We consider convection-diffusion-reaction equations with parametrized random and deterministic inputs. For fixed values of the deterministic parameters, the problem reduces to a linear elliptic PDE with random input data and statistical moments of its solution such as mean and variance can be approximated by a stochastic Galerkin finite element (SGFE) method. There are scenarios, like robust optimization or real-time evaluation, where these statistical information must be computable for numerous different values of the deterministic parameter in a short period of time. In these particular cases, it can be computationally beneficial to conduct a certain number of expensive preliminary computations in order to set up a reduced order model (ROM). The reduction of the overall computational costs than results from the fact that this ROM is low dimensional and can thus be evaluated cheaply for each point in the domain of the deterministic parameters. We construct a ROM for our problem using a proper orthogonal decomposition (POD) of SGFE snapshots [1]. As a consequence, there is no need for an additional sampling procedure in order to evaluate the statistics of the solution of the reduced order model. Computing the snapshots for the ROM means that several different SGFE problems have to be solved, each associated with a large block-structured system of equations. Since the computational costs of solving these systems are high, we use adaptive discretization techniques to find favorable discrete spaces and lower the computational burden of the preliminary computations. Using adaptive approaches leads, however, to a setting where the snapshots belong to different SGFE subspaces. This fact interferes the standard POD procedure. It is still possible to construct a reduced order model based on adaptive snapshots [2] but there are different
{"title":"A POD-Galerkin Model for Convection-Diffusion-Reaction Equations with Parametric Data based on Adaptive Snapshots","authors":"Christopher M¨uller, J. Lang","doi":"10.23967/admos.2023.006","DOIUrl":"https://doi.org/10.23967/admos.2023.006","url":null,"abstract":"We consider convection-diffusion-reaction equations with parametrized random and deterministic inputs. For fixed values of the deterministic parameters, the problem reduces to a linear elliptic PDE with random input data and statistical moments of its solution such as mean and variance can be approximated by a stochastic Galerkin finite element (SGFE) method. There are scenarios, like robust optimization or real-time evaluation, where these statistical information must be computable for numerous different values of the deterministic parameter in a short period of time. In these particular cases, it can be computationally beneficial to conduct a certain number of expensive preliminary computations in order to set up a reduced order model (ROM). The reduction of the overall computational costs than results from the fact that this ROM is low dimensional and can thus be evaluated cheaply for each point in the domain of the deterministic parameters. We construct a ROM for our problem using a proper orthogonal decomposition (POD) of SGFE snapshots [1]. As a consequence, there is no need for an additional sampling procedure in order to evaluate the statistics of the solution of the reduced order model. Computing the snapshots for the ROM means that several different SGFE problems have to be solved, each associated with a large block-structured system of equations. Since the computational costs of solving these systems are high, we use adaptive discretization techniques to find favorable discrete spaces and lower the computational burden of the preliminary computations. Using adaptive approaches leads, however, to a setting where the snapshots belong to different SGFE subspaces. This fact interferes the standard POD procedure. It is still possible to construct a reduced order model based on adaptive snapshots [2] but there are different","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126732665","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mesh deformation is a key point in fluid structure interaction problems. The efficiency of such simulations relies on the efficiency of the mesh deformation algorithms used for as long periods of time as possible without degenerating the mesh. Many solutions are well described in the literature, from those based on the solutions of elliptic PDEs to those based on both explicit and implicit interpolations [3]. The approach considered here is based on the solution of an algebraic linear system raised from Radial Basis Function (RBF) interpolation. At an extreme scale, the resolution of such linear systems is very expensive [1]. The present work aims to speed-up the solving of such systems by using randomized linear algebra [2]. Over the past decade, a new paradigm has emerged introducing randomization to speed-up linear algebra operations [2]. The efficiency of such an approach can reach linear complexity O(N) regarding the problem size and this has been confirmed on several dense linear systems from integral equations, statistics, and machine learning. This talk investigates the extension of this approach to complex systems resulting from Fluid-Structure interaction problems that are sparse and ill-conditioned [3]. The focus will be on how to speed-up the algebraic solvers used to deform the mesh in FSI simulations. 2D and 3D applications will be presented to assess the new paradigm.
{"title":"Efficient unstructured mesh deformation using randomized linear algebra in Fluid Structure Interaction","authors":"Y. Mesri","doi":"10.23967/admos.2023.067","DOIUrl":"https://doi.org/10.23967/admos.2023.067","url":null,"abstract":"Mesh deformation is a key point in fluid structure interaction problems. The efficiency of such simulations relies on the efficiency of the mesh deformation algorithms used for as long periods of time as possible without degenerating the mesh. Many solutions are well described in the literature, from those based on the solutions of elliptic PDEs to those based on both explicit and implicit interpolations [3]. The approach considered here is based on the solution of an algebraic linear system raised from Radial Basis Function (RBF) interpolation. At an extreme scale, the resolution of such linear systems is very expensive [1]. The present work aims to speed-up the solving of such systems by using randomized linear algebra [2]. Over the past decade, a new paradigm has emerged introducing randomization to speed-up linear algebra operations [2]. The efficiency of such an approach can reach linear complexity O(N) regarding the problem size and this has been confirmed on several dense linear systems from integral equations, statistics, and machine learning. This talk investigates the extension of this approach to complex systems resulting from Fluid-Structure interaction problems that are sparse and ill-conditioned [3]. The focus will be on how to speed-up the algebraic solvers used to deform the mesh in FSI simulations. 2D and 3D applications will be presented to assess the new paradigm.","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115754292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The boundary element method (BEM) is known to be efficient for elastic wave propagation when unbounded domains are involved, like in the diffraction of waves on elastic inclusions. At the interface between the inclusion and the outer domain, stress concentration occurs, which can lead to material damage in the case of the forward. The stress concentration factor is not a direct output of the BEM but is obtained with a special output treatment of the tangential surface derivatives of the displacements so that the error estimation on this quantity is not straightforward. To provide a stable computation of this quantity, we propose a symmetric, regularized variational formulation of the integral boundary equations. Then, an adjoint BEM formulation is used for the goal-oriented error estimation. It is strongly connected with the equivalent of a seismic moment of the residual error at the interface. Several numerical examples will be provided for the diffraction of plane waves against a cavity and an elastic inclusion to show the efficiency of the proposed approach.
{"title":"Goal oriented error adaptivity for dynamic stress concentration With a Symmetric Boundary Element Galerkin Method","authors":"S. Touhami, D. Aubry","doi":"10.23967/admos.2023.032","DOIUrl":"https://doi.org/10.23967/admos.2023.032","url":null,"abstract":"The boundary element method (BEM) is known to be efficient for elastic wave propagation when unbounded domains are involved, like in the diffraction of waves on elastic inclusions. At the interface between the inclusion and the outer domain, stress concentration occurs, which can lead to material damage in the case of the forward. The stress concentration factor is not a direct output of the BEM but is obtained with a special output treatment of the tangential surface derivatives of the displacements so that the error estimation on this quantity is not straightforward. To provide a stable computation of this quantity, we propose a symmetric, regularized variational formulation of the integral boundary equations. Then, an adjoint BEM formulation is used for the goal-oriented error estimation. It is strongly connected with the equivalent of a seismic moment of the residual error at the interface. Several numerical examples will be provided for the diffraction of plane waves against a cavity and an elastic inclusion to show the efficiency of the proposed approach.","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130282328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Tailings dam management systems require technologies to both alert on potential emergency scenarios and respond to the threats that can result in serious safety incidents with unwanted consequences. This usually requires the effective integration of physical and digital technologies that mining operators can adopt in a robust but also user-friendly way. In fact, the orchestration of heterogeneous tools, such as predictive algorithms, visualization software and a risk management platform, is crucial to provide meaningful information to the decision-making stakeholders. In this context, the effective capture and consolidation of data become a cornerstone to ensure that tailings dam management systems will lead to meaningful outputs. Historically, this required the use of complex data collection campaigns, and because of this, data availability was limited to gain a holistic view of such complex infrastructures. Here, we propose the adoption of IoT technologies to overcome this problem. The deployment of end-to-end data acquisition and monitoring systems which combine wireless IoT nodes with multiple sensors together with data processing tools has demonstrated that they can make mining operations safer while reducing OPEX costs by reducing the need for manual inspections or unnecessary travel. Here, some examples of how commercial IoT technologies are contributing to increase safety in tailings dams will be presented and discussed. This also actively contributes to more environmental-friendly management of the infrastructures.
{"title":"The use of IoT technologies for advanced risk management in tailings dams","authors":"A. Bartoli, F. Hernandez-Ramírez","doi":"10.23967/admos.2023.075","DOIUrl":"https://doi.org/10.23967/admos.2023.075","url":null,"abstract":"Tailings dam management systems require technologies to both alert on potential emergency scenarios and respond to the threats that can result in serious safety incidents with unwanted consequences. This usually requires the effective integration of physical and digital technologies that mining operators can adopt in a robust but also user-friendly way. In fact, the orchestration of heterogeneous tools, such as predictive algorithms, visualization software and a risk management platform, is crucial to provide meaningful information to the decision-making stakeholders. In this context, the effective capture and consolidation of data become a cornerstone to ensure that tailings dam management systems will lead to meaningful outputs. Historically, this required the use of complex data collection campaigns, and because of this, data availability was limited to gain a holistic view of such complex infrastructures. Here, we propose the adoption of IoT technologies to overcome this problem. The deployment of end-to-end data acquisition and monitoring systems which combine wireless IoT nodes with multiple sensors together with data processing tools has demonstrated that they can make mining operations safer while reducing OPEX costs by reducing the need for manual inspections or unnecessary travel. Here, some examples of how commercial IoT technologies are contributing to increase safety in tailings dams will be presented and discussed. This also actively contributes to more environmental-friendly management of the infrastructures.","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114870101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
S. Li, E. Johnson, Joseph G. Wallwork, S. Kramer, M. Piggott
Numerical simulations play a central role in understanding the impact and risks of pressing global engineering problems, such as the scale-up challenges of energy generation from complex, non-linear renewable sources including wind and tidal. Effectively discretizing over multiple spatial scales, as inherent in such geophysical fluid dynamics problems, can come at a high computational cost when targeting a reasonable level of accuracy for meaningful results. Mesh adaptation can improve the accuracy of numerical simulations by modifying the discretized structure. Guiding the mesh adaptation process with a goal-based approach can focus the discrete resolution distribution where it most directly contributes to improving the accuracy of the renewable energy problem being addressed. In addition to mesh adaptation, identifying opportunities to augment the numerical methods with machine learning workflows has potential to further reduce computational overhead by automating the process and incorporating prior knowledge. We review work extending Wallwork et al 2022 1 by substituting simple surrogate CNN and GNN machine learning methods for the costly dual-weighted residual error estimation step in a goal-based mesh adaptation workflow applied to numerical simulations motivated by tidal energy applications. The steady-state tidal turbine array test case and promising results as outlined in Wallwork et al 2022 1 serve as a foundation for investigating faster data-driven methods to replace the highly accurate dual-weighted error estimation step. We directly use the renewable energy scale-up goal of maximizing tidal turbine array power generation as the error estimation functional driving the mesh adaptation process. We explore surrogate architectures which incorporate additional patch-based or nearest neighbour information and have a reasonable chance of generalization. The discussion is focused on trade-offs between accuracy preservation and efficiency gain for the machine learning based surrogate methods.
{"title":"Machine Learning Assisted Mesh Adaptation for Geophysical Fluid Dynamics","authors":"S. Li, E. Johnson, Joseph G. Wallwork, S. Kramer, M. Piggott","doi":"10.23967/admos.2023.051","DOIUrl":"https://doi.org/10.23967/admos.2023.051","url":null,"abstract":"Numerical simulations play a central role in understanding the impact and risks of pressing global engineering problems, such as the scale-up challenges of energy generation from complex, non-linear renewable sources including wind and tidal. Effectively discretizing over multiple spatial scales, as inherent in such geophysical fluid dynamics problems, can come at a high computational cost when targeting a reasonable level of accuracy for meaningful results. Mesh adaptation can improve the accuracy of numerical simulations by modifying the discretized structure. Guiding the mesh adaptation process with a goal-based approach can focus the discrete resolution distribution where it most directly contributes to improving the accuracy of the renewable energy problem being addressed. In addition to mesh adaptation, identifying opportunities to augment the numerical methods with machine learning workflows has potential to further reduce computational overhead by automating the process and incorporating prior knowledge. We review work extending Wallwork et al 2022 1 by substituting simple surrogate CNN and GNN machine learning methods for the costly dual-weighted residual error estimation step in a goal-based mesh adaptation workflow applied to numerical simulations motivated by tidal energy applications. The steady-state tidal turbine array test case and promising results as outlined in Wallwork et al 2022 1 serve as a foundation for investigating faster data-driven methods to replace the highly accurate dual-weighted error estimation step. We directly use the renewable energy scale-up goal of maximizing tidal turbine array power generation as the error estimation functional driving the mesh adaptation process. We explore surrogate architectures which incorporate additional patch-based or nearest neighbour information and have a reasonable chance of generalization. The discussion is focused on trade-offs between accuracy preservation and efficiency gain for the machine learning based surrogate methods.","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114954414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
V. Zambrano, I. Viejo, J. M. Rodríguez, Guillermo, López, Jesús Alfonso, Daniel Cáceres, Maŕıa López-Blanco, Prasad, Talasila, Mario Sánchez, Susana Calvo
{"title":"Interpretable and Reusable Reduced Order Models for Digital Twins in Manufactory as a Service","authors":"V. Zambrano, I. Viejo, J. M. Rodríguez, Guillermo, López, Jesús Alfonso, Daniel Cáceres, Maŕıa López-Blanco, Prasad, Talasila, Mario Sánchez, Susana Calvo","doi":"10.23967/admos.2023.070","DOIUrl":"https://doi.org/10.23967/admos.2023.070","url":null,"abstract":"","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"114 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124072398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This contribution concerns the multi-scale and multi-physics Finite Element Analysis of the electro-chemically coupled ion transport [1] . In particular, we are interested in predicting the electro-chemical performance of the Structural Battery Electrolyte (SBE) by utilizing computational homogenization and numerical model reduction [2] (NMR). A sub-scale Representative Volume Element (RVE) is generated for the two-scale modeling approach. It represents the random bicontinuous microstructure of an SBE (porous polymer skeleton filled with liquid electrolyte). The governing equations consist of Gauss’ law, mass balance of the pertinent ions and linear constitutive relations. Periodic boundary conditions are imposed on the RVE according to first order homogenization on the electrical and the chemical potential fields. The fully coupled electro-chemical problem is solved to obtain the macroscopic (homogenized) transient response. By solving the RVE problem for various loading cases, we obtain training data that are used for NMR based on a snapshot Proper Orthogonal Decomposition (POD). The end product of the NMR-POD framework is a surrogate model which replaces RVE computations. Since the surrogate model consists of a system of ODEs, it requires less computational effort to solve compared to the full RVE problem. The final goal is to investigate how the choice of training data and POD modes affect the simulation accuracy, and also quantify the speed-up by exploiting the surrogate model.
{"title":"Numerical model reduction of the electro-chemically coupled ion transport","authors":"V. Tu, K. Runesson, F. Larsson, Ralf J¨anicke","doi":"10.23967/admos.2023.008","DOIUrl":"https://doi.org/10.23967/admos.2023.008","url":null,"abstract":"This contribution concerns the multi-scale and multi-physics Finite Element Analysis of the electro-chemically coupled ion transport [1] . In particular, we are interested in predicting the electro-chemical performance of the Structural Battery Electrolyte (SBE) by utilizing computational homogenization and numerical model reduction [2] (NMR). A sub-scale Representative Volume Element (RVE) is generated for the two-scale modeling approach. It represents the random bicontinuous microstructure of an SBE (porous polymer skeleton filled with liquid electrolyte). The governing equations consist of Gauss’ law, mass balance of the pertinent ions and linear constitutive relations. Periodic boundary conditions are imposed on the RVE according to first order homogenization on the electrical and the chemical potential fields. The fully coupled electro-chemical problem is solved to obtain the macroscopic (homogenized) transient response. By solving the RVE problem for various loading cases, we obtain training data that are used for NMR based on a snapshot Proper Orthogonal Decomposition (POD). The end product of the NMR-POD framework is a surrogate model which replaces RVE computations. Since the surrogate model consists of a system of ODEs, it requires less computational effort to solve compared to the full RVE problem. The final goal is to investigate how the choice of training data and POD modes affect the simulation accuracy, and also quantify the speed-up by exploiting the surrogate model.","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129368431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Comparing FE2 procedures with seamless scale-bridging using a primal and dual formulation","authors":"K. Carlsson, F. Larsson, K. Runesson","doi":"10.23967/admos.2023.055","DOIUrl":"https://doi.org/10.23967/admos.2023.055","url":null,"abstract":"","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"1560 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129135469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Summary. Reduced-order (single-degree-of-freedom) models of buildings subjected to wind loads were analyzed to determine the effect of gravity loads on inelastic behavior. The lateral wind loads were based on data from atmospheric boundary layer wind tunnel tests to capture the temporal and spatial variation of wind pressure on a building envelope. The lateral load resisting system of the building was idealized using a bilinear relationship, and gravity load effects were introduced using a stability coefficient. Nonlinear response history analyses were solved using direct implicit integration of the equation of motion, and an energy balance was used to assess the quality of the numerical solution. The resulting response histories were used to interrogate the relationship between inelastic displacement, ductility, period of vibration, and gravity loads. The results indicate that inelastic displacements were approximately equal to the elastic displacements even in the presence of gravity loads for cross wind excitation. For along wind excitation, the inelastic displacements were approximately equal to the elastic displacements regardless of gravity loads. The findings suggest that the equal displacement concept may have application to the wind design of high-rise buildings where cross-wind loads control the design of the lateral system.
{"title":"Gravity Load Effects on Inelastic Simulation of Buildings Subjected to Wind Loads","authors":"J. Judd, J. Niedens","doi":"10.23967/admos.2023.072","DOIUrl":"https://doi.org/10.23967/admos.2023.072","url":null,"abstract":"Summary. Reduced-order (single-degree-of-freedom) models of buildings subjected to wind loads were analyzed to determine the effect of gravity loads on inelastic behavior. The lateral wind loads were based on data from atmospheric boundary layer wind tunnel tests to capture the temporal and spatial variation of wind pressure on a building envelope. The lateral load resisting system of the building was idealized using a bilinear relationship, and gravity load effects were introduced using a stability coefficient. Nonlinear response history analyses were solved using direct implicit integration of the equation of motion, and an energy balance was used to assess the quality of the numerical solution. The resulting response histories were used to interrogate the relationship between inelastic displacement, ductility, period of vibration, and gravity loads. The results indicate that inelastic displacements were approximately equal to the elastic displacements even in the presence of gravity loads for cross wind excitation. For along wind excitation, the inelastic displacements were approximately equal to the elastic displacements regardless of gravity loads. The findings suggest that the equal displacement concept may have application to the wind design of high-rise buildings where cross-wind loads control the design of the lateral system.","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127940669","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A common task in inverse problems and imaging is finding a solution that is sparse, in the sense that most of its components vanish. In the framework of compressed sensing, general results guaranteeing exact recovery have been proven. In practice, sparse solutions are often computed combining ℓ 1 - penalized least squares optimization with an appropriate numerical scheme to accomplish the task - see, e.g., [1]. A computationally efficient alternative for finding sparse solutions to linear inverse problems is provided by Bayesian hierarchical models, in which the sparsity is encoded by defining a conditionally Gaussian prior model with the prior parameter obeying a generalized gamma distribution [2]. An iterative alternating sequential (IAS) algorithm has been demonstrated to lead to a computationally efficient scheme, and combined with Krylov subspace iterations with an early termination condition, the approach is particularly well suited for large scale problems [3]. Here, we will discuss two hybrid versions of the original IAS that first exploit the global convergence associated with gamma hyperpriors to arrive in a neighborhood of the unique minimizer, then adopt a generalized gamma hyperprior that promote sparsity more strongly. The proposed algorithms will be tested on traditional imaging applications and to problems whose solution allows a sparse coding in an overcomplete system such as composite frames.
{"title":"Sparse recovery problem in a hierarchical Bayesian framework","authors":"D. Calvetti, M. Pragliola, E. Somersalo","doi":"10.23967/admos.2023.012","DOIUrl":"https://doi.org/10.23967/admos.2023.012","url":null,"abstract":"A common task in inverse problems and imaging is finding a solution that is sparse, in the sense that most of its components vanish. In the framework of compressed sensing, general results guaranteeing exact recovery have been proven. In practice, sparse solutions are often computed combining ℓ 1 - penalized least squares optimization with an appropriate numerical scheme to accomplish the task - see, e.g., [1]. A computationally efficient alternative for finding sparse solutions to linear inverse problems is provided by Bayesian hierarchical models, in which the sparsity is encoded by defining a conditionally Gaussian prior model with the prior parameter obeying a generalized gamma distribution [2]. An iterative alternating sequential (IAS) algorithm has been demonstrated to lead to a computationally efficient scheme, and combined with Krylov subspace iterations with an early termination condition, the approach is particularly well suited for large scale problems [3]. Here, we will discuss two hybrid versions of the original IAS that first exploit the global convergence associated with gamma hyperpriors to arrive in a neighborhood of the unique minimizer, then adopt a generalized gamma hyperprior that promote sparsity more strongly. The proposed algorithms will be tested on traditional imaging applications and to problems whose solution allows a sparse coding in an overcomplete system such as composite frames.","PeriodicalId":414984,"journal":{"name":"XI International Conference on Adaptive Modeling and Simulation","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131333374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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