Article
Mathematics
Gabor Balassa
Summary: In this paper, a finite memory, non-causal Volterra model is proposed to estimate the potential functions in various inverse quantum mechanical problems. The model capabilities are demonstrated through two simple examples, showing good match for a wide range of potential functions. The model also exhibits robustness to input perturbations and can be useful in situations where the precise governing equations are unknown.
Article
Agronomy
Yibo Li, Ye Liu, Xiaoyi Ma
Summary: Accurate inversion of soil hydraulic parameters based on the van Genuchten-Mualem model has been achieved through a hybrid algorithm method using particle swarm optimization and vector-evaluated genetic algorithm. The inverse method was verified through numerical experiments and laboratory experiments, showing good accuracy and robustness. The method is found to be practical in field experiments, even with substantial measurement errors.
Article
Engineering, Mechanical
Konstantinos G. Papakonstantinou, Hamed Nikbakht, Elsayed Eshra
Summary: Accurate estimation of rare event probabilities is crucial due to their widespread impacts. This work proposes the Approximate Sampling Target with Post-processing Adjustment (ASTPA) framework integrated with gradient-based Hamiltonian Markov Chain Monte Carlo (HMCMC) methods. The proposed technique is applicable in low-to high-dimensional stochastic spaces, utilizing a one-dimensional output likelihood model to construct a relevant target distribution. A new Quasi-Newton mass preconditioned HMCMC scheme (QNp-HMCMC) is developed for efficient sampling in high-dimensional spaces. An original post-sampling step using an inverse importance sampling procedure is devised to compute the rare event probability. The statistical properties and performance of the proposed methodology are analyzed and compared against Subset Simulation.
PROBABILISTIC ENGINEERING MECHANICS
(2023)
Article
Computer Science, Interdisciplinary Applications
N. Antoni
Summary: This paper presents an inverse method using least squares minimization technique and a non-linear numerical solving procedure for identifying frictional parameters in beam contact models. The method offers a more efficient and accurate approach for parameter identification.
JOURNAL OF COMPUTATIONAL SCIENCE
(2023)
Article
Thermodynamics
Feiding Zhu, Jincheng Chen, Yuge Han, Dengfeng Ren
Summary: This study proposed a simple method based on deep learning to estimate thermal boundary condition parameters in the transient inverse heat transfer problem. By combining convolutional neural network (CNN) and long short-term memory networks (LSTM), real-time prediction of multiple time-varying parameters can be achieved. Experimental results showed that the proposed model outperformed standalone models in estimating multiple time-varying parameters.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2022)
Article
Mathematics, Applied
Shengda Zeng, Yunru Bai, Patrick Winkert, Jen-Chih Yao
Summary: This article investigates the inverse problem of identifying a discontinuous parameter and a discontinuous boundary datum in an elliptic inclusion problem involving a double phase differential operator. By applying a surjectivity theorem for multivalued mappings and introducing the parameter-to-solution-map, the existence of nontrivial solutions and solvability of the inverse problem are examined and established.
ADVANCES IN NONLINEAR ANALYSIS
(2023)
Article
Materials Science, Multidisciplinary
V. D. Vijayanand, M. Mokhtarishirazabad, Y. Wang, M. Gorley, D. M. Knowles, M. Mostafavi
Summary: This study examined the performance differences of Copper-Chromium-Zirconium alloy under different heat treatment conditions in small punch testing, attributing variations in load displacement characteristics to differences in plastic and damage properties. The research discussed estimating elastic and plastic properties, as well as damage model parameters using an inverse finite element method, and correlated damage model parameters with fractographic observations. Additionally, a formulation for compliance correction in small punch testing rig using finite element model was presented.
JOURNAL OF NUCLEAR MATERIALS
(2021)
Article
Computer Science, Interdisciplinary Applications
Peishi Jiang, Xingyuan Chen, Kewei Chen, Jeffrey Anderson, Nancy Collins, Mohamad EL. Gharamti
Summary: By linking DART with PFLOTRAN, the DART-PFLOTRAN software framework enables an iterative EDA workflow to improve estimation accuracy for nonlinear forward problems. Through validation using two synthetic cases, DART-PFLOTRAN paves the way for large-scale inverse modeling using the sequential ES-MDA.
ENVIRONMENTAL MODELLING & SOFTWARE
(2021)
Article
Mathematics
Jun Lu, Lianpeng Shi, Chein-Shan Liu, C. S. Chen
Summary: In this paper, a family of two-parameter homogenization functions is derived for the doubly connected domain, which is utilized as the basis of trial solutions for inverse conductivity problems. By imposing an extra boundary condition on the inner boundary, expansion coefficients are obtained, resulting in a linear system for the interpolation of the solution. The spatial- or temperature-dependent conductivity function can be retrieved by solving a linear system obtained from the collocation method applied to the nonlinear elliptic equation after inserting the solution.
Article
Geochemistry & Geophysics
Shihuan Liu, Jiashu Zhang
Summary: Regularization parameter selection (RPS) is a crucial task in solving inverse problems, and the most common approach seeks the optimal regularization parameter (ORP) from a sequence of candidate values. This paper proposes a novel machine learning-based prediction framework (MLBP) for RPS, which generates synthetic data, extracts features, and trains a regression model to predict ORP for practical inverse problems. The numerical results demonstrate that MLBP outperforms traditional methods by requiring less computing time and providing more accurate solutions.
Article
Engineering, Multidisciplinary
Dariusz Ucinski
Summary: The study addresses the design of observation locations in a spatiotemporal system model and focuses on accurately estimating a subset of parameters. To address computational challenges, a convex relaxation method is introduced, and issues of potential singularity and nondifferentiability are resolved. The excellent performance of the proposed technique is illustrated through an example involving sensor node activation in a large sensor network.
Article
Engineering, Civil
Halimeh Maroufi, Behrouz Mehdinejadiani
Summary: This work developed four inverse models based on different optimization algorithms to identify parameters of space fractional advection-dispersion equation. TLBO algorithm showed the best performance in terms of convergence trend, repeatability of results, and modeling complexity.
JOURNAL OF HYDROLOGY
(2021)
Article
Computer Science, Artificial Intelligence
Shima Kamyab, Zohreh Azimifar, Rasool Sabzi, Paul Fieguth
Summary: This paper investigates various deep learning strategies for solving inverse problems, classifying them into three categories and studying their robustness through extensive experiments on representative samples. Based on statistical analyses, the most robust solution category for each type of inverse problem is proposed.
PEERJ COMPUTER SCIENCE
(2022)
Article
Engineering, Chemical
Piran Goudarzi, Awatef Abidi, Seyed Abdollah Mansouri Mehryan, Mohammad Ghalambaz, Mikhail A. Sheremet
Summary: In this work, the relaxation parameter (tau) and fractionality order (alpha) in the FSPL non-Fourier heat conduction model were estimated using the CGIM method. The results demonstrated the efficiency of CGIM in estimating the unknown parameters in the FSPL model, showing excellent compatibility with the theoretical model.
Article
Mathematics, Applied
Guidong Zhang, Yuhong Sheng
Summary: This paper investigates methods for estimating unknown parameters in uncertain differential equations, considering time-varying parameters and rewriting the least squares estimation method. The feasibility of this method is demonstrated through numerical examples.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mathematics, Applied
Nick Luiken, Tristan Van Leeuwen
Summary: The paper discusses an algorithm called SR3 for solving regularized least-squares problems and analyzes the conditions, errors, and numerical examples encountered during the solution process.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2021)
Article
Optics
Allard A. Hendriksen, Dirk Schut, Willem Jan Palenstijn, Nicola Vigano, Jisoo Kim, Daniel M. Pelt, Tristan van Leeuwen, K. Joost Batenburg
Summary: Tomography is a powerful tool for reconstructing the interior of objects using projection images. Current software lack the flexibility to handle complex geometries, necessitating the need for software like tomosipo which offers concise representation and visualization capabilities. Through case studies, the power and flexibility of tomosipo are demonstrated.
Article
Mathematics
Andreas Tataris, Tristan van Leeuwen
Summary: In this paper, we study the inverse scattering problem for a Schrodinger operator related to a static wave operator with variable velocity using the GLM integral equation. We assume the presence of noisy scattering data and derive a stability estimate for the error of the solution of the GLM integral equation by showing the invertibility of the GLM operator between suitable function spaces. To regularize the problem, we formulate a variational total least squares problem and prove the existence of minimizers under certain regularity assumptions. Finally, we compute the regularized solution of the GLM equation numerically using the total least squares method in a discrete sense.
Article
Geochemistry & Geophysics
Frenk Out, David Cortes-Ortuno, Karl Fabian, Tristan van Leeuwen, Lennart de Groot
Summary: The Micromagnetic Tomography (MMT) technique, which combines high resolution scanning magnetometry and micro X-ray computed tomography, allows for the precise recovery of magnetic moments of individual magnetic grains in a sample. This study investigates the mathematical validity of MMT solutions by examining five factors: grain concentration, sample thickness, sample surface size, noise level in the magnetic scan, and sampling interval of the magnetic scan. Through numerical models, the influence of these parameters on the accuracy of the magnetizations of the grains is assessed. The authors also introduce a statistical uncertainty ratio and signal strength ratio to determine the most accurate solutions.
GEOCHEMISTRY GEOPHYSICS GEOSYSTEMS
(2022)
Article
Geochemistry & Geophysics
J. H. E. de Jong, H. Paulssen, T. van Leeuwen, J. Trampert
Summary: Receiver functions have long been used to study Earth's major discontinuities. The traditional assumptions for mapping locations in the subsurface have been found to have limitations, but the use of adjoint tomography provides a potential solution. Sensitivity kernels for P-to-S converted waves have been calculated, revealing differences in sensitivity to P-wave speed and S-wave speed. The well-known trade-off between depth of the discontinuity and wave speed has also been observed, but can be significantly reduced by considering longer waveforms that include more surface reverberations.
GEOPHYSICAL JOURNAL INTERNATIONAL
(2022)
Article
Computer Science, Artificial Intelligence
Mathe T. Zeegers, Tristan van Leeuwen, Daniel M. Pelt, Sophia Bethany Coban, Robert van Liere, Kees Joost Batenburg
Summary: X-ray imaging is a fast and non-invasive method for foreign object detection, and deep learning has been applied to automate this process. This study proposes a Computed Tomography (CT) based method for generating training data with minimal labor requirements. The results demonstrate that a small number of representative objects are sufficient for achieving adequate detection performance in an industrial setting.
EXPERT SYSTEMS WITH APPLICATIONS
(2022)
Article
Mathematics, Applied
Mathe T. Zeegers, Ajinkya Kadu, Tristan van Leeuwen, Kees Joost Batenburg
Summary: Advancements in multi-spectral detectors are transforming the field of x-ray computed tomography by allowing the extraction of volumetric material composition maps. A dictionary-based joint reconstruction and unmixing method called ADJUST is proposed, which shows excellent performance compared to other state-of-the-art methods in synthetic phantom experiments and demonstrates robustness against limited and noisy measurement patterns.
Article
Physics, Mathematical
Tristan van Leeuwen, Andreas Tataris
Summary: This paper studies the inverse scattering problem for the Helmholtz equation on the whole line and aims to obtain a Gelfand-Levitan-Marchenko (GLM)-type equation for the Jost solution corresponding to the 1D Helmholtz differential operator. The possible application of this new generalized GLM equation to the inverse medium problem is also discussed.
JOURNAL OF MATHEMATICAL PHYSICS
(2022)
Article
Geochemistry & Geophysics
Yuzhao Lin, Tristan van Leeuwen, Huaishan Liu, Jian Sun, Lei Xing
Summary: Full-waveform inversion (FWI) estimates subsurface parameters by minimizing misfit between simulated and observed data, while wavefield reconstruction inversion (WRI) is more robust but computationally expensive. We developed a new form of WRI by incorporating a medium-dependent weight function into the FWI workflow. This weight function uses covariance matrices to characterize uncertainties in measurements and physical assumptions.
Article
Multidisciplinary Sciences
Vladyslav Andriiashen, Robert van Liere, Tristan van Leeuwen, K. Joost Batenburg
Summary: X-ray imaging is commonly used for quality control in industry, but has limitations in detecting internal defects. We propose a computationally efficient approach for creating artificial single-view X-ray data based on a few physically CT-scanned objects. Our results show that applying this method to a single CT-scanned object achieves accuracy comparable to scanning multiple real-world samples.
SCIENTIFIC REPORTS
(2023)
Article
Geochemistry & Geophysics
Leon Diekmann, Ivan Vasconcelos, Tristan van Leeuwen
Summary: Full waveform inversion and least-squares reverse time migration are commonly used for seismic wave imaging, relying on the Born approximation to compute gradients and update models. We propose using the Marchenko integral to obtain an alternative linear equation that includes all orders of scattering. This new linearization strategy, although relying on the quality of the Marchenko-derived Green's functions, produces slightly better inverted models than the single-scattering approximation.
GEOPHYSICAL JOURNAL INTERNATIONAL
(2023)
Article
Nanoscience & Nanotechnology
Tristan van Leeuwen, Andreas Tataris
Summary: This paper extends a recently proposed approach for inverse scattering to the 1D Schrodinger equation with impedance boundary conditions. The method involves extracting a reduced order model directly from the data and then using it to extract the scattering potential. A novel data-assimilation inversion method based on the reduced order model approach is also proposed, which eliminates the need for a Lanczos-orthogonalization step. Furthermore, a detailed numerical study and comparison of the accuracy and stability of the data-assimilation and Lanczos-orthogonalization methods are presented.
Article
Engineering, Electrical & Electronic
Dirk Elias Schut, Kees Joost Batenburg, Robert van Liere, Tristan van Leeuwen
Summary: TOP-CT is a new CT scanning geometry for high throughput industrial CT scanning, which allows overlapped projection data for simultaneous scanning and reconstruction, resulting in higher reconstruction quality.
IEEE TRANSACTIONS ON COMPUTATIONAL IMAGING
(2022)
Article
Engineering, Electrical & Electronic
Gabrio Rizzuti, Alessandro Sbrizzi, Tristan van Leeuwen
Summary: The article presents a retrospective joint motion correction and reconstruction scheme to reduce the impact of subject motion on MRI images. The scheme leverages uncorrupted reconstructions to post-process contrasts most affected by motion, assuming a shared underlying anatomy. Rigid motion is considered, and classical motion correction schemes are combined with weighted total-variation regularization.
IEEE TRANSACTIONS ON COMPUTATIONAL IMAGING
(2022)
Article
Imaging Science & Photographic Technology
Vladyslav Andriiashen, Robert van Liere, Tristan van Leeuwen, Kees Joost Batenburg
Summary: This article introduces a method for unsupervised foreign object detection based on dual-energy X-ray absorptiometry, using a thickness correction model to enhance contrast. Experimental results show that the method can achieve an accuracy of 95% in detecting foreign objects in meat products.
JOURNAL OF IMAGING
(2021)