FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2912649832> ?p ?o ?g. }

• W2912649832 endingPage "109120" @default.
• W2912649832 startingPage "109120" @default.
• W2912649832 abstract "Stochastic partial differential equations (SPDEs) are ubiquitous in engineering and computational sciences. The stochasticity arises as a consequence of uncertainty in input parameters, constitutive relations, initial/boundary conditions, etc. Because of these functional uncertainties, the stochastic parameter space is often high-dimensional, requiring hundreds, or even thousands, of parameters to describe it. This poses an insurmountable challenge to response surface modeling since the number of forward model evaluations needed to construct an accurate surrogate grows exponentially with the dimension of the uncertain parameter space; a phenomenon referred to as the curse of dimensionality. State-of-the-art methods for high-dimensional uncertainty propagation seek to alleviate the curse of dimensionality by performing dimensionality reduction in the uncertain parameter space. However, one still needs to perform forward model evaluations that potentially carry a very high computational burden. We propose a novel methodology for high-dimensional uncertainty propagation of elliptic SPDEs which lifts the requirement for a deterministic forward solver. Our approach is as follows. We parameterize the solution of the elliptic SPDE using a deep residual network (ResNet). In a departure from traditional squared residual (SR) based loss function for training the ResNet, we introduce a physics-informed loss function derived from variational principles. Specifically, our loss function is the expectation of the energy functional of the PDE over the stochastic variables. We demonstrate our solver-free approach through various examples where the elliptic SPDE is subjected to different types of high-dimensional input uncertainties. Also, we solve high-dimensional uncertainty propagation and inverse problems." @default.
• W2912649832 created "2019-02-21" @default.
• W2912649832 creator A5036201536 @default.
• W2912649832 creator A5043072708 @default.
• W2912649832 creator A5077873393 @default.
• W2912649832 creator A5089311247 @default.
• W2912649832 date "2020-03-01" @default.
• W2912649832 modified "2023-10-15" @default.
• W2912649832 title "Simulator-free solution of high-dimensional stochastic elliptic partial differential equations using deep neural networks" @default.
• W2912649832 cites W1612404967 @default.
• W2912649832 cites W1859126261 @default.
• W2912649832 cites W1973569609 @default.
• W2912649832 cites W1985926778 @default.
• W2912649832 cites W1987043741 @default.
• W2912649832 cites W1991767606 @default.
• W2912649832 cites W2013596835 @default.
• W2912649832 cites W2018159038 @default.
• W2912649832 cites W2021125631 @default.
• W2912649832 cites W2029164135 @default.
• W2912649832 cites W2042996313 @default.
• W2912649832 cites W2043976332 @default.
• W2912649832 cites W2044147720 @default.
• W2912649832 cites W2060682310 @default.
• W2912649832 cites W2069157151 @default.
• W2912649832 cites W2080971404 @default.
• W2912649832 cites W2108001913 @default.
• W2912649832 cites W2135459060 @default.
• W2912649832 cites W2137983211 @default.
• W2912649832 cites W2148532962 @default.
• W2912649832 cites W2150062983 @default.
• W2912649832 cites W2156677085 @default.
• W2912649832 cites W2282795067 @default.
• W2912649832 cites W2558580397 @default.
• W2912649832 cites W2685500084 @default.
• W2912649832 cites W2760972773 @default.
• W2912649832 cites W2770250658 @default.
• W2912649832 cites W2784733489 @default.
• W2912649832 cites W3101260193 @default.
• W2912649832 cites W3103869760 @default.
• W2912649832 cites W3104291870 @default.
• W2912649832 cites W3105524653 @default.
• W2912649832 cites W3123551284 @default.
• W2912649832 cites W601879004 @default.
• W2912649832 doi "https://doi.org/10.1016/j.jcp.2019.109120" @default.
• W2912649832 hasPublicationYear "2020" @default.
• W2912649832 type Work @default.
• W2912649832 sameAs 2912649832 @default.
• W2912649832 citedByCount "84" @default.
• W2912649832 countsByYear W29126498322019 @default.
• W2912649832 countsByYear W29126498322020 @default.
• W2912649832 countsByYear W29126498322021 @default.
• W2912649832 countsByYear W29126498322022 @default.
• W2912649832 countsByYear W29126498322023 @default.
• W2912649832 crossrefType "journal-article" @default.
• W2912649832 hasAuthorship W2912649832A5036201536 @default.
• W2912649832 hasAuthorship W2912649832A5043072708 @default.
• W2912649832 hasAuthorship W2912649832A5077873393 @default.
• W2912649832 hasAuthorship W2912649832A5089311247 @default.
• W2912649832 hasBestOaLocation W29126498321 @default.
• W2912649832 hasConcept C111030470 @default.
• W2912649832 hasConcept C119857082 @default.
• W2912649832 hasConcept C126255220 @default.
• W2912649832 hasConcept C134306372 @default.
• W2912649832 hasConcept C154945302 @default.
• W2912649832 hasConcept C2778770139 @default.
• W2912649832 hasConcept C28826006 @default.
• W2912649832 hasConcept C32230216 @default.
• W2912649832 hasConcept C33923547 @default.
• W2912649832 hasConcept C41008148 @default.
• W2912649832 hasConcept C50644808 @default.
• W2912649832 hasConcept C54067925 @default.
• W2912649832 hasConcept C70518039 @default.
• W2912649832 hasConcept C84629840 @default.
• W2912649832 hasConcept C93779851 @default.
• W2912649832 hasConceptScore W2912649832C111030470 @default.
• W2912649832 hasConceptScore W2912649832C119857082 @default.
• W2912649832 hasConceptScore W2912649832C126255220 @default.
• W2912649832 hasConceptScore W2912649832C134306372 @default.
• W2912649832 hasConceptScore W2912649832C154945302 @default.
• W2912649832 hasConceptScore W2912649832C2778770139 @default.
• W2912649832 hasConceptScore W2912649832C28826006 @default.
• W2912649832 hasConceptScore W2912649832C32230216 @default.
• W2912649832 hasConceptScore W2912649832C33923547 @default.
• W2912649832 hasConceptScore W2912649832C41008148 @default.
• W2912649832 hasConceptScore W2912649832C50644808 @default.
• W2912649832 hasConceptScore W2912649832C54067925 @default.
• W2912649832 hasConceptScore W2912649832C70518039 @default.
• W2912649832 hasConceptScore W2912649832C84629840 @default.
• W2912649832 hasConceptScore W2912649832C93779851 @default.
• W2912649832 hasFunder F4320332180 @default.
• W2912649832 hasLocation W29126498321 @default.
• W2912649832 hasLocation W29126498322 @default.
• W2912649832 hasLocation W29126498323 @default.
• W2912649832 hasOpenAccess W2912649832 @default.
• W2912649832 hasPrimaryLocation W29126498321 @default.
• W2912649832 hasRelatedWork W1552543208 @default.
• W2912649832 hasRelatedWork W1641615907 @default.
• W2912649832 hasRelatedWork W1995622179 @default.

• next