Unsupervised deep learning method for single image super-resolution of the thick pinhole imaging system using deep image prior by Guoguang Li, Liang Sheng, Baojun Duan, Yang Li, Dongwei Hei, Qingzi Xing

“…To solve the ill-posed inverse problem, we adopt randomly initialized deep convolutional neural networks (DCNNs) as an image prior without pre-training, which is named deep image prior (DIP). …”
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MINIMIZATION OF RISK OF THE ERRONEOUS DECISION IN THE ASSESSMENT OF THE IMPORTANCE OF STATISTICAL RELATIONS OF TECHNICAL AND ECONOMIC INDICATORS OF THE OBJECTS OF ELECTRIC POWER SY... by E. M. Farhadzadeh, A. Z. Muradaliyev, Yu. Z. Farzaliyev, T. K. Rafiyeva, S. A. Abdullayeva

“…The novelty consists in the application of fiducial approach; the calculation of critical values are fulfilled with the aid of computer technologies of simulation of possible realizations of the correlation coefficients for the two assumptions, viz. technical and economic indicators of the independent and dependent; simulation is fulfilled with the method of solving the “inverse problem”, which enables the possible implementation of the correlation coefficients for the really dependent and independent samples of random variables at a given sample size; the developed algorithms and programs for calculation made it possible to obtain the critical values of correlation coefficients for independent and dependent samples; in conditions of the sameness of the consequences of erroneous decisions it is proposed to make a decision not based on critical value but based on the boundary values of the correlation coefficients that correspond to the minimum total risk of erroneous decisions; the exemplification of the recommendations application was made on example of technical and economic parameters of boilers of power units of 300 MWt. …”
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Method for assessing the theoretical characteristics of small axial hydraulic turbines by D. V. Mylkin, A. V. Volkov, B. M. Orakhelashvili, A. A. Druzhinin, V. Yu. Lyapin

“…Designing hydraulic turbines is a complex task that requires solving the inverse problem of hydrodynamics and finding the optimal shape of the flow path. …”
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Exploring parameter dependence of atomic minima with implicit differentiation by Ivan Maliyov, Petr Grigorev, Thomas D. Swinburne

“…Forward propagation of parameter variation is key for uncertainty quantification, whilst backpropagation has found application for emerging inverse problems such as fine-tuning or targeted design. …”
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Data Fusion for Electromagnetic and Electrical Resistive Tomography Based on Maximum Likelihood by Sven Nordebo, Mats Gustafsson, Therese Sjöden, Francesco Soldovieri

“…The statistical maximum likelihood criterion is closely linked to the additive Fisher information measure, and it facilitates an appropriate weighting of the measurement data which can be useful with multiphysics inverse problems. The Fisher information is particularly useful for inverse problems which can be linearized similar to the Born approximation. …”
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Intelligent phase imaging guided by physics models by Zhen LIU, Hao ZHU, You ZHOU, Zhan MA, Xun CAO

“…Implicit neural representation characterizes the mapping between the signal’s coordinate to its attributes, and has been widely used in the optimization of inverse problems by embedding the physics process into the loss function.However, the implicit neural representation is suffering the low convergence speed and accuracy from the random initialization of the network parameters.The meta-learning algorithm for providing implicit neural representation with a strong prior of network parameters was proposed, thus enhancing the optimization efficiency and accuracy for solving inverse problems.To address the important issue of lens less phase imaging, an intelligent method on phase imaging was proposed based on the snapshot lens less sensing model.By embedding the optical diffraction propagation theory into the design of loss function for implicit neural representation, the dependency of large-scale labelled dataset in traditional deep learning-based methods was eliminated and accurate phase image from a single diffraction measurement image was provided.Furthermore, the meta-learning model was introduced for initializing network to further improve the efficiency and accuracy of network training.Numerical simulation results show that the proposed method can achieve a PSNR improvement of more than 11 dB compared to the conventional method.The experimental results in real data show that the phase image reconstructed by the proposed method is clearer and has fewer artifacts.…”
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Computing the Fixed Points of Strictly Pseudocontractive Mappings by the Implicit and Explicit Iterations by Yeong-Cheng Liou

“…It is known that strictly pseudocontractive mappings have more powerful applications than nonexpansive mappings in solving inverse problems. In this paper, we devote to study computing the fixed points of strictly pseudocontractive mappings by the iterations. …”
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Nonlinear stochastic Markov processes and modeling uncertainty in populations by H.Thomas Banks, Shuhua Hu

“…Moreover, these alternate formulations lead to fast efficient calculations in inverse problems as well as in forward simulations. Here we derive a class of stochastic formulations for which such an alternate representation is readily found.…”
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The estimation of the effective reproductive number from disease outbreak data by Ariel Cintrón-Arias, Carlos Castillo-Chávez, Luís M. A. Bettencourt, Alun L. Lloyd, H. T. Banks

“…We use asymptotic statisticaltheories to derive the mean and variance of the limiting(Gaussian) sampling distribution and to perform post statisticalanalysis of the inverse problems. We illustrate the ideas andpitfalls (e.g., large condition numbers on the correspondingFisher information matrix) with both synthetic and influenzaincidence data sets.…”
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A General Result on the Mean Integrated Squared Error of the Hard Thresholding Wavelet Estimator under α-Mixing Dependence by Christophe Chesneau

“…Applications are given for two types of inverse problems: the deconvolution density estimation and the density estimation in a GARCH-type model, both improve existing results in this dependent context. …”
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Applications of Fixed-Point and Optimization Methods to the Multiple-Set Split Feasibility Problem by Yonghong Yao, Rudong Chen, Giuseppe Marino, Yeong Cheng Liou

“…It can be a model for many inverse problems where constraints are imposed on the solutions in the domain of a linear operator as well as in the operator’s range. …”
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An Optimally Generalized Steepest-Descent Algorithm for Solving Ill-Posed Linear Systems by Chein-Shan Liu

“…The optimally generalized steepest-descent algorithm (OGSDA) is proven to be convergent with very fast convergence speed, accurate and robust against noisy disturbance, which is confirmed by numerical tests of some well-known ill-posed linear problems and linear inverse problems.…”
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Total Variation Regularization Algorithms for Images Corrupted with Different Noise Models: A Review by Paul Rodríguez

“…Total Variation (TV) regularization has evolved from an image denoising method for images corrupted with Gaussian noise into a more general technique for inverse problems such as deblurring, blind deconvolution, and inpainting, which also encompasses the Impulse, Poisson, Speckle, and mixed noise models. …”
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Numerical differentiation of fractional order derivatives based on inverse source problems of hyperbolic equations by Zewen Wang, Shufang Qiu, Xiuxing Rui, Wen Zhang

“…It can be conclude that the proposed methods are very effective for small noise levels, and they are simpler and easier to be implemented than the previous PDEs-based numerical differentiation method based on direct and inverse problems of parabolic equations. …”
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Magnetoacoustic Heating in Nonisentropic Plasma Caused by Different Kinds of Heating-Cooling Function by Anna Perelomova

“…The conclusions concern nonlinear effects of fast and slow magnetoacoustic perturbations and may be useful in direct and inverse problems.…”
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A Comparative Study of Regularization Method in Structure Load Identification by Bingrong Miao, Feng Zhou, Chuanying Jiang, Xiangyu Chen, Shuwang Yang

“…The proposed two kinds of load identification procedure based on vibration response can be applied to the safety performance evaluation of the railway track structure in future inverse problems research.…”
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Physics-informed deep learning quantifies propagated uncertainty in seismic structure and hypocenter determination by Ryoichiro Agata, Kazuya Shiraishi, Gou Fujie

“…Our results highlight the potential of PIDL for various geophysical inverse problems, such as investigating earthquake source parameters, which inherently suffer from uncertainty propagation.…”
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Load Identification Method Based on Interval Analysis and Tikhonov Regularization and Its Application by Chunsheng Liu, Chunping Ren, Nengjian Wang

“…By using the interval analysis method of the first-order Taylor expansion, the dynamic force identification is transformed into two kinds of deterministic inverse problems at the midpoint of the uncertain parameter and its gradient identification. …”
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Adapting physics-informed neural networks to improve ODE optimization in mosquito population dynamics. by Dinh Viet Cuong, Branislava Lalić, Mina Petrić, Nguyen Thanh Binh, Mark Roantree

“…In this research, we propose a PINN framework with several improvements for forward and inverse problems for ODE systems with a case study application in modelling the dynamics of mosquito populations. …”
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Seismic Waveform Inversion Using the Finite-Difference Contrast Source Inversion Method by Bo Han, Qinglong He, Yong Chen, Yixin Dou

“…Another attractive feature of the inversion method is that it is of strong capability in dealing with nonlinear inverse problems in an inhomogeneous background medium, because a finite-difference operator is used to represent the differential operator governing the two-dimensional elastic wave propagation. …”
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