameters may vary with time without known evolution models. In this work, we propose a novel approximation method inspired by the Fourier series to estimate time-varying parameters (TVPs) in deterministic dynamical systems modeled with ordinary differential equations. Using ensemble Kalman filtering in conjunction with Fourier series-based approximation models, we detail two possible implementation schemes for sequentially updating the time-varying parameter estimates given noisy observations of the system states. We demonstrate the capabilities of the proposed approach in estimating periodic parameters, both when the period is known and unknown, as well as non-periodic TVPs of different forms with several computed examples using a forced harmonic oscillator. Results emphasize the importance of the frequencies and number of approximation model terms on the time-varying parameter estimates and corresponding dynamical system predictions.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139762863","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

V-line 2-tensor tomography in the plane 平面 V 线 2 张量断层扫描

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-01-31 DOI: 10.1088/1361-6420/ad1f83

Gaik Ambartsoumian, Rohit Kumar Mishra, Indrani Zamindar

{"title":"V-line 2-tensor tomography in the plane","authors":"Gaik Ambartsoumian, Rohit Kumar Mishra, Indrani Zamindar","doi":"10.1088/1361-6420/ad1f83","DOIUrl":"https://doi.org/10.1088/1361-6420/ad1f83","url":null,"abstract":"In this article, we introduce and study various V-line transforms (VLTs) defined on symmetric 2-tensor fields in <inline-formula>\u0000<tex-math><?CDATA $mathbb{R}^2$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:msup><mml:mrow><mml:mi mathvariant=\"double-struck\">R</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:math>\u0000<inline-graphic xlink:href=\"ipad1f83ieqn1.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula>. The operators of interest include the longitudinal, transverse, and mixed VLTs, their integral moments, and the star transform. With the exception of the star transform, all these operators are natural generalizations to the broken-ray trajectories of the corresponding well-studied concepts defined for straight-line paths of integration. We characterize the kernels of the VLTs and derive exact formulas for reconstruction of tensor fields from various combinations of these transforms. The star transform on tensor fields is an extension of the corresponding concepts that have been previously studied on vector fields and scalar fields (functions). We describe all injective configurations of the star transform on symmetric 2-tensor fields and derive an exact, closed-form inversion formula for that operator.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139762535","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

Regularization of the inverse Laplace transform by mollification 反拉普拉斯变换的规范化摩尔化

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-01-16 DOI: 10.1088/1361-6420/ad1609

Pierre Maréchal, Faouzi Triki, Walter C Simo Tao Lee

引用次数: 0

Assessing the potential of using a virtual Veselago lens in quantitative microwave imaging 评估在微波定量成像中使用虚拟 Veselago 透镜的潜力

IF 2.1 2区数学

Inverse Problems Pub Date : 2024-01-12 DOI: 10.1088/1361-6420/ad1e2d

Marzieh Eini Keleshteri, Vladimir Okhmatovski, Ian Jeffrey, M. Bevacqua, J. Lovetri

{"title":"Assessing the potential of using a virtual Veselago lens in quantitative microwave imaging","authors":"Marzieh Eini Keleshteri, Vladimir Okhmatovski, Ian Jeffrey, M. Bevacqua, J. Lovetri","doi":"10.1088/1361-6420/ad1e2d","DOIUrl":"https://doi.org/10.1088/1361-6420/ad1e2d","url":null,"abstract":"\u0000 This study explores the potential of implementing the focusing properties of a virtual ideal Veselago lens within a standard free-space microwave imaging scenario. To achieve this, the virtual lens is introduced as an inhomogeneous numerical background for the inverse source problem. This numerical Vesealgo lens is incorporated into the incident and scattered field decomposition, resulting in a new data equation that involves the Veselago Lens Green's function. In addition to the contrast sources within the object-of-interest, the lens introduces virtual contrast sources along the lens boundaries that depend on the total tangential magnetic field. It is shown that a surface integral contribution that takes into account these surface contrast sources must be added to the collected free-space data before one can invert using the well-conditioned Veselago lens inversion operator. A preliminary investigation of the accuracy to which this surface integral contribution must be computed is performed using additive Gaussian noise. Results show that an error of less than one percent is required to achieve imaging performance similar to utilizing an actual Veselago lens. All results are performed within a 2D simulation environment.","PeriodicalId":50275,"journal":{"name":"Inverse Problems","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139533134","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