Article
Computer Science, Artificial Intelligence
Mario Gonzalez, Andres Almansa, Pauline Tan
Summary: This work addresses the ill-posed inverse problems in imaging by using a variational autoencoder (VAE) as a prior. The proposed joint MAP algorithm computes the joint posterior maximization using an autoencoding prior and utilizes a stochastic encoder to accelerate computations. The experimental results demonstrate the effectiveness of the proposed objective function and the importance of correctly training the VAE using a denoising criterion. The JPMAP approach provides higher quality solutions compared to other nonconvex MAP approaches.
SIAM JOURNAL ON IMAGING SCIENCES
(2022)
Article
Engineering, Mechanical
Xiaoluo Yu, Changming Cheng, Yang Yang, Minggang Du, Qingbo He, Zhike Peng
Summary: This paper proposes a Maximumly Weighted Iteration (MWI) approach to solve ill-conditioned inverse problems in dynamics. The ill-condition of the system coefficient matrix is controlled by iterative weighted decomposition and a weighted term, avoiding matrix inversion. The numerical results show that MWI outperforms Truncated Singular Value Decomposition and Tikhonov regularization in terms of accuracy and anti-noise property. Two application cases demonstrate the potential of MWI in engineering practice.
INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
(2023)
Article
Computer Science, Artificial Intelligence
Zhengxia Zou, Tianyang Shi, Zhenwei Shi, Jieping Ye
Summary: Inverse problems are important mathematical problems that aim at estimating source data and operation parameters from inadequate observations. In this paper, a novel framework is proposed for solving certain types of inverse problems in image processing by training a deep neural network to estimate degradation parameters instead of predicting source data directly. The method is shown to be effective in various real-world image processing tasks.
IEEE TRANSACTIONS ON IMAGE PROCESSING
(2021)
Article
Mathematics
Hassan K. Ibrahim Al-Mahdawi, Mostafa Abotaleb, Hussein Alkattan, Al-Mahdawi Zena Tareq, Amr Badr, Ammar Kadi
Summary: This paper discusses and solves the inverse problems for the boundary value and initial value in a heat equation. By reformulating the problems as integral equations and discretizing them, an approximation solution is obtained using the Landweber-type iterative method and the V-cycle multigrid method.
Article
Thermodynamics
Andrzej Frackowiak, Agnieszka Wroblewska, Michal Cialkowski
Summary: This paper presents a concept of solving the inverse heat conduction problem using Trefftz functions and provides two examples to validate the effectiveness of the method.
INTERNATIONAL JOURNAL OF THERMAL SCIENCES
(2022)
Article
Mathematics, Applied
Yuxin Xia, Bo Han, Ruixue Gu
Summary: In this paper, an accelerated homotopy-perturbation-Kaczmarz iteration method based on sequential subspace optimization is proposed for solving nonlinear systems of inverse problems. The method iteratively projects the initial value onto stripes controlled by the search direction, forward operator, and noise level to expedite convergence. Convergence and regularization analysis are provided under general assumptions, and numerical examples demonstrate the effectiveness of reconstructing solutions and acceleration effects of the method.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Mathematics
Hassan K. Ibrahim Al-Mahdawi, Hussein Alkattan, Mostafa Abotaleb, Ammar Kadi, El-Sayed M. El-kenawy
Summary: The Landweber iteration method is a popular approach for solving linear discrete ill-posed problems. This paper presents a new version of the method that utilizes a polar decomposition to improve the speed and accuracy of the iteration process. Convergence and analysis were conducted to validate the usability of the new method, which was compared to the classical Landweber method. A numerical experiment demonstrated the effectiveness of the new method in solving an inverse boundary value problem of the heat equation (IBVP).
Article
Engineering, Electrical & Electronic
Tiantian Yin, Li Pan, Xudong Chen
Summary: This article proposes an iterative method called the subspace-based distorted-Rytov iterative method (S-DRIM) for solving inverse scattering problems. The method utilizes the subspace-Rytov approximation (SRA) and updates the parameters of the background medium in each iteration of S-DRIM. Through simulations, the approximation errors of both the Rytov Approximation (RA) and SRA are analyzed and compared in various background media. The performance of S-DRIM is verified using both synthetic and experimental data, showing that it outperforms the non-iterative SRA inversion method for mild scatterer reconstructions and has a smaller reconstruction error in optimization processes compared to the distorted-Rytov iterative method (DRIM).
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION
(2023)
Article
Engineering, Electrical & Electronic
Jose O. Vargas, Ricardo Adriano
Summary: A subspace-based conjugate-gradient method (S-CGM) is proposed in this article to improve the performance of the linearized CGM. By retrieving the deterministic part of the variational-induced current, the S-CGM estimates the total electric field more accurately, resulting in faster convergence speed and higher accuracy.
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION
(2022)
Article
Engineering, Electrical & Electronic
Rencheng Song, Qiao Zhou, Yu Liu, Chang Li, Xun Chen
Summary: In this letter, convolutional sparsity regularization (CSR) is introduced into the framework of nonlinear iterative methods for solving inverse scattering problems (ISPs), whereby the permittivity image of scatterers is sparsely represented in a convolutional form with prelearned dictionary filters. The CSR is then incorporated with the subspace-based optimization method (SOM) to reconstruct the target image as a sparse coding by dictionary filters, and the whole optimization function of SOM-CSR is solved using an alternative iteration method. The results from both synthetic and experimental data confirm the effectiveness of the proposed SOM-CSR method, showing that CSR, as a structural constraint, is beneficial for nonlinear iterative reconstruction methods in solving ISPs compared to pixel-based inversion.
IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS
(2021)
Article
Engineering, Electrical & Electronic
Jian Liu, Huilin Zhou, Tao Ouyang, Qiegen Liu, Yuhao Wang
Summary: This article proposes a physical model-inspired deep unrolling network, PM-Net, to solve nonlinear inverse scattering problems. The network transforms the constrained optimization problem into an unconstrained problem and decomposes it into subproblems, which are then unfolded into a deep neural network. PM-Net effectively combines neural networks with the knowledge of underlying physics for better performance.
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION
(2022)
Article
Engineering, Electrical & Electronic
Tao Shan, Zhichao Lin, Xiaoqian Song, Maokun Li, Fan Yang, Shenheng Xu
Summary: In this article, the authors propose the neural Born iterative method (NeuralBIM) for solving 2-D inverse scattering problems (ISPs) by using the physics-informed supervised residual learning (PhiSRL). NeuralBIM employs independent convolutional neural networks (CNNs) to learn the alternate update rules for two candidate solutions. The article presents two schemes: supervised NeuralBIM, trained with knowledge of total fields and contrasts, and unsupervised NeuralBIM, guided by a physics-embedded objective function. Numerical and experimental results confirm the effectiveness of NeuralBIM.
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION
(2023)
Article
Mathematics, Interdisciplinary Applications
Yan Jiang, Wuyue Yang, Yi Zhu, Liu Hong
Summary: Entropy has been widely applied in various disciplines since its discovery, and this paper proposes a new method for solving inverse XDE problems using the entropy balance equation, which shows excellent accuracy, robustness, and reliability when compared to the classical method SINDy.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Computer Science, Interdisciplinary Applications
A. Adamu, D. Kitkuan, A. Padcharoen, C. E. Chidume, P. Kumam
Summary: An inertial viscosity-type iterative method that approximates a solution of an inclusion problem and a fixed point problem is introduced and studied. Strong convergence theorem is proved in some Banach spaces. The theorem is applied to image restoration, convex minimization and signal processing problems. Numerical illustrations are presented to support the main theorem and its applications.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2022)
Article
Thermodynamics
Yogesh Jaluria
Summary: This paper discusses the inverse problems in various practical thermal processes and systems, presenting approaches to obtain results within a small region of uncertainty. The non-uniqueness of the solutions is reduced in order to determine final design and boundary conditions. Optimization methods are used to reduce uncertainty, select experimental data locations, and minimize errors.
INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW
(2021)
Article
Geosciences, Multidisciplinary
Chloe Fandel, Francois Miville, Ty Ferre, Nico Goldscheider, Philippe Renard
Summary: Anisotropic fast-marching algorithms are efficient tools for generating realistic maps of karst conduit networks. This new method can rapidly generate a stochastic ensemble of plausible networks from basic geologic information. The implementation through pyKasso was successfully applied to a well-mapped karst system.
HYDROGEOLOGY JOURNAL
(2022)
Article
Geosciences, Multidisciplinary
Ludovic Schorpp, Julien Straubhaar, Philippe Renard
Summary: This paper presents a new method for automatically generating realistic geological and parameter models in Quaternary formations when modeling groundwater systems. The approach, utilizing the ArchPy Python module, operates in a hierarchical manner and streamlines the modeling process by automatically simulating stratigraphic unit boundaries, filling lithologies, and simulating petrophysical properties inside lithologies. The automation provides a flexible framework for generating stochastic models end-to-end and allows for uncertainty quantification at any level.
FRONTIERS IN EARTH SCIENCE
(2022)
Article
Environmental Sciences
S. Banusch, M. Somogyvari, M. Sauter, P. Renard, I Engelhardt
Summary: This study presents a method using a stochastic karst simulator to generate a karst conduit network for a highly karstified carbonate aquifer. The generated network geometry is robust and adjustable, and the resulting stochastic conductivity distribution can be used for parameterizing regional karst groundwater models.
WATER RESOURCES RESEARCH
(2022)
Article
Multidisciplinary Sciences
Alexis Neven, Anders Vest Christiansen, Philippe Renard
Summary: This study proposes a new methodology for integrating borehole and geophysical data with uncertainty, demonstrating its effectiveness and accuracy through a case study.
SCIENTIFIC REPORTS
(2022)
Article
Engineering, Geological
Valentin Dall'Alba, Alexis Neven, Rob de Rooij, Marco Filipponi, Philippe Renard
Summary: This paper presents a workflow for probabilistic estimation of water inflow from karst conduits in tunnels using a Monte-Carlo approach. The procedure includes generating stochastic karstic conduit network geometries, employing a numerical modeling approach, conducting uncertainty analysis, and performing statistical analysis. The results demonstrate the potential and advantages of using stochastic analysis in predicting long-term water inflow in tunnels during the early phases of project planning.
ENGINEERING GEOLOGY
(2023)
Article
Environmental Sciences
Ludovic Schorpp, Valentin Dall'Alba, Philippe Renard, Sandra Lanini, Yvan Caballero
Summary: Global climate change causes stresses on coastal water resources, including water use restrictions and saline intrusions. In this study, we focus on the coastal aquifer in southern France and develop a groundwater flow model to understand its response to climate change. The results show significant impacts on the water table, with aquifer drawdowns and seawater intrusions endangering water wells and their sustainability. Properly characterizing the geology and its heterogeneity is crucial for understanding and managing at-risk aquifers in coastal environments.
ENVIRONMENTAL EARTH SCIENCES
(2023)
Editorial Material
Geosciences, Multidisciplinary
Philippe Renard, J. Jaime Gomez-Hernandez, Maria-Theresia Schafmeister, Emmanouil A. Varouchakis
HYDROGEOLOGY JOURNAL
(2023)
Article
Environmental Sciences
Alexis Neven, Philippe Renard
Summary: This paper presents a methodology for integrating geological, geophysical, and hydrogeological data to develop a robust and accurate groundwater model. The methodology combines the Ensemble Smoother with Multiple Data Assimilation algorithm and hierarchical geological modeling approach. By computing forward responses in lower-dimensional spaces, the models take into account multiple data sources and regional conceptual geological knowledge.
WATER RESOURCES RESEARCH
(2023)
Correction
Geosciences, Multidisciplinary
Philippe Renard, Rachid Ababou
Proceedings Paper
Geography, Physical
Manon Trottet, Przemyslaw Juda, Arnulf Schiller, Philippe Renard
Summary: Traditional inverse methods are not suitable for characterizing karst environments due to their inability to handle the strong contrast between conduits and the surrounding matrix. The PoPEx method, designed to deal with abrupt variations in data, is capable of identifying caves by providing maps indicating the probabilities of encountering conduits. However, further research is needed to test its applicability in the field.
EUROKARST 2022: ADVANCES IN THE HYDROGEOLOGY OF KARST AND CARBONATE RESERVOIRS
(2023)
Article
Geosciences, Multidisciplinary
Prashanth Khambhammettu, Philippe Renard, John Doherty, Jeremy White, Marc Killingstad, Michael Kladias
Summary: This paper presents a novel approach to solve the difficult task of parameter estimation in contaminated sites using Traveling Pilot Points (TRIPS) and an iterative ensemble smoother (IES). The method is tested on a hypothetical aquifer to predict solute concentrations and mass, and the results show the influence of measurement quantity and geological prior on the predictions.
Article
Computer Science, Interdisciplinary Applications
Przemyslaw Juda, Philippe Renard, Julien Straubhaar
Summary: Multiple-point statistics algorithms allow modeling spatial variability. The proposed DSBC method efficiently selects parameters to achieve comparable or better quality and computational time than the standard parametrization.
APPLIED COMPUTING AND GEOSCIENCES
(2022)
Article
Water Resources
Alexis Neven, Ludovic Schorpp, Philippe Renard
Summary: This study proposes a method to reduce the uncertainty of the final model by combining different data types through joint inversion. The use of multi-fidelity models allows for a reduction in the time required for inversion. The method involves constraining a simplified geological model using a simple and fast geophysical direct problem, and then incorporating a high-fidelity groundwater flow model to generate plausible subsurface realizations.
FRONTIERS IN WATER
(2022)
Review
Geosciences, Multidisciplinary
Philippe Renard, Rachid Ababou
Summary: When conducting numerical upscaling, it is important to consider anisotropy as the resulting upscaled conductivity is generally anisotropic. Measurements at different scales also show the existence of anisotropy in hydraulic conductivity. Various approaches exist to define and calculate the equivalent conductivity tensor, resulting in non-equal and mathematically different equivalent conductivities. This paper presents different techniques for evaluating anisotropic equivalent conductivity in heterogeneous porous media, including numerical simulations and analytical approaches, and explores the relations between these definitions and the resulting properties of the anisotropic equivalent conductivity.
