Model order reduction of parametrized systems with sparse grid learning techniques:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
2013
|
| Schlagworte: | |
| Online-Zugang: | kostenfrei https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20130918-1163421-0-8 Inhaltsverzeichnis |
| Beschreibung: | 189 S. Ill., graph. Darst. |
Internformat
MARC
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| 245 | 1 | 0 | |a Model order reduction of parametrized systems with sparse grid learning techniques |c Benjamin Peherstorfer |
| 264 | 1 | |c 2013 | |
| 300 | |a 189 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 502 | |a München, Techn. Univ., Diss., 2013 | ||
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| 650 | 0 | 7 | |a Dünnes Gitter |0 (DE-588)4411841-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Parametrisiertes System |0 (DE-588)4770404-4 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804151487895437312 |
|---|---|
| adam_text | CONTENTS
1. INTRODUCTION 9
2. PRELIMINARIES 13
2.1. GENERAL NOTATION OF VECTORS, MATRICES, SETS, AND SPACES 13
2.2. LEARNING FROM
DATA 13
2.2.1. SUPERVISED LEARNING 13
2.2.2. UNSUPERVISED LEARNING 16
2.3. MODEL ORDER
REDUCTION OF PARAMETRIZED SYSTEMS 18
2.3.1. REDUCED-ORDER
MODELS OF PARAMETRIZED SYSTEMS 19
2.3.2. SELECTED MODEL REDUCTION TECHNIQUES 20
2.4. THE CURSE OF DIMENSIONALITY, SPARSE GRIDS, AND ADAPTIVITY 23
2.4.1. ADAPTIVE SPARSE GRIDS 24
2.4.2. REGRESSION AND CLASSIFICATION WITH SPARSE GRIDS 29
I. MOR I: A PRIORI MODEL ORDER REDUCTION 33
3. ADAPTIVE SPARSE GRID DISCRETIZATION OF ELLIPTIC PDES 35
3.1. ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS AND SPARSE GRIDS 35
3.2. SPARSE GRID SOLVERS 36
3.3. MULTIGRID METHODS AND SPARSE GRIDS 38
4. MULTIGRID FOR ADAPTIVE SPARSE GRIDS WITH ANOVA-LIKE
DECOMPOSITION 41
4.1. DIMENSION-WISE DECOMPOSITION OF SPARSE GRID FUNCTIONS 41
4.2. MULTILEVEL ALGORITHM 45
4.2.1. IN-PLACE STORAGE SCHEME 45
4.2.2. UPDATE OF ANOVA QUANTITIES AND MULTILEVEL ALGORITHM 46
4.2.3. RUNTIME AND STORAGE COMPLEXITY 49
5. CASE STUDY: MULTI-DIMENSIONAL CONVECTION-DIFFUSION EQUATION 51
5.1. PROBLEM FORMULATION 52
5.2. Q-CYCLE 53
5.3. NUMERICAL RESULTS 54
6. REMARKS 59
II. MOR II: A POSTERIORI MODEL ORDER REDUCTION 61
7. SUPERVISED LEARNING WITH SPARSE GRIDS 63
7.1. DENSITY ESTIMATION WITH ADAPTIVE SPARSE GRIDS 63
7.1.1. GRID-BASED DENSITY ESTIMATION 63
5
HTTP://D-NB.INFO/1044886811
7.1.2. WORKING WITH ESTIMATED SPARSE GRID
DENSITY FUNCTIONS 65
7.1.3. SAMPLING FROM SPARSE GRID DENSITY FUNCTIONS 68
7.1.4. NUMERICAL RESULTS 72
7.2. CLASSIFICATION WITH DENSITY FUNCTIONS 81
7.2.1. CLASSIFICATION WITH SPARSE GRID DENSITY ESTIMATION 84
7.2.2. OFFLINE/ONLINE SPLITTING 87
7.2.3. NUMERICAL RESULTS 89
7.3. ENSEMBLE LEARNING WITH SPARSE GRID CLASSIFIERS 92
7.3.1. ENSEMBLE LEARNING
AND ADABOOST 93
7.3.2. SPARSE GRID BASE LEARNERS FOR ADABOOST 96
7.3.3. NUMERICAL RESULTS 96
8. CASE STUDY: THERMAL CONDUCTION PROBLEM AND HEAT SHIELD 100
8.1. SPARSE GRID INTERPOLATION OF OUTPUT OF INTEREST 100
8.2. REGRESSION AND PRE-COMPUTED DATA REPOSITORIES 104
9. REMARKS 108
III.
MOR III: POST ANALYSIS MODEL ORDER
REDUCTION 111
10. UNSUPERVISED LEARNING WITH SPARSE GRIDS 114
10.1. SPARSE-GRID-BASED OUT-OF-SAMPLE EXTENSION FOR SPECTRAL CLUSTERING
. . . 114
10.1.1. LAPLACIAN EIGENMAPS AND SPECTRAL CLUSTERING 114
10.1.2. SPARSE-GRID-BASED OUT-OF-SAMPLE EXTENSION 117
10.1.3. BENCHMARKS AND OTHER LEARNING PROBLEMS 119
10.1.4. REAL-WORLD EXAMPLE: IMAGE SEGMENTATION 124
10.2. CLUSTERING WITH SPARSE GRID DENSITY ESTIMATION 129
10.2.1. CLUSTERING WITH ESTIMATED DENSITIES 129
10.2.2. BENCHMARK PROBLEMS 133
10.2.3. REAL-WORLD
EXAMPLE: ANALYSIS OF CAR CRASH DATA 134
11.
CASE STUDY: CAR CRASH SIMULATION - CLUSTERING OF NODES 138
11.1. THE SIMDATA-NL SIMULATION DATA ANALYSIS WORKFLOW 138
11.2. CHEVROLET C2500 PICK-UP TRUCK 141
11.3. FORD
TAURUS 148
12.
CASE STUDY: REACTING FLOW - CLUSTERING OF SNAPSHOTS 153
12.1. POD-DEIM-GALERKIN REDUCED-ORDER MODELS 154
12.2. LOCALIZED DISCRETE EMPIRICAL INTERPOLATION METHOD 156
12.3. FEATURE EXTRACTION FOR STATE-BASED LDEIM 158
12.4. OFFLINE AND ONLINE PROCEDURE OF LDEIM 160
12.5. SIMULATION OF AN H2-AIR FLAME 162
13. REMARKS 167
6
14.
CONCLUSIONS AND FUTURE WORK 169
A. DATA SETS 171
B. SOFTWARE 1^2
REFERENCES 175
7
|
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| dewey-ones | 610 - Medicine and health |
| dewey-raw | 610 |
| dewey-search | 610 |
| dewey-sort | 3610 |
| dewey-tens | 610 - Medicine and health |
| discipline | Informatik Mathematik Medizin |
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| spelling | Peherstorfer, Benjamin Verfasser aut Model order reduction of parametrized systems with sparse grid learning techniques Benjamin Peherstorfer 2013 189 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier München, Techn. Univ., Diss., 2013 Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Ordnungsreduktion (DE-588)4136085-0 gnd rswk-swf Dünnes Gitter (DE-588)4411841-7 gnd rswk-swf Parametrisiertes System (DE-588)4770404-4 gnd rswk-swf Maschinelles Lernen (DE-588)4193754-5 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Mathematisches Modell (DE-588)4114528-8 s Ordnungsreduktion (DE-588)4136085-0 s Parametrisiertes System (DE-588)4770404-4 s Dünnes Gitter (DE-588)4411841-7 s Maschinelles Lernen (DE-588)4193754-5 s DE-604 Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:91-diss-20130918-1163421-0-8 http://mediatum.ub.tum.de/node?id=1163421 Verlag kostenfrei Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20130918-1163421-0-8 Resolving-System DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026836777&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Peherstorfer, Benjamin Model order reduction of parametrized systems with sparse grid learning techniques Mathematisches Modell (DE-588)4114528-8 gnd Ordnungsreduktion (DE-588)4136085-0 gnd Dünnes Gitter (DE-588)4411841-7 gnd Parametrisiertes System (DE-588)4770404-4 gnd Maschinelles Lernen (DE-588)4193754-5 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4136085-0 (DE-588)4411841-7 (DE-588)4770404-4 (DE-588)4193754-5 (DE-588)4113937-9 |
| title | Model order reduction of parametrized systems with sparse grid learning techniques |
| title_auth | Model order reduction of parametrized systems with sparse grid learning techniques |
| title_exact_search | Model order reduction of parametrized systems with sparse grid learning techniques |
| title_full | Model order reduction of parametrized systems with sparse grid learning techniques Benjamin Peherstorfer |
| title_fullStr | Model order reduction of parametrized systems with sparse grid learning techniques Benjamin Peherstorfer |
| title_full_unstemmed | Model order reduction of parametrized systems with sparse grid learning techniques Benjamin Peherstorfer |
| title_short | Model order reduction of parametrized systems with sparse grid learning techniques |
| title_sort | model order reduction of parametrized systems with sparse grid learning techniques |
| topic | Mathematisches Modell (DE-588)4114528-8 gnd Ordnungsreduktion (DE-588)4136085-0 gnd Dünnes Gitter (DE-588)4411841-7 gnd Parametrisiertes System (DE-588)4770404-4 gnd Maschinelles Lernen (DE-588)4193754-5 gnd |
| topic_facet | Mathematisches Modell Ordnungsreduktion Dünnes Gitter Parametrisiertes System Maschinelles Lernen Hochschulschrift |
| url | http://mediatum.ub.tum.de/node?id=1163421 https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20130918-1163421-0-8 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026836777&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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