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B-splines on sparse grids for surrogates in uncertainty quantification
- Source :
- Reliability Engineering & System Safety. 209:107430
- Publication Year :
- 2021
- Publisher :
- Elsevier BV, 2021.
-
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. Their efficient tensor product structure allows the creation of accurate 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 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.
- Subjects :
- 021110 strategic, defence & security studies
Mathematical optimization
021103 operations research
Probabilistic risk assessment
Computer science
B-spline
0211 other engineering and technologies
Sparse grid
Basis function
02 engineering and technology
Industrial and Manufacturing Engineering
Tensor product
Benchmark (computing)
Uncertainty quantification
Safety, Risk, Reliability and Quality
Curse of dimensionality
Subjects
Details
- ISSN :
- 09518320
- Volume :
- 209
- Database :
- OpenAIRE
- Journal :
- Reliability Engineering & System Safety
- Accession number :
- edsair.doi...........c672428f90f99dca79db5e9d5425d725