
{  
   "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/2e713e387fceab5392f1023cdd980ef14/ipvs-sc",         
         "tags" : [
            "Uncertaintysend:unibiblio","Simtech","Grid","from:michaelrehme","Sparse","UQ","B-splines","myownsend:unibibliosend:unibibliosend:unibiblio"
         ],
         
         "intraHash" : "e713e387fceab5392f1023cdd980ef14",
         "interHash" : "6595ddb3b0db0e1f58d85bd7f986fc55",
         "label" : "B-Splines on Sparse Grids for Surrogates in Uncertainty\r\nQuantification",
         "user" : "ipvs-sc",
         "description" : "",
         "date" : "2020-07-29 14:08:55",
         "changeDate" : "2020-07-29 15:12:11",
         "count" : 2,
         "pub-type": "preprint",
         "journal": "Reliability Engineering and System Safety","booktitle": "Special issue on Surrogate Models for Uncertainty Quantification","publisher":"Elsevier","address":"Radarweg 29, 1043 NX Amsterdam, The Netherlands",
         "year": "2019", 
         "url": "", 
         
         "author": [ 
            "Michael F. Rehme","Fabian Franzelin","Dirk Pflüger"
         ],
         "authors": [
         	
            	{"first" : "Michael F.",	"last" : "Rehme"},
            	{"first" : "Fabian",	"last" : "Franzelin"},
            	{"first" : "Dirk",	"last" : "Pflüger"}
         ],
         "abstract": "Robust prediction of the behavior of complex physical and engineering systems relies on approximating solutions in terms of physical and stochastic domains. For higher resolution and accuracy, simulation models must increase the number of deterministic and stochastic variables and therefore further increase the dimensionality of the problem. Sparse grids are an established technique to tackle higher-dimensional problems in the context of uncertainty quantification and allow the creation of surrogates from few model evaluations. Classical approaches use hat functions, resulting in non-differentiable surrogates, or global basis functions, resulting in potential instabilities. Therefore, we propose using modified not-a-knot B-splines to overcome both problems. Additionally, we use established spatially adaptive refinement criteria to reduce the costs, i.e., the number of model evaluations, even further. We compare our technique to other data-driven uncertainty quantification methods in a real-world benchmark for probabilistic risk assessment for carbon dioxide storage in geological formations.",
         "bibtexKey": "rehme2019bsplines"

      }
,
      {
         "type" : "Publication",
         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/2c517d5d2e0d56e7ec38af4773a24d5d9/ipvs-sc",         
         "tags" : [
            "Grids","Extensionsend:unibiblio","Simtech","from:michaelrehme","Sparse","B-splines","myownsend:unibibliosend:unibibliosend:unibibliosend:unibiblio"
         ],
         
         "intraHash" : "c517d5d2e0d56e7ec38af4773a24d5d9",
         "interHash" : "2397bcde9d87458eeec8356957b4eb66",
         "label" : "Hierarchical Extended B-splines for Approximations on Sparse Grids",
         "user" : "ipvs-sc",
         "description" : "",
         "date" : "2020-07-29 14:08:37",
         "changeDate" : "2020-07-29 15:12:11",
         "count" : 2,
         "pub-type": "preprint",
         "booktitle": "Sparse Grids and Applications 2018","publisher":"Springer",
         "year": "2018", 
         "url": "", 
         
         "author": [ 
            "Michael F. Rehme","Dirk Pflüger"
         ],
         "authors": [
         	
            	{"first" : "Michael F.",	"last" : "Rehme"},
            	{"first" : "Dirk",	"last" : "Pflüger"}
         ],
         "abstract": "B-splines on sparse grids are a versatile method for higher-dimensional approximation, especially in smooth settings or if gradient information is advantageous. With increasing dimension, grid points on the boundary become prohibitively expensive and have to be avoided. To compensate for the missing boundary points, the basis functions are typically modified according to natural boundary conditions. However, the resulting splines do not span the polynomial space anymore. In this work we introduce extended B-splines that are based on the polynomial basis property. We apply them on spatially adaptive sparse grids. We proof their basis property and show improved convergence results for analytical objective functions and a real-world model.",
         "bibtexKey": "rehme2019hierarchical"

      }
,
      {
         "type" : "Publication",
         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/21cf548030bfa12290089120ef66e6257/ipvs-sc",         
         "tags" : [
            "simtech","from:michaelrehme","grid","sparse"
         ],
         
         "intraHash" : "1cf548030bfa12290089120ef66e6257",
         "interHash" : "cecbd9bbc12d4b08bad473f580e1d028",
         "label" : "Active Subspaces with B-splines on Sparse Grids",
         "user" : "ipvs-sc",
         "description" : "",
         "date" : "2020-07-29 14:08:16",
         "changeDate" : "2020-07-29 15:12:11",
         "count" : 2,
         "pub-type": "inproceedings",
         "journal": "Proceedings of the 3rd ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering",
         "year": "2019", 
         "url": "", 
         
         "author": [ 
            "Michael F. Rehme","Dirk Pflüger"
         ],
         "authors": [
         	
            	{"first" : "Michael F.",	"last" : "Rehme"},
            	{"first" : "Dirk",	"last" : "Pflüger"}
         ],
         
         "bibtexKey": "rehmeActive2019"

      }
,
      {
         "type" : "Publication",
         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/2a7cefbdfc4b92da3b600efb1fe58f706/ipvs-sc",         
         "tags" : [
            "b-splines","simtech","from:michaelrehme","grid","sparse"
         ],
         
         "intraHash" : "a7cefbdfc4b92da3b600efb1fe58f706",
         "interHash" : "ac83a12db601eef234d0e8663b54805f",
         "label" : "Stochastic Collocation with hierarchical extended B-splines on Sparse Grids",
         "user" : "ipvs-sc",
         "description" : "",
         "date" : "2020-07-29 14:07:31",
         "changeDate" : "2020-07-29 15:12:11",
         "count" : 2,
         "pub-type": "inproceedings",
         "booktitle": "Approximation Theory XVI","publisher":"Springer",
         "year": "2019", 
         "url": "", 
         
         "author": [ 
            "Michael F. Rehme","Dirk Pflüger"
         ],
         "authors": [
         	
            	{"first" : "Michael F.",	"last" : "Rehme"},
            	{"first" : "Dirk",	"last" : "Pflüger"}
         ],
         
         "editor": [ 
            "Gregory E. Fasshauer","Marian Neamtu","Larry Schumaker"
         ],
         "editors": [
         	
            	{"first" : "Gregory E.",	"last" : "Fasshauer"},
            	{"first" : "Marian",	"last" : "Neamtu"},
            	{"first" : "Larry",	"last" : "Schumaker"}
         ],
         
         "venue" : "Nashville,TN,USA",
         
         "bibtexKey": "rehmeStochastic2019"

      }
,
      {
         "type" : "Publication",
         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/2a7cefbdfc4b92da3b600efb1fe58f706/michaelrehme",         
         "tags" : [
            "b-splines","simtech","grid","sparse"
         ],
         
         "intraHash" : "a7cefbdfc4b92da3b600efb1fe58f706",
         "interHash" : "ac83a12db601eef234d0e8663b54805f",
         "label" : "Stochastic Collocation with hierarchical extended B-splines on Sparse Grids",
         "user" : "michaelrehme",
         "description" : "",
         "date" : "2020-07-27 15:42:26",
         "changeDate" : "2020-07-29 12:07:31",
         "count" : 2,
         "pub-type": "inproceedings",
         "booktitle": "Approximation Theory XVI","publisher":"Springer",
         "year": "2019", 
         "url": "", 
         
         "author": [ 
            "Michael F. Rehme","Dirk Pflüger"
         ],
         "authors": [
         	
            	{"first" : "Michael F.",	"last" : "Rehme"},
            	{"first" : "Dirk",	"last" : "Pflüger"}
         ],
         
         "editor": [ 
            "Gregory E. Fasshauer","Marian Neamtu","Larry Schumaker"
         ],
         "editors": [
         	
            	{"first" : "Gregory E.",	"last" : "Fasshauer"},
            	{"first" : "Marian",	"last" : "Neamtu"},
            	{"first" : "Larry",	"last" : "Schumaker"}
         ],
         
         "venue" : "Nashville,TN,USA",
         
         "bibtexKey": "rehmeStochastic2019"

      }
,
      {
         "type" : "Publication",
         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/21cf548030bfa12290089120ef66e6257/michaelrehme",         
         "tags" : [
            "simtech","grid","sparse"
         ],
         
         "intraHash" : "1cf548030bfa12290089120ef66e6257",
         "interHash" : "cecbd9bbc12d4b08bad473f580e1d028",
         "label" : "Active Subspaces with B-splines on Sparse Grids",
         "user" : "michaelrehme",
         "description" : "",
         "date" : "2020-07-27 15:03:13",
         "changeDate" : "2020-07-29 12:08:16",
         "count" : 2,
         "pub-type": "inproceedings",
         "journal": "Proceedings of the 3rd ECCOMAS Thematic Conference on Uncertainty Quantification in Computational Sciences and Engineering",
         "year": "2019", 
         "url": "", 
         
         "author": [ 
            "Michael F. Rehme","Dirk Pflüger"
         ],
         "authors": [
         	
            	{"first" : "Michael F.",	"last" : "Rehme"},
            	{"first" : "Dirk",	"last" : "Pflüger"}
         ],
         
         "bibtexKey": "rehmeActive2019"

      }
,
      {
         "type" : "Publication",
         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/2c517d5d2e0d56e7ec38af4773a24d5d9/michaelrehme",         
         "tags" : [
            "Grids","Extensionsend:unibiblio","Simtech","Sparse","B-splines","myownsend:unibibliosend:unibibliosend:unibibliosend:unibiblio"
         ],
         
         "intraHash" : "c517d5d2e0d56e7ec38af4773a24d5d9",
         "interHash" : "2397bcde9d87458eeec8356957b4eb66",
         "label" : "Hierarchical Extended B-splines for Approximations on Sparse Grids",
         "user" : "michaelrehme",
         "description" : "",
         "date" : "2019-11-08 08:39:55",
         "changeDate" : "2020-07-29 12:08:37",
         "count" : 2,
         "pub-type": "preprint",
         "booktitle": "Sparse Grids and Applications 2018","publisher":"Springer",
         "year": "2018", 
         "url": "", 
         
         "author": [ 
            "Michael F. Rehme","Dirk Pflüger"
         ],
         "authors": [
         	
            	{"first" : "Michael F.",	"last" : "Rehme"},
            	{"first" : "Dirk",	"last" : "Pflüger"}
         ],
         "abstract": "B-splines on sparse grids are a versatile method for higher-dimensional approximation, especially in smooth settings or if gradient information is advantageous. With increasing dimension, grid points on the boundary become prohibitively expensive and have to be avoided. To compensate for the missing boundary points, the basis functions are typically modified according to natural boundary conditions. However, the resulting splines do not span the polynomial space anymore. In this work we introduce extended B-splines that are based on the polynomial basis property. We apply them on spatially adaptive sparse grids. We proof their basis property and show improved convergence results for analytical objective functions and a real-world model.",
         "bibtexKey": "rehme2019hierarchical"

      }
,
      {
         "type" : "Publication",
         "id"   : "https://puma.ub.uni-stuttgart.de/bibtex/2e713e387fceab5392f1023cdd980ef14/michaelrehme",         
         "tags" : [
            "Uncertaintysend:unibiblio","Simtech","Grid","Sparse","UQ","B-splines","myownsend:unibibliosend:unibibliosend:unibiblio"
         ],
         
         "intraHash" : "e713e387fceab5392f1023cdd980ef14",
         "interHash" : "6595ddb3b0db0e1f58d85bd7f986fc55",
         "label" : "B-Splines on Sparse Grids for Surrogates in Uncertainty\r\nQuantification",
         "user" : "michaelrehme",
         "description" : "",
         "date" : "2019-11-08 08:30:39",
         "changeDate" : "2020-07-29 12:08:55",
         "count" : 2,
         "pub-type": "preprint",
         "journal": "Reliability Engineering and System Safety","booktitle": "Special issue on Surrogate Models for Uncertainty Quantification","publisher":"Elsevier","address":"Radarweg 29, 1043 NX Amsterdam, The Netherlands",
         "year": "2019", 
         "url": "", 
         
         "author": [ 
            "Michael F. Rehme","Fabian Franzelin","Dirk Pflüger"
         ],
         "authors": [
         	
            	{"first" : "Michael F.",	"last" : "Rehme"},
            	{"first" : "Fabian",	"last" : "Franzelin"},
            	{"first" : "Dirk",	"last" : "Pflüger"}
         ],
         "abstract": "Robust prediction of the behavior of complex physical and engineering systems relies on approximating solutions in terms of physical and stochastic domains. For higher resolution and accuracy, simulation models must increase the number of deterministic and stochastic variables and therefore further increase the dimensionality of the problem. Sparse grids are an established technique to tackle higher-dimensional problems in the context of uncertainty quantification and allow the creation of surrogates from few model evaluations. Classical approaches use hat functions, resulting in non-differentiable surrogates, or global basis functions, resulting in potential instabilities. Therefore, we propose using modified not-a-knot B-splines to overcome both problems. Additionally, we use established spatially adaptive refinement criteria to reduce the costs, i.e., the number of model evaluations, even further. We compare our technique to other data-driven uncertainty quantification methods in a real-world benchmark for probabilistic risk assessment for carbon dioxide storage in geological formations.",
         "bibtexKey": "rehme2019bsplines"

      }
	  
   ]
}
