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         "type" : "Publication",
         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/20d9e4f97e9687f82660bcd471d24e67a/iew_homepage",         
         "tags" : [
            "Computational_modeling","Convolution","Convolutional_neural_networks","Kernel","Kriging","Mathematical_models","Neurons","Synchronous_Reluctance_Machine","Topology","Training","convolutional_neural_network","data-driven_surrogate_model","drive_cycle_optimization","fully_connected_deep_neural_network","hp_iew","operating_point_dependent_optimization","optimization","support_vector_regression","torque"
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         "interHash" : "9d6e9b793abf92ce931d18c2b3cbde40",
         "label" : "Comparative Study of Different Data-Driven Surrogate Models for Optimization of Synchronous Reluctance Machine",
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         "description" : "",
         "date" : "2025-07-21 13:10:51",
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         "pub-type": "article",
         "journal": "IEEE Transactions on Industry Applications",
         "year": "2025", 
         "url": "", 
         
         "author": [ 
            "Yuancong Gong","Andreas Gneiting","Chongshen Zhao","Nejila Parspour","Hao Chen"
         ],
         "authors": [
         	
            	{"first" : "Yuancong",	"last" : "Gong"},
            	{"first" : "Andreas",	"last" : "Gneiting"},
            	{"first" : "Chongshen",	"last" : "Zhao"},
            	{"first" : "Nejila",	"last" : "Parspour"},
            	{"first" : "Hao",	"last" : "Chen"}
         ],
         "pages": "1--13","abstract": "The optimization of synchronous reluctance machine (SynRM) involves multi-physical considerations and highdimensional input parameters, making it highly time-consuming, especially in drive cycle optimization. To accelerate the design optimization process of SynRM, this study focuses on constructing and comparing four data-driven surrogate models in both operating point dependent optimization and drive cycle optimization. The models compared include Kriging, support vector regression (SVR), fully connected deep neural network (FC-DNN), and convolutional neural network (CNN) models. Through analysis, it is found that the mechanical safety factor, torque ripple and efficiency of SynRM are highly sensitive to geometry variations and difficult to predict. Thus, a hybrid optimization strategy assisted by finite-element-analysis (FEA) is proposed. The results from both operating point-dependent and drive cycle optimization confirm that the proposed hybrid optimization strategy is able to achieve superior optimal designs with only a minimal number of FEA simulations. Moreover, the computation time is reduced by 47\\% and 44.3\\% for operating point-dependent and drive cycle optimization, respectively (using Kriging model). Additionally, among the four surrogate models, the Kriging model is found to be the most capable model for the parameter optimization in terms of both model construction expenses and optimization results",
         "file" : "Comparative\\_Study\\_of\\_Different\\_Data-Driven\\_Surrogate\\_Models\\_for\\_Optimization\\_of\\_Synchronous\\_Reluctance\\_Machine:Attachments/Comparative\\_Study\\_of\\_Different\\_Data-Driven\\_Surrogate\\_Models\\_for\\_Optimization\\_of\\_Synchronous\\_Reluctance\\_Machine.pdf:application/pdf",
         
         "issn" : "0093-9994",
         
         "doi" : "10.1109/TIA.2025.3587180",
         
         "bibtexKey": "GongYuancong.2025.ComparativeStudyofDifferent"

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         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/2170332c3f0ced359dd0fcfb339ab061b/mathematik",         
         "tags" : [
            "Kernel","anm","approximation,","control,","dynamic","feedback","from:britsteiner","greedy","ians","optimal","principle,","programming","techniques"
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         "label" : "Data-driven surrogates of value functions and applications to feedback control for dynamical systems",
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         "year": "2018", 
         "url": "http://www.sciencedirect.com/science/article/pii/S2405896318300570", 
         
         "author": [ 
            "A. Schmidt","Bernard Haasdonk"
         ],
         "authors": [
         	
            	{"first" : "A.",	"last" : "Schmidt"},
            	{"first" : "Bernard",	"last" : "Haasdonk"}
         ],
         "volume": "51","number": "2","pages": "307--312","note": "9th Vienna International Conference on Mathematical Modelling","abstract": "Dealing with high-dimensional feedback control problems is a difficult\n\ttask when the classical dynamic programming principle is applied.\n\tExisting techniques restrict the application to relatively low dimensions\n\tsince the discretizations typically suffer from the curse of dimensionality.\n\tIn this paper we introduce a novel approximation technique for the\n\tvalue function of an infinite horizon optimal control. The method\n\tis based on solving optimal open loop control problems on a finite\n\thorizon with a sampling of the global value function along the generated\n\ttrajectories. For the interpolation we choose a kernel orthogonal\n\tgreedy strategy, because these methods are able to produce extreme\n\tsparse surrogates and enable rapid evaluations in high dimensions.\n\tTwo numerical examples prove the performance of the approach and\n\tshow that the method is able to deal with high-dimensional feedback\n\tcontrol problems, where the dimensionality prevents the approximation\n\tby most existing methods.",
         "owner" : "santinge",
         
         "issn" : "2405-8963",
         
         "doi" : "https://doi.org/10.1016/j.ifacol.2018.03.053",
         
         "bibtexKey": "Schmidt2018f"

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         "type" : "Publication",
         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/291f54fe318fd82138164bcd9e2763d27/mathematik",         
         "tags" : [
            "anm","blood","dimensionally","flow","from:britsteiner","ians","kernel","methods,","mixedâ\u0080\u0090dimension","models,","peripheral","realâ\u0080\u0090time","reduced","simulations","simulations,","stenosis,","surrogate"
         ],
         
         "intraHash" : "91f54fe318fd82138164bcd9e2763d27",
         "interHash" : "979f2097ba9c22d67096e59e5c6d7a3e",
         "label" : "Numerical modelling of a peripheral arterial stenosis using dimensionally reduced models and kernel methods",
         "user" : "mathematik",
         "description" : "",
         "date" : "2021-09-29 14:35:10",
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         "pub-type": "article",
         "journal": "International Journal for Numerical Methods in Biomedical Engineering",
         "year": "2018", 
         "url": "https://onlinelibrary.wiley.com/doi/abs/10.1002/cnm.3095", 
         
         "author": [ 
            "Tobias Köppl","Gabriele Santin","Bernard Haasdonk","Rainer Helmig"
         ],
         "authors": [
         	
            	{"first" : "Tobias",	"last" : "Köppl"},
            	{"first" : "Gabriele",	"last" : "Santin"},
            	{"first" : "Bernard",	"last" : "Haasdonk"},
            	{"first" : "Rainer",	"last" : "Helmig"}
         ],
         "volume": "34","number": "8","pages": "e3095","note": "e3095 cnm.3095","abstract": "Summary In this work, we consider two kinds of model reduction techniques\n\tto simulate blood flow through the largest systemic arteries, where\n\ta stenosis is located in a peripheral artery i.e. in an artery that\n\tis located far away from the heart. For our simulations we place\n\tthe stenosis in one of the tibial arteries belonging to the right\n\tlower leg (right post tibial artery). The model reduction techniques\n\tthat are used are on the one hand dimensionally reduced models (1â\u0080\u0090D\n\tand 0â\u0080\u0090D models, the soâ\u0080\u0090called mixedâ\u0080\u0090dimension model) and on\n\tthe other hand surrogate models produced by kernel methods. Both\n\tmethods are combined in such a way that the mixedâ\u0080\u0090dimension models\n\tyield training data for the surrogate model, where the surrogate\n\tmodel is parametrised by the degree of narrowing of the peripheral\n\tstenosis. By means of a wellâ\u0080\u0090trained surrogate model, we show that\n\tsimulation data can be reproduced with a satisfactory accuracy and\n\tthat parameter optimisation or state estimation problems can be solved\n\tin a very efficient way. Furthermore it is demonstrated that a surrogate\n\tmodel enables us to present after a very short simulation time the\n\timpact of a varying degree of stenosis on blood flow, obtaining a\n\tspeedup of several orders over the full model.",
         "owner" : "santinge",
         
         "groups" : "haasdonk, santin",
         
         "eprint" : "https://onlinelibrary.wiley.com/doi/pdf/10.1002/cnm.3095",
         
         "file" : ":PDF/KSHH2017_www_preprint.pdf:PDF",
         
         "doi" : "10.1002/cnm.3095",
         
         "bibtexKey": "KSHH2018"

      }
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         "type" : "Publication",
         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/288e9a857661efa99f399e9d4f24b559e/mathematik",         
         "tags" : [
            "subspace","error","dynamical","kernel","a-posteriori","from:britsteiner","methods,","ians","nonlinear","systems,","offline/online","decomposition,","projection","estimates,","model","anm","reduction,"
         ],
         
         "intraHash" : "88e9a857661efa99f399e9d4f24b559e",
         "interHash" : "e80ae72fe2c1f9f79f4f7f8f5ce00735",
         "label" : "Efficient a-posteriori error estimation for nonlinear kernel-based reduced systems",
         "user" : "mathematik",
         "description" : "",
         "date" : "2021-09-29 14:35:08",
         "changeDate" : "2021-09-29 12:35:08",
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         "pub-type": "article",
         "journal": "Systems & Control Letters","publisher":"Elsevier BV",
         "year": "2012", 
         "url": "http://dx.doi.org/10.1016/j.sysconle.2011.10.012", 
         
         "author": [ 
            "Daniel Wirtz","Bernard Haasdonk"
         ],
         "authors": [
         	
            	{"first" : "Daniel",	"last" : "Wirtz"},
            	{"first" : "Bernard",	"last" : "Haasdonk"}
         ],
         "volume": "61","number": "1","pages": "203--211","abstract": "In this paper, we consider the topic of model reduction for nonlinear\n\tdynamical systems based on kernel expansions. Our approach allows\n\tfor a full offline/online decomposition and efficient online computation\n\tof the reduced model. In particular, we derive an a-posteriori state-space\n\terror estimator for the reduction error. A key ingredient is a local\n\tLipschitz constant estimation that enables rigorous a-posteriori\n\terror estimation. The computation of the error estimator is realized\n\tby solving an auxiliary differential equation during online simulations.\n\tEstimation iterations can be performed that allow a balancing between\n\testimation sharpness and computation time. Numerical experiments\n\tdemonstrate the estimation improvement over different estimator versions\n\tand the rigor and effectiveness of the error bounds.",
         "owner" : "schmidta",
         
         "groups" : "haasdonk, haasdonk_all_papers",
         
         "file" : ":PDF/WH12_www_preprint_error_estimation_nonlinear_kernel_based_reduced_systems.pdf:PDF",
         
         "doi" : "10.1016/j.sysconle.2011.10.012",
         
         "bibtexKey": "WH12"

      }
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         "type" : "Publication",
         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/2c9ff784e6a0440b80b45055fa2c9df7e/britsteiner",         
         "tags" : [
            "a-posteriori","anm","decomposition,","dynamical","error","estimates,","ians","kernel","methods,","model","nonlinear","offline/online","parameterized","projection","reduction,","subspace","systems,"
         ],
         
         "intraHash" : "c9ff784e6a0440b80b45055fa2c9df7e",
         "interHash" : "e6dce191069323c30bda8a87cce2913a",
         "label" : "A-posteriori error estimation for parameterized kernel-based systems",
         "user" : "britsteiner",
         "description" : "",
         "date" : "2021-09-29 14:33:27",
         "changeDate" : "2021-09-29 12:35:04",
         "count" : 8,
         "pub-type": "inproceedings",
         "booktitle": "Proc. MATHMOD 2012 - 7th Vienna International Conference on Mathematical Modelling",
         "year": "2012", 
         "url": "http://www.ifac-papersonline.net/", 
         
         "author": [ 
            "Daniel Wirtz","Bernard Haasdonk"
         ],
         "authors": [
         	
            	{"first" : "Daniel",	"last" : "Wirtz"},
            	{"first" : "Bernard",	"last" : "Haasdonk"}
         ],
         "abstract": "This work is concerned with derivation of fully offine/online decomposable\n\teffcient aposteriori error estimators for reduced parameterized nonlinear\n\tkernel-based systems. The dynamical systems under consideration consist\n\tof a nonlinear, time- and parameter-dependent kernel expansion representing\n\tthe system's inner dynamics as well as time- and parameter-affne\n\tinputs, initial conditions and outputs. The estimators are established\n\tfor a reduction technique originally proposed in [7] and are an extension\n\tof the estimators derived in [11] to the fully time-dependent, parameterized\n\tsetting. Key features for the effcient error estimation are to use\n\tlocal Lipschitz constants provided by a certain class of kernels\n\tand an iterative scheme to balance computation cost against estimation\n\tsharpness. Together with the affnely time/parameter-dependent system\n\tcomponents a full offine/online decomposition for both the reduction\n\tprocess and the error estimators is possible. Some experimental results\n\tfor synthetic systems illustrate the effcient evaluation of the derived\n\terror estimators for different parameters.",
         "owner" : "haasdonk",
         
         "file" : ":PDF/WH12b_preprint.pdf:PDF",
         
         "groups" : "haasdonk, haasdonk_all_papers",
         
         "bibtexKey": "Wirtz2012a"

      }
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         "type" : "Publication",
         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/291f54fe318fd82138164bcd9e2763d27/britsteiner",         
         "tags" : [
            "anm","blood","dimensionally","flow","ians","kernel","methods,","mixedâ\u0080\u0090dimension","models,","peripheral","realâ\u0080\u0090time","reduced","simulations","simulations,","stenosis,","surrogate"
         ],
         
         "intraHash" : "91f54fe318fd82138164bcd9e2763d27",
         "interHash" : "979f2097ba9c22d67096e59e5c6d7a3e",
         "label" : "Numerical modelling of a peripheral arterial stenosis using dimensionally reduced models and kernel methods",
         "user" : "britsteiner",
         "description" : "",
         "date" : "2021-09-29 14:33:27",
         "changeDate" : "2021-09-29 12:35:04",
         "count" : 4,
         "pub-type": "article",
         "journal": "International Journal for Numerical Methods in Biomedical Engineering",
         "year": "2018", 
         "url": "https://onlinelibrary.wiley.com/doi/abs/10.1002/cnm.3095", 
         
         "author": [ 
            "Tobias Köppl","Gabriele Santin","Bernard Haasdonk","Rainer Helmig"
         ],
         "authors": [
         	
            	{"first" : "Tobias",	"last" : "Köppl"},
            	{"first" : "Gabriele",	"last" : "Santin"},
            	{"first" : "Bernard",	"last" : "Haasdonk"},
            	{"first" : "Rainer",	"last" : "Helmig"}
         ],
         "volume": "34","number": "8","pages": "e3095","note": "e3095 cnm.3095","abstract": "Summary In this work, we consider two kinds of model reduction techniques\n\tto simulate blood flow through the largest systemic arteries, where\n\ta stenosis is located in a peripheral artery i.e. in an artery that\n\tis located far away from the heart. For our simulations we place\n\tthe stenosis in one of the tibial arteries belonging to the right\n\tlower leg (right post tibial artery). The model reduction techniques\n\tthat are used are on the one hand dimensionally reduced models (1â\u0080\u0090D\n\tand 0â\u0080\u0090D models, the soâ\u0080\u0090called mixedâ\u0080\u0090dimension model) and on\n\tthe other hand surrogate models produced by kernel methods. Both\n\tmethods are combined in such a way that the mixedâ\u0080\u0090dimension models\n\tyield training data for the surrogate model, where the surrogate\n\tmodel is parametrised by the degree of narrowing of the peripheral\n\tstenosis. By means of a wellâ\u0080\u0090trained surrogate model, we show that\n\tsimulation data can be reproduced with a satisfactory accuracy and\n\tthat parameter optimisation or state estimation problems can be solved\n\tin a very efficient way. Furthermore it is demonstrated that a surrogate\n\tmodel enables us to present after a very short simulation time the\n\timpact of a varying degree of stenosis on blood flow, obtaining a\n\tspeedup of several orders over the full model.",
         "owner" : "santinge",
         
         "groups" : "haasdonk, santin",
         
         "eprint" : "https://onlinelibrary.wiley.com/doi/pdf/10.1002/cnm.3095",
         
         "file" : ":PDF/KSHH2017_www_preprint.pdf:PDF",
         
         "doi" : "10.1002/cnm.3095",
         
         "bibtexKey": "KSHH2018"

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         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/2170332c3f0ced359dd0fcfb339ab061b/britsteiner",         
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            "Kernel","anm","approximation,","control,","dynamic","feedback","greedy","ians","optimal","principle,","programming","techniques"
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         "label" : "Data-driven surrogates of value functions and applications to feedback control for dynamical systems",
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         "year": "2018", 
         "url": "http://www.sciencedirect.com/science/article/pii/S2405896318300570", 
         
         "author": [ 
            "A. Schmidt","Bernard Haasdonk"
         ],
         "authors": [
         	
            	{"first" : "A.",	"last" : "Schmidt"},
            	{"first" : "Bernard",	"last" : "Haasdonk"}
         ],
         "volume": "51","number": "2","pages": "307--312","note": "9th Vienna International Conference on Mathematical Modelling","abstract": "Dealing with high-dimensional feedback control problems is a difficult\n\ttask when the classical dynamic programming principle is applied.\n\tExisting techniques restrict the application to relatively low dimensions\n\tsince the discretizations typically suffer from the curse of dimensionality.\n\tIn this paper we introduce a novel approximation technique for the\n\tvalue function of an infinite horizon optimal control. The method\n\tis based on solving optimal open loop control problems on a finite\n\thorizon with a sampling of the global value function along the generated\n\ttrajectories. For the interpolation we choose a kernel orthogonal\n\tgreedy strategy, because these methods are able to produce extreme\n\tsparse surrogates and enable rapid evaluations in high dimensions.\n\tTwo numerical examples prove the performance of the approach and\n\tshow that the method is able to deal with high-dimensional feedback\n\tcontrol problems, where the dimensionality prevents the approximation\n\tby most existing methods.",
         "owner" : "santinge",
         
         "issn" : "2405-8963",
         
         "doi" : "https://doi.org/10.1016/j.ifacol.2018.03.053",
         
         "bibtexKey": "Schmidt2018f"

      }
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            "a-posteriori","anm","decomposition,","dynamical","error","estimates,","ians","kernel","methods,","model","nonlinear","offline/online","projection","reduction,","subspace","systems,"
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         "label" : "Efficient a-posteriori error estimation for nonlinear kernel-based reduced systems",
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         "journal": "Systems & Control Letters","publisher":"Elsevier BV",
         "year": "2012", 
         "url": "http://dx.doi.org/10.1016/j.sysconle.2011.10.012", 
         
         "author": [ 
            "Daniel Wirtz","Bernard Haasdonk"
         ],
         "authors": [
         	
            	{"first" : "Daniel",	"last" : "Wirtz"},
            	{"first" : "Bernard",	"last" : "Haasdonk"}
         ],
         "volume": "61","number": "1","pages": "203--211","abstract": "In this paper, we consider the topic of model reduction for nonlinear\n\tdynamical systems based on kernel expansions. Our approach allows\n\tfor a full offline/online decomposition and efficient online computation\n\tof the reduced model. In particular, we derive an a-posteriori state-space\n\terror estimator for the reduction error. A key ingredient is a local\n\tLipschitz constant estimation that enables rigorous a-posteriori\n\terror estimation. The computation of the error estimator is realized\n\tby solving an auxiliary differential equation during online simulations.\n\tEstimation iterations can be performed that allow a balancing between\n\testimation sharpness and computation time. Numerical experiments\n\tdemonstrate the estimation improvement over different estimator versions\n\tand the rigor and effectiveness of the error bounds.",
         "owner" : "schmidta",
         
         "groups" : "haasdonk, haasdonk_all_papers",
         
         "file" : ":PDF/WH12_www_preprint_error_estimation_nonlinear_kernel_based_reduced_systems.pdf:PDF",
         
         "doi" : "10.1016/j.sysconle.2011.10.012",
         
         "bibtexKey": "WH12"

      }
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         "type" : "Publication",
         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/2699c9caf6155e0598d9c980105b8118d/mathematik",         
         "tags" : [
            "a-posteriori","decomposition,","dynamical","error","estimates,","from:mhartmann","ians","kernel","methods,","model","nonlinear","offline/online","projection","reduction,","subspace","systems,","vorlaeufig"
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         "label" : "Efficient a-posteriori error estimation for nonlinear kernel-based\n\treduced systems",
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         "pub-type": "article",
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         "year": "2012", 
         "url": "http://www.sciencedirect.com/science/article/pii/S0167691111002672", 
         
         "author": [ 
            "D. Wirtz","B. Haasdonk"
         ],
         "authors": [
         	
            	{"first" : "D.",	"last" : "Wirtz"},
            	{"first" : "B.",	"last" : "Haasdonk"}
         ],
         "volume": "61","number": "1","pages": "203 - 211","abstract": "In this paper, we consider the topic of model reduction for nonlinear\n\tdynamical systems based on kernel expansions. Our approach allows\n\tfor a full offline/online decomposition and efficient online computation\n\tof the reduced model. In particular, we derive an a-posteriori state-space\n\terror estimator for the reduction error. A key ingredient is a local\n\tLipschitz constant estimation that enables rigorous a-posteriori\n\terror estimation. The computation of the error estimator is realized\n\tby solving an auxiliary differential equation during online simulations.\n\tEstimation iterations can be performed that allow a balancing between\n\testimation sharpness and computation time. Numerical experiments\n\tdemonstrate the estimation improvement over different estimator versions\n\tand the rigor and effectiveness of the error bounds.",
         "file" : ":/home/dwirtz/dwirtzwww/WH10_preprint.pdf:PDF",
         
         "doi" : "10.1016/j.sysconle.2011.10.012",
         
         "bibtexKey": "wirtz2012efficient"

      }
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      {
         "type" : "Publication",
         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/2832dacbae634d8ae21c67ac44f94850c/mathematik",         
         "tags" : [
            "blood","dimensionally","flow","from:mhartmann","ians","kernel","methods,","mixed-dimension","models,","peripheral","real-time","reduced","simulations","simulations,","stenosis,","surrogate","vorlaeufig"
         ],
         
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         "interHash" : "979f2097ba9c22d67096e59e5c6d7a3e",
         "label" : "Numerical modelling of a peripheral arterial stenosis using dimensionally\n\treduced models and kernel methods",
         "user" : "mathematik",
         "description" : "",
         "date" : "2018-07-20 10:54:55",
         "changeDate" : "2019-12-18 14:37:55",
         "count" : 4,
         "pub-type": "article",
         "journal": "International Journal for Numerical Methods in Biomedical Engineering",
         "year": "2018", 
         "url": "https://onlinelibrary.wiley.com/doi/abs/10.1002/cnm.3095", 
         
         "author": [ 
            "Tobias Köppl","Gabriele Santin","Bernard Haasdonk","Rainer Helmig"
         ],
         "authors": [
         	
            	{"first" : "Tobias",	"last" : "Köppl"},
            	{"first" : "Gabriele",	"last" : "Santin"},
            	{"first" : "Bernard",	"last" : "Haasdonk"},
            	{"first" : "Rainer",	"last" : "Helmig"}
         ],
         "volume": "0","number": "ja","pages": "e3095","note": "e3095 cnm.3095","abstract": "Summary In this work, we consider two kinds of model reduction techniquesto\n\tsimulate blood flow through the largest systemic arteries, where\n\ta stenosis is located in a peripheral artery i.e. in an artery that\n\tis located far away from the heart. For our simulations we place\n\tthe stenosis in one of the tibial arteries belonging to the right\n\tlower leg (right post tibial artery). The model reduction techniques\n\tthat are used are on the one hand dimensionally reduced models (1-Dand\n\t0-D models, the so-called mixed-dimension model) and on the other\n\thand surrogate models produced by kernel methods. Both methods are\n\tcombined in such a way that the mixed-dimension models yield training\n\tdata for the surrogate model, where the surrogate model is parametrisedby\n\tthe degree of narrowing of the peripheral stenosis. By means of a\n\twell-trained surrogate model, we show that simulation data can be\n\treproduced with a satisfactory accuracy and that parameter optimisation\n\tor state estimation problems can be solved in a very efficient way.\n\tFurthermore it is demonstrated that a surrogate model enables us\n\tto present after a very short simulation time the impact of a varying\n\tdegree of stenosis on blood flow, obtaining a speedup of several\n\torders over the full model.",
         "file" : ":http\\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/KSHH2017_www_preprint.pdf:PDF",
         
         "owner" : "santinge",
         
         "doi" : "10.1002/cnm.3095",
         
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         "label" : "A-posteriori error estimation for parameterized kernel-based systems",
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         "date" : "2018-07-20 10:54:37",
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         "booktitle": "Proc. MATHMOD 2012 - 7th Vienna International Conference on Mathematical\n\tModelling",
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         "url": "http://www.ifac-papersonline.net/", 
         
         "author": [ 
            "Daniel Wirtz","Bernard Haasdonk"
         ],
         "authors": [
         	
            	{"first" : "Daniel",	"last" : "Wirtz"},
            	{"first" : "Bernard",	"last" : "Haasdonk"}
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         "abstract": "This work is concerned with derivation of fully offine/online decomposable\n\teffcient aposteriori error estimators for reduced parameterized nonlinear\n\tkernel-based systems. The dynamical systems under consideration consist\n\tof a nonlinear, time- and parameter-dependent kernel expansion representing\n\tthe system's inner dynamics as well as time- and parameter-affne\n\tinputs, initial conditions and outputs. The estimators are established\n\tfor a reduction technique originally proposed in [7] and are an extension\n\tof the estimators derived in [11] to the fully time-dependent, parameterized\n\tsetting. Key features for the effcient error estimation are to use\n\tlocal Lipschitz constants provided by a certain class of kernels\n\tand an iterative scheme to balance computation cost against estimation\n\tsharpness. Together with the affnely time/parameter-dependent system\n\tcomponents a full offine/online decomposition for both the reduction\n\tprocess and the error estimators is possible. Some experimental results\n\tfor synthetic systems illustrate the effcient evaluation of the derived\n\terror estimators for different parameters.",
         "owner" : "haasdonk",
         
         "bibtexKey": "wirtz2012aposteriori"

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         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/2699c9caf6155e0598d9c980105b8118d/mhartmann",         
         "tags" : [
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         "label" : "Efficient a-posteriori error estimation for nonlinear kernel-based\n\treduced systems",
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         "date" : "2018-07-20 10:54:15",
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         "journal": "Systems and Control Letters",
         "year": "2012", 
         "url": "http://www.sciencedirect.com/science/article/pii/S0167691111002672", 
         
         "author": [ 
            "D. Wirtz","B. Haasdonk"
         ],
         "authors": [
         	
            	{"first" : "D.",	"last" : "Wirtz"},
            	{"first" : "B.",	"last" : "Haasdonk"}
         ],
         "volume": "61","number": "1","pages": "203 - 211","abstract": "In this paper, we consider the topic of model reduction for nonlinear\n\tdynamical systems based on kernel expansions. Our approach allows\n\tfor a full offline/online decomposition and efficient online computation\n\tof the reduced model. In particular, we derive an a-posteriori state-space\n\terror estimator for the reduction error. A key ingredient is a local\n\tLipschitz constant estimation that enables rigorous a-posteriori\n\terror estimation. The computation of the error estimator is realized\n\tby solving an auxiliary differential equation during online simulations.\n\tEstimation iterations can be performed that allow a balancing between\n\testimation sharpness and computation time. Numerical experiments\n\tdemonstrate the estimation improvement over different estimator versions\n\tand the rigor and effectiveness of the error bounds.",
         "file" : ":/home/dwirtz/dwirtzwww/WH10_preprint.pdf:PDF",
         
         "doi" : "10.1016/j.sysconle.2011.10.012",
         
         "bibtexKey": "wirtz2012efficient"

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         "type" : "Publication",
         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/2832dacbae634d8ae21c67ac44f94850c/mhartmann",         
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         "label" : "Numerical modelling of a peripheral arterial stenosis using dimensionally\n\treduced models and kernel methods",
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         "changeDate" : "2018-07-20 08:54:15",
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         "pub-type": "article",
         "journal": "International Journal for Numerical Methods in Biomedical Engineering",
         "year": "2018", 
         "url": "https://onlinelibrary.wiley.com/doi/abs/10.1002/cnm.3095", 
         
         "author": [ 
            "Tobias Köppl","Gabriele Santin","Bernard Haasdonk","Rainer Helmig"
         ],
         "authors": [
         	
            	{"first" : "Tobias",	"last" : "Köppl"},
            	{"first" : "Gabriele",	"last" : "Santin"},
            	{"first" : "Bernard",	"last" : "Haasdonk"},
            	{"first" : "Rainer",	"last" : "Helmig"}
         ],
         "volume": "0","number": "ja","pages": "e3095","note": "e3095 cnm.3095","abstract": "Summary In this work, we consider two kinds of model reduction techniquesto\n\tsimulate blood flow through the largest systemic arteries, where\n\ta stenosis is located in a peripheral artery i.e. in an artery that\n\tis located far away from the heart. For our simulations we place\n\tthe stenosis in one of the tibial arteries belonging to the right\n\tlower leg (right post tibial artery). The model reduction techniques\n\tthat are used are on the one hand dimensionally reduced models (1-Dand\n\t0-D models, the so-called mixed-dimension model) and on the other\n\thand surrogate models produced by kernel methods. Both methods are\n\tcombined in such a way that the mixed-dimension models yield training\n\tdata for the surrogate model, where the surrogate model is parametrisedby\n\tthe degree of narrowing of the peripheral stenosis. By means of a\n\twell-trained surrogate model, we show that simulation data can be\n\treproduced with a satisfactory accuracy and that parameter optimisation\n\tor state estimation problems can be solved in a very efficient way.\n\tFurthermore it is demonstrated that a surrogate model enables us\n\tto present after a very short simulation time the impact of a varying\n\tdegree of stenosis on blood flow, obtaining a speedup of several\n\torders over the full model.",
         "file" : ":http\\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/KSHH2017_www_preprint.pdf:PDF",
         
         "owner" : "santinge",
         
         "doi" : "10.1002/cnm.3095",
         
         "bibtexKey": "koppl2018numerical"

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         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/2c9ff784e6a0440b80b45055fa2c9df7e/mhartmann",         
         "tags" : [
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         "author": [ 
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         ],
         "authors": [
         	
            	{"first" : "Daniel",	"last" : "Wirtz"},
            	{"first" : "Bernard",	"last" : "Haasdonk"}
         ],
         "abstract": "This work is concerned with derivation of fully offine/online decomposable\n\teffcient aposteriori error estimators for reduced parameterized nonlinear\n\tkernel-based systems. The dynamical systems under consideration consist\n\tof a nonlinear, time- and parameter-dependent kernel expansion representing\n\tthe system's inner dynamics as well as time- and parameter-affne\n\tinputs, initial conditions and outputs. The estimators are established\n\tfor a reduction technique originally proposed in [7] and are an extension\n\tof the estimators derived in [11] to the fully time-dependent, parameterized\n\tsetting. Key features for the effcient error estimation are to use\n\tlocal Lipschitz constants provided by a certain class of kernels\n\tand an iterative scheme to balance computation cost against estimation\n\tsharpness. Together with the affnely time/parameter-dependent system\n\tcomponents a full offine/online decomposition for both the reduction\n\tprocess and the error estimators is possible. Some experimental results\n\tfor synthetic systems illustrate the effcient evaluation of the derived\n\terror estimators for different parameters.",
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