{ "types" : { "Bookmark" : { "pluralLabel" : "Bookmarks" }, "Publication" : { "pluralLabel" : "Publications" }, "GoldStandardPublication" : { "pluralLabel" : "GoldStandardPublications" }, "GoldStandardBookmark" : { "pluralLabel" : "GoldStandardBookmarks" }, "Tag" : { "pluralLabel" : "Tags" }, "User" : { "pluralLabel" : "Users" }, "Group" : { "pluralLabel" : "Groups" }, "Sphere" : { "pluralLabel" : "Spheres" } }, "properties" : { "count" : { "valueType" : "number" }, "date" : { "valueType" : "date" }, "changeDate" : { "valueType" : "date" }, "url" : { "valueType" : "url" }, "id" : { "valueType" : "url" }, "tags" : { "valueType" : "item" }, "user" : { "valueType" : "item" } }, "items" : [ { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/2699c9caf6155e0598d9c980105b8118d/mhartmann", "tags" : [ "a-posteriori","decomposition,","dynamical","error","estimates,","kernel","methods,","model","nonlinear","offline/online","projection","reduction,","subspace","systems,","vorlaeufig" ], "intraHash" : "699c9caf6155e0598d9c980105b8118d", "interHash" : "e80ae72fe2c1f9f79f4f7f8f5ce00735", "label" : "Efficient a-posteriori error estimation for nonlinear kernel-based\n\treduced systems", "user" : "mhartmann", "description" : "", "date" : "2018-07-20 10:54:15", "changeDate" : "2018-07-20 08:54:15", "count" : 11, "pub-type": "article", "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" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/2832dacbae634d8ae21c67ac44f94850c/mhartmann", "tags" : [ "blood","dimensionally","flow","kernel","methods,","mixed-dimension","models,","peripheral","real-time","reduced","simulations","simulations,","stenosis,","surrogate","vorlaeufig" ], "intraHash" : "832dacbae634d8ae21c67ac44f94850c", "interHash" : "979f2097ba9c22d67096e59e5c6d7a3e", "label" : "Numerical modelling of a peripheral arterial stenosis using dimensionally\n\treduced models and kernel methods", "user" : "mhartmann", "description" : "", "date" : "2018-07-20 10:54:15", "changeDate" : "2018-07-20 08:54:15", "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", "bibtexKey": "koppl2018numerical" } , { "type" : "Publication", "id" : "https://puma.ub.uni-stuttgart.de/bibtex/2c9ff784e6a0440b80b45055fa2c9df7e/mhartmann", "tags" : [ "a-posteriori","decomposition,","dynamical","error","estimates,","kernel","methods,","model","nonlinear","offline/online","parameterized","projection","reduction,","subspace","systems,","vorlaeufig" ], "intraHash" : "c9ff784e6a0440b80b45055fa2c9df7e", "interHash" : "e6dce191069323c30bda8a87cce2913a", "label" : "A-posteriori error estimation for parameterized kernel-based systems", "user" : "mhartmann", "description" : "", "date" : "2018-07-20 10:54:15", "changeDate" : "2018-07-20 08:54:15", "count" : 8, "pub-type": "inproceedings", "booktitle": "Proc. MATHMOD 2012 - 7th Vienna International Conference on Mathematical\n\tModelling", "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", "bibtexKey": "wirtz2012aposteriori" } ] }