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Journal articles on the topic 'Inverse linear model'

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Published: 25 May 2024

Last updated: 19 July 2025

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BERNARD, James, and Mark PICKELMANN. "An Inverse Linear Model of a Vehicle." Vehicle System Dynamics 15, no. 4 (1986): 179–86. http://dx.doi.org/10.1080/00423118608968850.

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Zhanatauov, S. U. "INVERSE MODEL OF MULTIPLE LINEAR REGRESSION ANALYSIS." Theoretical & Applied Science 60, no. 04 (2018): 201–12. http://dx.doi.org/10.15863/tas.2018.04.60.38.

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Borneman, Joshua, Kuo-Ping Chen, Alex Kildishev, and Vladimir Shalaev. "Simplified model for periodic nanoantennae: linear model and inverse design." Optics Express 17, no. 14 (2009): 11607. http://dx.doi.org/10.1364/oe.17.011607.

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Ayala, A., M. Loewe, and R. Zamora. "Inverse magnetic catalysis in the linear sigma model." Journal of Physics: Conference Series 720 (May 2016): 012026. http://dx.doi.org/10.1088/1742-6596/720/1/012026.

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Fang, Ximing. "A hybrid regularization model for linear inverse problems." Filomat 36, no. 8 (2022): 2739–48. http://dx.doi.org/10.2298/fil2208739f.

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For the ill-posed linear inverse problem, we propose a hybrid regularization model, which possesses the characters of Tikhonov regularization and TV regularization to some extent. Through transformation, the hybrid regularization is reformulated as an equivalent minimization problem. To solve the minimization problem, we present two modified iterative shrinkage-thresholding algorithms (MISTA) based on the fast iterative shrinkage-thresholding algorithm (FISTA) and the iterative shrinkagethresholding algorithm (ISTA). The numerical experiments are performed to show the effectiveness and superiority of the regularization model and the presented algorithms.

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Hansen, Thomas Mejer, Andre G. Journel, Albert Tarantola, and Klaus Mosegaard. "Linear inverse Gaussian theory and geostatistics." GEOPHYSICS 71, no. 6 (2006): R101—R111. http://dx.doi.org/10.1190/1.2345195.

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Inverse problems in geophysics require the introduction of complex a priori information and are solved using computationally expensive Monte Carlo techniques (where large portions of the model space are explored). The geostatistical method allows for fast integration of complex a priori information in the form of covariance functions and training images. We combine geostatistical methods and inverse problem theory to generate realizations of the posterior probability density function of any Gaussian linear inverse problem, honoring a priori information in the form of a covariance function describing the spatial connectivity of the model space parameters. This is achieved using sequential Gaussian simulation, a well-known, noniterative geostatisticalmethod for generating samples of a Gaussian random field with a given covariance function. This work is a contribution to both linear inverse problem theory and geostatistics. Our main result is an efficient method to generate realizations, actual solutions rather than the conventional least-squares-based approach, to any Gaussian linear inverse problem using a noniterative method. The sequential approach to solving linear and weakly nonlinear problems is computationally efficient compared with traditional least-squares-based inversion. The sequential approach also allows one to solve the inverse problem in only a small part of the model space while conditioned to all available data. From a geostatistical point of view, the method can be used to condition realizations of Gaussian random fields to the possibly noisy linear average observations of the model space.

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Cho, Jeong-Mok, Bong-Soo Yoo, and Joong-Seon Joh. "A Fuzzy Skyhook Algorithm Using Piecewise Linear Inverse Model." International Journal of Fuzzy Logic and Intelligent Systems 6, no. 3 (2006): 190–96. http://dx.doi.org/10.5391/ijfis.2006.6.3.190.

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Zhou, Huilin, Tao Ouyang, Yadan Li, Jian Liu, and Qiegen Liu. "Linear-Model-Inspired Neural Network for Electromagnetic Inverse Scattering." IEEE Antennas and Wireless Propagation Letters 19, no. 9 (2020): 1536–40. http://dx.doi.org/10.1109/lawp.2020.3008720.

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Penland, Cécile, and Ludmila Matrosova. "Expected and Actual Errors of Linear Inverse Model Forecasts." Monthly Weather Review 129, no. 7 (2001): 1740–45. http://dx.doi.org/10.1175/1520-0493(2001)129<1740:eaaeol>2.0.co;2.

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Jiang, Wen, Yi Xin Su, and Dan Hong Zhang. "Research on Inverse Control of Active Magnetic Bearing Based on Fuzzy Inverse Model." Applied Mechanics and Materials 575 (June 2014): 744–48. http://dx.doi.org/10.4028/www.scientific.net/amm.575.744.

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For magnetic bearing system with characteristics of zero damping, negative stiffness and nonlinearity, this paper put forward a method of inverse control based on the fuzzy inverse model. The fuzzy system with fuzzifier and defuzzifier was used as an interpolator to approximate the inverse model of magnetic bearing. Then we connected the fuzzy inverse model in series with the magnetic bearing system to form a generalized pseudo linear plant, and selected a PID controller to control the pseudo linear plant. The fuzzy inverse model and the PID controller together formed an inverse controller to implement the closed-loop inverse control of the system. The simulation results demonstrate that the inverse control can reduce the overshoot, shorten the settling time, and make the rotor levitate in a larger range.

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Yip, K. M., and G. Leng. "Stability analysis for inverse simulation of aircraft." Aeronautical Journal 102, no. 1016 (1998): 345–51. http://dx.doi.org/10.1017/s0001924000027597.

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AbstractThe integration inverse method has been extensively investigated in the past decade; however, none of the researches fully addresses the stability analysis of the method that is crucial to successful implementation. This paper presents a stability test to analyse the global stability of the integration inverse method for linear time-invariant systems. A stable solution may be obtained from careful selection of the discretisation interval using the proposed stability test. A discrete model is derived to approximate the Newton's scheme in the inverse method. With this approximate model, the stability of the inverse method can be examined. The stability test is exact for linear systems and can be extended to the inverse method for non-linear aircraft simulations by considering an equivalent linear model for each point of the flight envelopes. Guidelines for selection of appropriate reference points in the inverse simulation are given.

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Keneskyzy, K., та S. B. Yeskermes. "Метод машинного обучения для обратных задач теплопроводности". INTERNATIONAL JOURNAL OF INFORMATION AND COMMUNICATION TECHNOLOGIES 2, № 1(5) (2021): 59–64. http://dx.doi.org/10.54309/ijict.2021.05.1.008.

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Investigated in this work is the potential of carrying out inverse problems with linear and non-linear behavior using machine learning methods and the neural network method. With the advent of ma-chine learning algorithms it is now possible to model inverse problems faster and more accurately. In order to demonstrate the use of machine learning and neural networks in solving inverse problems, we propose a fusion between computational mechanics and machine learning. The forward problems are solved first to create a database. This database is then used to train the machine learning and neural network algorithms. The trained algorithm is then used to determine the boundary conditions of a problem from assumed meas-urements. The proposed method is tested for the linear/non-linear heat conduction problems in which the boundary conditions are determined by providing three, four, and five temperature measurements. This re-search demonstrates that the proposed fusion of computational mechanics and machine learning is an effec-tive way of tackling complex inverse problems.

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Liu, Xian Xing, Jie Chen, Yi Du, and Kai Shi. "Model Reference Adaptive Control of HMB Based on PSO-LS-SVM Inverse." Applied Mechanics and Materials 416-417 (September 2013): 870–75. http://dx.doi.org/10.4028/www.scientific.net/amm.416-417.870.

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To realize the hybrid magnetic bearing (HMB) nonlinear decoupling control with high precision, a strategy of model reference adaptive control (MRAC) based on the least square support vector machine (LS-SVM) inverse is proposed. After analyzing the reversibility of HMB, the LS-SVM regression theory is used to identify the inverse model, the parameters of LS-SVM are optimized by Particle Swarm Optimization (PSO) algorithm. Then the nonlinear system is transformed into a pseudo-linear system by connecting the optimized the inverse model and the original unit. MRAC is designed to realize the compound linear control for HMB. Simulation results confirm that the identified inverse model has high precision and the compound control strategy has good performance.

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Fosgerau, Mogens, Julien Monardo, and André de Palma. "The Inverse Product Differentiation Logit Model." American Economic Journal: Microeconomics 16, no. 4 (2024): 329–70. http://dx.doi.org/10.1257/mic.20210066.

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We introduce the inverse product differentiation logit (IPDL) model, a micro-founded inverse market share model for differentiated products that captures market segmentation according to one or more characteristics. The IPDL model generalizes the nested logit model to allow richer substitution patterns, including complementarity in demand, and can be estimated by linear instrumental variable regression with market-level data. Furthermore, we provide Monte Carlo experiments comparing the IPDL model to the workhorse empirical models of the literature. Lastly, we demonstrate the empirical performance of the IPDL model using a well-known dataset on the ready-to-eat cereal market. (JEL C25, D11, D12, L66, L81)

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Lyubchyk, Leonid M. "Disturbance Rejection in Linear Discrete Multivariable Systems: Inverse Model Approach." IFAC Proceedings Volumes 44, no. 1 (2011): 7921–26. http://dx.doi.org/10.3182/20110828-6-it-1002.02121.

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Alexander, Michael A., Ludmila Matrosova, Cécile Penland, James D. Scott, and Ping Chang. "Forecasting Pacific SSTs: Linear Inverse Model Predictions of the PDO." Journal of Climate 21, no. 2 (2008): 385–402. http://dx.doi.org/10.1175/2007jcli1849.1.

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Abstract A linear inverse model (LIM) is used to predict Pacific (30°S–60°N) sea surface temperature anomalies (SSTAs), including the Pacific decadal oscillation (PDO). The LIM is derived from the observed simultaneous and lagged covariance statistics of 3-month running mean Pacific SSTA for the years 1951–2000. The model forecasts exhibit significant skill over much of the Pacific for two to three seasons in advance and up to a year in some locations, particulary for forecasts initialized in winter. The predicted and observed PDO are significantly correlated at leads of up to four seasons, for example, the correlation exceeds 0.6 for 12-month forecasts initialized in January–March (JFM). The LIM-based PDO forecasts are more skillful than persistence or a first-order autoregressive model, and have comparable skill to LIM forecasts of El Niño SSTAs. Filtering the data indicates that much of the PDO forecast skill is due to ENSO teleconnections and the global trend. Within LIM, SST anomalies can grow due to constructive interference of the empirically determined modes, even though the individual modes are damped over time. For the Pacific domain, the basinwide SST variance can grow for ∼14 months, consistent with the skill of the actual predictions. The optimal structure (OS), the initial SSTA pattern that LIM indicates should increase the most rapidly with time, is clearly relevant to the predictions, as the OS develops into a mature ENSO and PDO event 6–10 months later. The OS is also consistent with the seasonal footprinting mechanism (SFM) and the meridional mode (MM); the SFM and MM involve a set of atmosphere–ocean interactions that have been hypothesized to initiate ENSO events.

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Martinez-Villalobos, Cristian, Daniel J. Vimont, Cécile Penland, Matthew Newman, and J. David Neelin. "Calculating State-Dependent Noise in a Linear Inverse Model Framework." Journal of the Atmospheric Sciences 75, no. 2 (2018): 479–96. http://dx.doi.org/10.1175/jas-d-17-0235.1.

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Abstract The most commonly used version of a linear inverse model (LIM) is forced by state-independent noise. Although having several desirable qualities, this formulation can only generate long-term Gaussian statistics. LIM-like systems forced by correlated additive–multiplicative (CAM) noise have been shown to generate deviations from Gaussianity, but parameter estimation methods are only known in the univariate case, limiting their use for the study of coupled variability. This paper presents a methodology to calculate the parameters of the simplest multivariate LIM extension that can generate long-term deviations from Gaussianity. This model (CAM-LIM) consists of a linear deterministic part forced by a diagonal CAM noise formulation, plus an independent additive noise term. This allows for the possibility of representing asymmetric distributions with heavier- or lighter-than-Gaussian tails. The usefulness of this methodology is illustrated in a locally coupled two-variable ocean–atmosphere model of midlatitude variability. Here, a CAM-LIM is calculated from ocean weather station data. Although the time-resolved dynamics is very close to linear at a time scale of a couple of days, significant deviations from Gaussianity are found. In particular, individual probability density functions are skewed with both heavy and light tails. It is shown that these deviations from Gaussianity are well accounted for by the CAM-LIM formulation, without invoking nonlinearity in the time-resolved operator. Estimation methods using knowledge of the CAM-LIM statistical constraints provide robust estimation of the parameters with data lengths typical of geophysical time series, for example, 31 winters for the ocean weather station here.

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Zhou, Junqiang, Marcello Canova, and Andrea Serrani. "Predictive inverse model allocation for constrained over-actuated linear systems." Automatica 67 (May 2016): 267–76. http://dx.doi.org/10.1016/j.automatica.2016.01.045.

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Wang, Lichun, and Lawrence Pettit. "Linear Bayes estimators applied to the inverse Gaussian lifetime model." Journal of Systems Science and Complexity 29, no. 6 (2016): 1683–92. http://dx.doi.org/10.1007/s11424-016-5030-7.

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Lavoie, Francis B., Alyssa Langlet, Koji Muteki, and Ryan Gosselin. "Likelihood Maximization Inverse Regression: A novel non-linear multivariate model." Chemometrics and Intelligent Laboratory Systems 194 (November 2019): 103844. http://dx.doi.org/10.1016/j.chemolab.2019.103844.

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Babier, Aaron, Timothy C. Y. Chan, Taewoo Lee, Rafid Mahmood, and Daria Terekhov. "An Ensemble Learning Framework for Model Fitting and Evaluation in Inverse Linear Optimization." INFORMS Journal on Optimization 3, no. 2 (2021): 119–38. http://dx.doi.org/10.1287/ijoo.2019.0045.

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We develop a generalized inverse optimization framework for fitting the cost vector of a single linear optimization problem given multiple observed decisions. This setting is motivated by ensemble learning, where building consensus from base learners can yield better predictions. We unify several models in the inverse optimization literature under a single framework and derive assumption-free and exact solution methods for each one. We extend a goodness-of-fit metric previously introduced for the problem with a single observed decision to this new setting and demonstrate several important properties. Finally, we demonstrate our framework in a novel inverse optimization-driven procedure for automated radiation therapy treatment planning. Here, the inverse optimization model leverages an ensemble of dose predictions from different machine learning models to construct a consensus treatment plan that outperforms baseline methods. The consensus plan yields better trade-offs between the competing clinical criteria used for plan evaluation.

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Uyar, Erol, and Lutfi Mutlu. "Modelling and Kinematic Analysis of a Built Up Linear Delta Robot." Applied Mechanics and Materials 186 (June 2012): 234–38. http://dx.doi.org/10.4028/www.scientific.net/amm.186.234.

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In this paper kinematic analysis of a 3-PUU translational parallel manipulator (TPM) is made by creating the forward and inverse Kinematic solutions. For a given position, control of the end effecter is then realized by using the calculated inverse kinematic parameters as reference values. For kinematic analysis relevant equations are derived from geometrical vector relations. For the forward and inverse kinematic solutions of the non-linear model a MATLAB based iterative algorithm is developed and the inverse kinematic solutions of limbs, are then used to control the end effecter position through screw rails which are driven by DC motors. After the general mechanical design of the manipulator all parts are drawn and modelled in SolidWorks, and a simulation of the motion in three dimensional space is made. To support the reliability of calculated parameters through inverse kinematic solutions, results are compared with the values of SolidWorks based simulation model of the manipulator. Furthermore a real position control with use of feed back encoders is applied and the evaluated results are compared with the results of a simulation model. Very similar and satisfactory results are obtained with both simulation and real application.

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Turetsky, Vladimir. "Two Inverse Problems Solution by Feedback Tracking Control." Axioms 10, no. 3 (2021): 137. http://dx.doi.org/10.3390/axioms10030137.

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Two inverse ill-posed problems are considered. The first problem is an input restoration of a linear system. The second one is a restoration of time-dependent coefficients of a linear ordinary differential equation. Both problems are reformulated as auxiliary optimal control problems with regularizing cost functional. For the coefficients restoration problem, two control models are proposed. In the first model, the control coefficients are approximated by the output and the estimates of its derivatives. This model yields an approximating linear-quadratic optimal control problem having a known explicit solution. The derivatives are also obtained as auxiliary linear-quadratic tracking controls. The second control model is accurate and leads to a bilinear-quadratic optimal control problem. The latter is tackled in two ways: by an iterative procedure and by a feedback linearization. Simulation results show that a bilinear model provides more accurate coefficients estimates.

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Shafiq, M., and M. Haseebuddin. "U-Model-Based Internal Model Control for Non-Linear Dynamic Plants." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 219, no. 6 (2005): 449–58. http://dx.doi.org/10.1243/095965105x33563.

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In this paper, a U-model in the internal model control (IMC) structure is used. The U-model is a control-oriented model applicable to a wide class of non-linear plants. It is a non-linear polynomial representation of the plant, which allows the use of well-established polynomial controller design methodologies. A learning rate parameter is introduced in the inverse finding computational algorithm in order to improve the convergence and stability properties. Computer simulation results and real-time experimental results are presented to show the effectiveness of the proposed method.

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Luh, G.-C., and C.-Y. Wu. "Inversion control of non-linear systems with an inverse NARX model identified using genetic algorithms." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 214, no. 4 (2000): 259–71. http://dx.doi.org/10.1243/0959651001540627.

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The inverse dynamics approach has been widely utilized in the control problem of various practical non-linear systems in recent years. This paper demonstrates a feedforward-feedback controller scheme of a non-linear plant whose dynamics are unknown and uncertain. The feedforward controller, an inverse NARX model (non-linear autoregressive model with exogenous inputs), provides only coarse control, whereas the feedback controller is used to handle unmodelled dynamics and disturbance. The inverse NARX model is derived by inverting the forward NARX model identified using genetic algorithms. A parallel-type NARX model whose outputs of the identification model are fed back into the identification model is adopted in the identification procedure to include the stability examination numerically. Both experimental and simulation results demonstrate that the proposed controller provides very good performance in the problems of input estimation and output tracking.

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Shipit’ko, Oleg, and Anatoly Kabakov. "Mapping of linear road features with the inverse visual detector observation model." Robotics and Technical Cybernetics 9, no. 3 (2021): 214–24. http://dx.doi.org/10.31776/rtcj.9307.

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The paper proposes an algorithm for mapping linear features detected on the roadway — road marking lines, curbs, road boundaries. The algorithm is based on a mapping method with an inverse observation model. An inverse observation model is proposed to take into account the spatial error of the linear feature visual detector. The influence of various parameters of the model on the resulting quality of mapping was studied. The mapping algorithm was tested on data recorded on an autonomous vehicle while driving at the test site. The quality of the mapping algorithm was assessed according to several quality metrics known from the literature. In addition, the mapping problem was considered as a binary classification problem, in which each map cell may or may not contain the desired feature, and the ROC curve and AUC-ROC metric were used to assess the quality. As a naive solution, a map was built containing all detected linear features without any additional filtering. For the map built on the basis of the raw data, the AUC-ROC was 0.75, and as a result of applying the algorithm, the value of 0.81 was reached. The experimental results have confirmed that the proposed algorithm can effectively filter noise and false-positive detections of the detector, which confirms the applicability of the proposed algorithm and the inverse observation model for solving practical problems. Key words Linear features, mapping, inverse observation model, road map, autonomous vehicle, digital road map.

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Sabaté Landman, Malena, Julianne Chung, Jiahua Jiang, Scot M. Miller, and Arvind K. Saibaba. "A joint reconstruction and model selection approach for large-scale linear inverse modeling (msHyBR v2)." Geoscientific Model Development 17, no. 23 (2024): 8853–72. https://doi.org/10.5194/gmd-17-8853-2024.

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Abstract. Inverse models arise in various environmental applications, ranging from atmospheric modeling to geosciences. Inverse models can often incorporate predictor variables, similar to regression, to help estimate natural processes or parameters of interest from observed data. Although a large set of possible predictor variables may be included in these inverse or regression models, a core challenge is to identify a small number of predictor variables that are most informative of the model, given limited observations. This problem is typically referred to as model selection. A variety of criterion-based approaches are commonly used for model selection, but most follow a two-step process: first, select predictors using some statistical criteria, and second, solve the inverse or regression problem with these predictor variables. The first step typically requires comparing all possible combinations of candidate predictors, which quickly becomes computationally prohibitive, especially for large-scale problems. In this work, we develop a one-step approach for linear inverse modeling, where model selection and the inverse model are performed in tandem. We reformulate the problem so that the selection of a small number of relevant predictor variables is achieved via a sparsity-promoting prior. Then, we describe hybrid iterative projection methods based on flexible Krylov subspace methods for efficient optimization. These approaches are well-suited for large-scale problems with many candidate predictor variables. We evaluate our results against traditional, criteria-based approaches. We also demonstrate the applicability and potential benefits of our approach using examples from atmospheric inverse modeling based on NASA's Orbiting Carbon Observatory-2 (OCO-2) satellite.

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Nie, Boxin, and Xiaojia Ran. "A Linear Discriminant Analysis model based on Sliced Inverse Regression lifting." Highlights in Science, Engineering and Technology 103 (June 26, 2024): 424–32. http://dx.doi.org/10.54097/07bdff79.

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Linear Discriminant Analysis is a dimension-reduction tool for high-dimensional data in the classical field of machine learning. However, for the binary classification problem in the case of high-dimensional prediction, the dimension of the dimension reduction space of the Linear Discriminant Analysis model cannot be greater than the number of categories, that is, it can only be reduced to one dimension, which will greatly lose the effective information of the original prediction variable for the response variable. Based on this, this paper proposes an improved Linear Discriminant Analysis model based on sufficient dimensionality reduction auxiliary slice. On the one hand, by using the Sliced Inverse Regression method, the proposed method can construct auxiliary slice response variables without losing any effective information about the response variables; On the other hand, this method can increase the number of reduced dimensions of the reduced dimension space to any dimension not greater than the number of slices. The analysis results of simulated data and real data show that the proposed method is more accurate and robust than the classical Linear Discriminant Analysis model.

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Goutsias, John I., and Jerry M. Mendel. "Inverse problems in two‐dimensional acoustic media: A linear imaging model." Journal of the Acoustical Society of America 81, no. 5 (1987): 1471–85. http://dx.doi.org/10.1121/1.394500.

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Lou, Jiale, Terence J. O’Kane, and Neil J. Holbrook. "A Linear Inverse Model of Tropical and South Pacific Seasonal Predictability." Journal of Climate 33, no. 11 (2020): 4537–54. http://dx.doi.org/10.1175/jcli-d-19-0548.1.

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AbstractA multivariate linear inverse model (LIM) is developed to demonstrate the mechanisms and seasonal predictability of the dominant modes of variability from the tropical and South Pacific Oceans. We construct a LIM whose covariance matrix is a combination of principal components derived from tropical and extratropical sea surface temperature, and South Pacific Ocean vertically averaged temperature anomalies. Eigen-decomposition of the linear deterministic system yields stationary and/or propagating eigenmodes, of which the least damped modes resemble El Niño–Southern Oscillation (ENSO) and the South Pacific decadal oscillation (SPDO). We show that although the oscillatory periods of ENSO and SPDO are distinct, they have very close damping time scales, indicating that the predictive skill of the surface ENSO and SPDO is comparable. The most damped noise modes occur in the midlatitude South Pacific Ocean, reflecting atmospheric eastward-propagating Rossby wave train variability. We argue that these ocean wave trains occur due to the high-frequency atmospheric variability of the Pacific–South American pattern imprinting onto the surface ocean. The ENSO spring predictability barrier is apparent in LIM predictions initialized in March–May (MAM) but displays a significant correlation skill of up to ~3 months. For the SPDO, the predictability barrier tends to appear in June–September (JAS), indicating remote but delayed influences from the tropics. We demonstrate that subsurface processes in the South Pacific Ocean are the main source of decadal variability and further that by characterizing the upper ocean temperature contribution in the LIM, the seasonal predictability of both ENSO and the SPDO variability is increased.

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Soufflet, Laurent, and Peter H. Boeijinga. "Linear Inverse Solutions: Simulations from a Realistic Head Model in MEG." Brain Topography 18, no. 2 (2005): 87–99. http://dx.doi.org/10.1007/s10548-005-0278-6.

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Filelis-Papadopoulos, Christos K., and George A. Gravvanis. "A class of generic factored and multi-level recursive approximate inverse techniques for solving general sparse systems." Engineering Computations 33, no. 1 (2016): 74–99. http://dx.doi.org/10.1108/ec-12-2014-0261.

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Purpose – The purpose of this paper is to propose novel factored approximate sparse inverse schemes and multi-level methods for the solution of large sparse linear systems. Design/methodology/approach – The main motive for the derivation of the various generic preconditioning schemes lies to the efficiency and effectiveness of factored preconditioning schemes in conjunction with Krylov subspace iterative methods as well as multi-level techniques for solving various model problems. Factored approximate inverses, namely, Generic Factored Approximate Sparse Inverse, require less fill-in and are computed faster due to the reduced number of nonzero elements. A modified column wise approach, namely, Modified Generic Factored Approximate Sparse Inverse, is also proposed to further enhance performance. The multi-level approximate inverse scheme, namely, Multi-level Algebraic Recursive Generic Approximate Inverse Solver, utilizes a multi-level hierarchy formed using Block Independent Set reordering scheme and an approximation of the Schur complement that results in the solution of reduced order linear systems thus enhancing performance and convergence behavior. Moreover, a theoretical estimate for the quality of the multi-level approximate inverse is also provided. Findings – Application of the proposed schemes to various model problems is discussed and numerical results are given concerning the convergence behavior and the convergence factors. The results are comparatively better than results by other researchers for some of the model problems. Research limitations/implications – Further enhancements are investigated for the proposed factored approximate inverse schemes as well as the multi-level techniques to improve quality of the schemes. Furthermore, the proposed schemes rely on the definition of multiple parameters that for some problems require thorough testing, thus adaptive techniques to define the values of the various parameters are currently under research. Moreover, parallel schemes will be investigated. Originality/value – The proposed approximate inverse preconditioning schemes as well as multi-level schemes are efficient computational methods that are valuable for computer scientists and for scientists and engineers in engineering computations.

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VanDecar, John C., and Roel Snieder. "Obtaining smooth solutions to large, linear, inverse problems." GEOPHYSICS 59, no. 5 (1994): 818–29. http://dx.doi.org/10.1190/1.1443640.

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It is not uncommon now for geophysical inverse problems to be parameterized by [Formula: see text] to [Formula: see text] unknowns associated with upwards of [Formula: see text] to [Formula: see text] data constraints. The matrix problem defining the linearization of such a system (e.g., [Formula: see text]m = b) is usually solved with a least‐squares criterion [Formula: see text]. The size of the matrix, however, discourages the direct solution of the system and researchers often turn to iterative techniques such as the method of conjugate gradients to obtain an estimate of the least‐squares solution. These iterative methods take advantage of the sparseness of [Formula: see text], which often has as few as 2–3 percent of its elements nonzero, and do not require the calculation (or storage) of the matrix [Formula: see text]. Although there are usually many more data constraints than unknowns, these problems are, in general, underdetermined and therefore require some sort of regularization to obtain a solution. When the regularization is simple damping, the conjugate gradients method tends to converge in relatively few iterations. However, when derivative‐type regularization is applied (first derivative constraints to obtain the flattest model that fits the data; second derivative to obtain the smoothest), the convergence of parts of the solution may be drastically inhibited. In a series of 1-D examples and a synthetic 2-D crosshole tomography example, we demonstrate this problem and also suggest a method of accelerating the convergence through the preconditioning of the conjugate gradient search directions. We derive a 1-D preconditioning operator for the case of first derivative regularization using a WKBJ approximation. We have found that preconditioning can reduce the number of iterations necessary to obtain satisfactory convergence by up to an order of magnitude. The conclusions we present are also relevant to Bayesian inversion, where a smoothness constraint is imposed through an a priori covariance of the model.

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Li, Youbing, Zhenning Zhu, and Zhixian Zhong. "Decoupling control of electromagnetic bearing rigid rotor system based on IGWO and linear active disturbance rejection inverse system." Journal of Physics: Conference Series 3024, no. 1 (2025): 012029. https://doi.org/10.1088/1742-6596/3024/1/012029.

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Abstract This study proposes a decoupling control strategy integrating an improved grey wolf optimization algorithm (IGWO) and a linear active disturbance rejection inverse system for rigid rotor system control in electromagnetic bearings. Initially, a mathematical model of the radial four-degree-of-freedom electromagnetic bearing rotor system is developed, and the system is decoupled into four pseudo-linear subsystems via the inverse system method. To address the model dependency of the inverse system, a linear active disturbance rejection controller (LADRC) is designed to regulate the decoupled subsystems. Furthermore, the IGWO algorithm is implemented to rapidly optimize LADRC parameters, enhancing the controller’s dynamic response. Comparative simulations and experiments against decentralized PID control demonstrate the proposed method’s superior performance in decoupling accuracy, settling time, and disturbance rejection.

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Weglein, Arthur B., Haiyan Zhang, Adriana C. Ramírez, Fang Liu, and Jose Eduardo Lira. "Clarifying the underlying and fundamental meaning of the approximate linear inversion of seismic data." GEOPHYSICS 74, no. 6 (2009): WCD1—WCD13. http://dx.doi.org/10.1190/1.3256286.

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Linear inversion is defined as the linear approximation of a direct-inverse solution. This definition leads to data requirements and specific direct-inverse algorithms, which differ with all current linear and nonlinear approaches, and is immediately relevant for target identification and inversion in an elastic earth. Common practice typically starts with a direct forward or modeling expression and seeks to solve a forward equation in an inverse sense. Attempting to solve a direct forward problem in an inverse sense is not the same as solving an inverse problem directly. Distinctions include differences in algorithms, in the need for a priori information, and in data requirements. The simplest and most accessible examples are the direct-inversion tasks, derived from the inverse scattering series (ISS), for the removal of free-surface and internal multiples. The ISS multiple-removal algorithms require no subsurface information, and they are independent of earth model type. A direct forward method solved in an inverse sense, for modeling and subtracting multiples, would require accurate knowledge of every detail of the subsurface the multiple has experienced. In addition, it requires a different modeling and subtraction algorithm for each different earth-model type. The ISS methods for direct removal of multiples are not a forward problem solved in an inverse sense. Similarly, the direct elastic inversion provided by the ISS is not a modeling formula for PP data solved in an inverse sense. Direct elastic inversion calls for [Formula: see text], [Formula: see text], [Formula: see text], … data, for direct linear and nonlinear estimates of changes in mechanical properties. In practice, a judicious combination of direct and indirect methods are called upon for effective field data application.

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Ji, Liya, Zhefan Rao, Sinno Jialin Pan, Chenyang Lei, and Qifeng Chen. "A Diffusion Model with State Estimation for Degradation-Blind Inverse Imaging." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 3 (2024): 2471–79. http://dx.doi.org/10.1609/aaai.v38i3.28023.

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Solving the task of inverse imaging problems can restore unknown clean images from input measurements that have incomplete information. Utilizing powerful generative models, such as denoising diffusion models, could better tackle the ill-posed issues of inverse problems with the distribution prior of the unknown clean images. We propose a learnable state-estimator-based diffusion model to incorporate the measurements into the reconstruction process. Our method makes efficient use of the pre-trained diffusion models with computational feasibility compared to the conditional diffusion models, which need to be trained from scratch. In addition, our pipeline does not require explicit knowledge of the image degradation operator or make the assumption of its form, unlike many other works that use the pre-trained diffusion models at the test time. The experiments on three typical inverse imaging problems (both linear and non-linear), inpainting, deblurring, and JPEG compression restoration, have comparable results with the state-of-the-art methods.

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Gao, Xudong, and Sheng Zhang. "Inverse scattering transform for a new non-isospectral integrable non-linear AKNS model." Thermal Science 21, suppl. 1 (2017): 153–60. http://dx.doi.org/10.2298/tsci17s1153g.

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Constructing integrable systems and solving non-linear partial differential equations are important and interesting in non-linear science. In this paper, Ablowitz-Kaup-Newell-Segur (AKNS)?s linear isospectral problem and its accompanied time evolution equation are first generalized by embedding a new non-isospectral parameter whose varying with time obeys an arbitrary smooth enough function of the spectral parameter. Based on the generalized AKNS linear problem and its evolution equation, a new non-isospectral Lax integrable non-linear AKNS model is then derived. Furthermore, exact solutions of the derived AKNS model is obtained by extending the inverse scattering transformation method with new time-varying spectral parameter. In the case of reflectinless potentials, explicit n-soliton solutions are finally formulated through the obtained exact solutions.

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Lounici, Yacine, Youcef Touati, Smail Adjerid, Djamel Benazzouz, and Billal Nazim Chebouba. "A novel fault-tolerant control strategy based on inverse bicausal bond graph model in linear fractional transformation." Advances in Mechanical Engineering 13, no. 11 (2021): 168781402110598. http://dx.doi.org/10.1177/16878140211059878.

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This article presents the development of a novel fault-tolerant control strategy. For this task, a bicausal bond graph model-based scheme is designed to generate online information to the inverse controller about the faults estimation. Secondly, a new approach is proposed for the fault-tolerant control based on the inverse bicausal bond graph in linear fractional transformation form. However, because of the time delay for fault estimation, the PI controller is used to reduce the error before the fault is estimated. Hence, the required input that compensates the fault is the sum of the control signal delivered by the PI controller and the control signal resulting from the inverse bicausal bond graph for fast fault compensation and for maintaining the control objectives. The novelties of the proposed approach are: (1) to exploit the power concept of the bond graph by feeding the power generated by the fault in the inverse model (2) to suitably combining the inverse bicausal bond graph with the PI feedback controller so that the proposed strategy can compensate for the fault with a very short time delay and stabilize the desired output. Finally, the experimental results illustrate the efficiency of the proposed strategy.

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Lobo, Daniel, Mauricio Solano, George A. Bubenik, and Michael Levin. "A linear-encoding model explains the variability of the target morphology in regeneration." Journal of The Royal Society Interface 11, no. 92 (2014): 20130918. http://dx.doi.org/10.1098/rsif.2013.0918.

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A fundamental assumption of today's molecular genetics paradigm is that complex morphology emerges from the combined activity of low-level processes involving proteins and nucleic acids. An inherent characteristic of such nonlinear encodings is the difficulty of creating the genetic and epigenetic information that will produce a given self-assembling complex morphology. This ‘inverse problem’ is vital not only for understanding the evolution, development and regeneration of bodyplans, but also for synthetic biology efforts that seek to engineer biological shapes. Importantly, the regenerative mechanisms in deer antlers, planarian worms and fiddler crabs can solve an inverse problem: their target morphology can be altered specifically and stably by injuries in particular locations. Here, we discuss the class of models that use pre-specified morphological goal states and propose the existence of a linear encoding of the target morphology, making the inverse problem easy for these organisms to solve. Indeed, many model organisms such as Drosophila , hydra and Xenopus also develop according to nonlinear encodings producing linear encodings of their final morphologies. We propose the development of testable models of regeneration regulation that combine emergence with a top-down specification of shape by linear encodings of target morphology, driving transformative applications in biomedicine and synthetic bioengineering.

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Ungureanu, Liviu Marian, Adriana Comanescu, and Dinu Comanescu. "Some Characteristics of the 3($P$) Parallel Manipulator Inverse Model." Applied Mechanics and Materials 555 (June 2014): 306–11. http://dx.doi.org/10.4028/www.scientific.net/amm.555.306.

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A 3($P$) parallel manipulator with three degrees of mobility may be used in different purposes, such as a spatial flight simulator. The same equations but with different unknowns characterize its direct and inverse positional model. By adopting the Euler angles for the mobile platform the inverse positional model is simplified. There are determined the parameters of the linear actuators, which are verified for different situations by graphical simulation in a suitable environment.

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Damayanti CR, Mey, and Teti Sofia Yanti. "Regresi Poisson Invers Gaussian (PIG) untuk Pemodelan Jumlah Kasus Pneumonia pada Balita di Provinsi Jawa Tengah Tahun 2019." Jurnal Riset Statistika 1, no. 2 (2022): 143–51. http://dx.doi.org/10.29313/jrs.v1i2.523.

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Abstract. Poisson regression is a non-linear regression model used on non-negative count or discrete data. Poisson regression is included in the Generalized Linear Model (GLM). In Poisson regression there is an assumption that must be met, that is equidispersion where the value of the variance in the response variable (Y) must be the same as the average value. If in Poisson regression modeling there is an overdispersion or underdispersion and it is ignored, the test will be less accurate because the standard error value will be underestimated. Poisson Inverse Gaussian Regression Model (PIG) can overcome overdispersion data. The Poisson Inverse Gaussian (PIG) distribution is a mixed Poisson distribution. PIG regression is used to model the count data which has a high slope and skews to the right. Maximum likelihood method was used to estimate the parameters in the PIG regression model. Pneumonia is an acute infection that causes inflammation of the lung tissue. The case of pneumonia in children under five is one form of discrete data. The results of the PIG regression model were compared based on the Akaike Information Criterion (AIC) to obtain the best model. From the results of hypothesis testing, it was concluded that the percentage of children under five who had received measles immunization and the percentage of children under five who had received DPT immunization had a significant effect on the of pneumonia cases in children under five. By using the AIC value, the Poisson Inverse Gaussian (PIG) regression model is obtained, that is: . Abstrak. Regresi poisson merupakan model regresi non-linear yang digunakan pada data cacah atau diskrit non-negatif. Regresi Poisson termasuk kedalam Generalized Linear Model (GLM). Pada regresi Poisson terdapat asumsi yang harus dipenuhi yaitu equidispersi dimana nilai variansi pada variabel respon (Y) harus sama dengan nilai rata-ratanya. Apabila dalam pemodelan regresi Poisson terjadi kasus overdispersi atau underdispersi dan hal tersebut diabaikan maka pengujian akan menjadi kurang akurat karena nilai standard error akan menjadi underestimate. Model Regresi Poisson Invers Gaussian (PIG) dapat mengatasi data overdispersi. Distribusi Poisson Invers Gaussian (PIG) merupakan mixed poisson distribution. Regresi PIG digunakan untuk memodelkan data cacah yang memiliki kemiringan yang tinggi dan menceng ke kanan. Metode maximum likelihood digunakan untuk menaksir parameter pada model regresi PIG.. Pneumonia merupakan infeksi akut yang menyebabkan peradangan pada jaringan paru-paru. Kasus pneumonia pada balita merupakan salah satu bentuk dari data diskrit. Hasil model regresi PIG dibandingkan berdasarkan Akaike Information Criterion (AIC) untuk memperoleh model terbaik. Dari hasil pengujian hipotesis diperoleh kesimpulan bahwa persentase balita yang pernah mendapatkan imunisasi campak dan persentase balita yang pernah mendapatkan imunisasi DPT berpengaruh signifikan terhadap jumlah kasus pneumonia pada balita. Dengan memperhatikan nilai AIC didapatkan model regresi Poisson Invers Gaussian (PIG) yaitu: .

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Zhang, Yi, and Gongsheng Li. "A Simplified Fractional Seir Epidemic Model and Unique Inversion of the Fractional Order." WSEAS TRANSACTIONS ON MATHEMATICS 21 (March 23, 2022): 113–18. http://dx.doi.org/10.37394/23206.2022.21.17.

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A simplified linear time-fractional SEIR epidemic system is set forth, and an inverse problem of determining the fractional order is discussed by using the measurement at one given time. By the Laplace transform the solution to the forward problem is obtained, by which the inverse problem is transformed to a nonlinear algebraic equation. By choosing suitable model parameters and the measured time, the nonlinear equation has a unique solution by the monotonicity of the Mittag-Lellfer function. Theoretical testification is presented to demonstrate the unique solvability of the inverse problem.

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Shi, Jianfei, Mingze Li, Baihong Tong, and Zhenlin Guo. "A New Control Strategy for Greenhouse Environment Control System Based on Inverse Model." International Journal of Heat and Technology 40, no. 5 (2022): 1271–76. http://dx.doi.org/10.18280/ijht.400520.

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The greenhouse environment control system is a type of non-linear system since the temperature and humidity of the system are highly coupled. Besides, the time lag of the temperature and humidity control process is large, so it’s quite difficult to linearize and decouple the temperature and humidity of the system. To cope with this issue, this paper proposed a novel control strategy for greenhouse environment control system based on Back Propagation Neural Network (BPNN) and inverse model, the proposed method can perform inverse identification on the temperature and humidity control system to attain higher accuracy. Then, the inverse model and the original system were connected in series to form a pseudo linear system to realize the decoupled control of temperature and humidity. After that, aiming at the impact of some non-linear factors on the greenhouse environment system, this paper adopted the adaptive fuzzy Proportion Integration Differentiation (PID) controller to enhance the adaptability of the system, thereby reducing control error and the interference caused by non-linear factors of the temperature and humidity control system. At last, the experimental results showed that, the temperature error of the system could be controlled within 1.2℃ and the error of relative humidity was less than 2.5%. The proposed method can improve the control effect of the greenhouse environment to a certain extent, and it provides a novel approach of greenhouse control.

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Sahinkaya, M. N. "Virtual non-linear disturbance observer by dual inverse dynamic modelling." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 221, no. 6 (2007): 677–88. http://dx.doi.org/10.1243/0954406jmes581.

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A method to predict unknown external disturbances and modelling errors for trajectory tracking of non-linear systems is presented. The technique involves dual inverse non-linear dynamics modelling based on Lagrangian dynamics and the use of redundant coordinates incorporating Lagrange multipliers. The first inverse dynamics model is a conventional formulation where the desired trajectory is used to calculate the required control inputs. The second inverse dynamics model treats the measured response as the desired motion, and calculates the inputs that would be required to achieve the measured motion. The method is applicable to cases where the acceleration signal is available. It can be used either to measure actual disturbances or to estimate virtual disturbances, which effectively represent all the disturbances and modelling errors on the control input coordinates. It is also suitable to be used in conjunction with or in addition to existing controllers. A numerical simulation of a two-link manipulator is used to demonstrate the effectiveness of the controller under various external disturbances, modelling errors, and unmodelled substructures.

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Perkins, Walter A., and Gregory J. Hakim. "Reconstructing paleoclimate fields using online data assimilation with a linear inverse model." Climate of the Past 13, no. 5 (2017): 421–36. http://dx.doi.org/10.5194/cp-13-421-2017.

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Abstract. We examine the skill of a new approach to climate field reconstructions (CFRs) using an online paleoclimate data assimilation (PDA) method. Several recent studies have foregone climate model forecasts during assimilation due to the computational expense of running coupled global climate models (CGCMs) and the relatively low skill of these forecasts on longer timescales. Here we greatly diminish the computational cost by employing an empirical forecast model (linear inverse model, LIM), which has been shown to have skill comparable to CGCMs for forecasting annual-to-decadal surface temperature anomalies. We reconstruct annual-average 2 m air temperature over the instrumental period (1850–2000) using proxy records from the PAGES 2k Consortium Phase 1 database; proxy models for estimating proxy observations are calibrated on GISTEMP surface temperature analyses. We compare results for LIMs calibrated using observational (Berkeley Earth), reanalysis (20th Century Reanalysis), and CMIP5 climate model (CCSM4 and MPI) data relative to a control offline reconstruction method. Generally, we find that the usage of LIM forecasts for online PDA increases reconstruction agreement with the instrumental record for both spatial fields and global mean temperature (GMT). Specifically, the coefficient of efficiency (CE) skill metric for detrended GMT increases by an average of 57 % over the offline benchmark. LIM experiments display a common pattern of skill improvement in the spatial fields over Northern Hemisphere land areas and in the high-latitude North Atlantic–Barents Sea corridor. Experiments for non-CGCM-calibrated LIMs reveal region-specific reductions in spatial skill compared to the offline control, likely due to aspects of the LIM calibration process. Overall, the CGCM-calibrated LIMs have the best performance when considering both spatial fields and GMT. A comparison with the persistence forecast experiment suggests that improvements are associated with the linear dynamical constraints of the forecast and not simply persistence of temperature anomalies.

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Clarke, Shanelle G., Sooyung Byeon, and Inseok Hwang. "A Low Complexity Approach to Model-Free Stochastic Inverse Linear Quadratic Control." IEEE Access 10 (2022): 9298–308. http://dx.doi.org/10.1109/access.2022.3144933.

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Gennarelli, Gianluca, Giovanni Ludeno, Noviello Carlo, Ilaria Catapano, and Francesco Soldovieri. "The Role of Model Dimensionality in Linear Inverse Scattering from Dielectric Objects." Remote Sensing 14, no. 1 (2022): 222. http://dx.doi.org/10.3390/rs14010222.

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This paper deals with 3D and 2D linear inverse scattering approaches based on the Born approximation, and investigates how the model dimensionality influences the imaging performance. The analysis involves dielectric objects hosted in a homogenous and isotropic medium and a multimonostatic/multifrequency measurement configuration. A theoretical study of the spatial resolution is carried out by exploiting the singular value decomposition of 3D and 2D scattering operators. Reconstruction results obtained from synthetic data generated by using a 3D full-wave electromagnetic simulator are reported to support the conclusions drawn from the analysis of resolution limits. The presented analysis corroborates that 3D and 2D inversion approaches have almost identical imaging performance, unless data are severely corrupted by the noise.

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Carcreff, Ewen, Sebastien Bourguignon, Jerome Idier, and Laurent Simon. "A linear model approach for ultrasonic inverse problems with attenuation and dispersion." IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 61, no. 7 (2014): 1191–203. http://dx.doi.org/10.1109/tuffc.2014.3018.

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Cavaterra, Cecilia, and Maurizio Grasselli. "On an Inverse Problem for a Model of Linear Viscoelastic Kirchhoff Plate." Journal of Integral Equations and Applications 9, no. 3 (1997): 179–218. http://dx.doi.org/10.1216/jiea/1181076012.

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Ahani, Alireza, and Mohammad Javad Ketabdari. "Alternative approach for dynamic-positioning thrust allocation using linear pseudo-inverse model." Applied Ocean Research 90 (September 2019): 101854. http://dx.doi.org/10.1016/j.apor.2019.101854.

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