FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W3048778144> ?p ?o ?g. }

• W3048778144 endingPage "109760" @default.
• W3048778144 startingPage "109760" @default.
• W3048778144 abstract "Physics-informed neural networks (PINNs) are effective in solving inverse problems based on differential and integro-differential equations with sparse, noisy, unstructured, and multi-fidelity data. PINNs incorporate all available information, including governing equations (reflecting physical laws), initial-boundary conditions, and observations of quantities of interest, into a loss function to be minimized, thus recasting the original problem into an optimization problem. In this paper, we extend PINNs to parameter and function inference for integral equations such as nonlocal Poisson and nonlocal turbulence models, and we refer to them as nonlocal PINNs (nPINNs). The contribution of the paper is three-fold. First, we propose a unified nonlocal Laplace operator, which converges to the classical Laplacian as one of the operator parameters, the nonlocal interaction radius δ goes to zero, and to the fractional Laplacian as δ goes to infinity. This universal operator forms a super-set of classical Laplacian and fractional Laplacian operators and, thus, has the potential to fit a broad spectrum of data sets. We provide theoretical convergence rates with respect to δ and verify them via numerical experiments. Second, we use nPINNs to estimate the two parameters, δ and α, characterizing the kernel of the unified operator. The strong non-convexity of the loss function yielding multiple (good) local minima reveals the occurrence of the operator mimicking phenomenon, that is, different pairs of estimated parameters could produce multiple solutions of comparable accuracy. Third, we propose another nonlocal operator with spatially variable order α(y), which is more suitable for modeling wall-bounded turbulence, e.g. turbulent Couette flow. Our results show that nPINNs can jointly infer this function as well as δ. More importantly, these parameters exhibit a universal behavior with respect to the Reynolds number, a finding that contributes to our understanding of nonlocal interactions in wall-bounded turbulence." @default.
• W3048778144 created "2020-08-18" @default.
• W3048778144 creator A5005886655 @default.
• W3048778144 creator A5028709260 @default.
• W3048778144 creator A5045341706 @default.
• W3048778144 creator A5091831529 @default.
• W3048778144 date "2020-12-01" @default.
• W3048778144 modified "2023-10-17" @default.
• W3048778144 title "nPINNs: Nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications" @default.
• W3048778144 cites W1973127220 @default.
• W3048778144 cites W1977452126 @default.
• W3048778144 cites W1980291921 @default.
• W3048778144 cites W1984320340 @default.
• W3048778144 cites W2001730319 @default.
• W3048778144 cites W2012828992 @default.
• W3048778144 cites W2016823491 @default.
• W3048778144 cites W2029529153 @default.
• W3048778144 cites W2062955239 @default.
• W3048778144 cites W2092721527 @default.
• W3048778144 cites W2099111135 @default.
• W3048778144 cites W2113916146 @default.
• W3048778144 cites W2114137384 @default.
• W3048778144 cites W2119104548 @default.
• W3048778144 cites W2139923370 @default.
• W3048778144 cites W2165529896 @default.
• W3048778144 cites W2186626130 @default.
• W3048778144 cites W2204986623 @default.
• W3048778144 cites W2564272570 @default.
• W3048778144 cites W2740626026 @default.
• W3048778144 cites W2745110207 @default.
• W3048778144 cites W2752130168 @default.
• W3048778144 cites W2899283552 @default.
• W3048778144 cites W2969381807 @default.
• W3048778144 cites W2999451223 @default.
• W3048778144 cites W3103424510 @default.
• W3048778144 cites W3105802035 @default.
• W3048778144 doi "https://doi.org/10.1016/j.jcp.2020.109760" @default.
• W3048778144 hasPublicationYear "2020" @default.
• W3048778144 type Work @default.
• W3048778144 sameAs 3048778144 @default.
• W3048778144 citedByCount "64" @default.
• W3048778144 countsByYear W30487781442020 @default.
• W3048778144 countsByYear W30487781442021 @default.
• W3048778144 countsByYear W30487781442022 @default.
• W3048778144 countsByYear W30487781442023 @default.
• W3048778144 crossrefType "journal-article" @default.
• W3048778144 hasAuthorship W3048778144A5005886655 @default.
• W3048778144 hasAuthorship W3048778144A5028709260 @default.
• W3048778144 hasAuthorship W3048778144A5045341706 @default.
• W3048778144 hasAuthorship W3048778144A5091831529 @default.
• W3048778144 hasBestOaLocation W30487781441 @default.
• W3048778144 hasConcept C104317684 @default.
• W3048778144 hasConcept C11413529 @default.
• W3048778144 hasConcept C134306372 @default.
• W3048778144 hasConcept C158448853 @default.
• W3048778144 hasConcept C165700671 @default.
• W3048778144 hasConcept C17020691 @default.
• W3048778144 hasConcept C185592680 @default.
• W3048778144 hasConcept C28826006 @default.
• W3048778144 hasConcept C33923547 @default.
• W3048778144 hasConcept C55493867 @default.
• W3048778144 hasConcept C70915906 @default.
• W3048778144 hasConcept C86339819 @default.
• W3048778144 hasConceptScore W3048778144C104317684 @default.
• W3048778144 hasConceptScore W3048778144C11413529 @default.
• W3048778144 hasConceptScore W3048778144C134306372 @default.
• W3048778144 hasConceptScore W3048778144C158448853 @default.
• W3048778144 hasConceptScore W3048778144C165700671 @default.
• W3048778144 hasConceptScore W3048778144C17020691 @default.
• W3048778144 hasConceptScore W3048778144C185592680 @default.
• W3048778144 hasConceptScore W3048778144C28826006 @default.
• W3048778144 hasConceptScore W3048778144C33923547 @default.
• W3048778144 hasConceptScore W3048778144C55493867 @default.
• W3048778144 hasConceptScore W3048778144C70915906 @default.
• W3048778144 hasConceptScore W3048778144C86339819 @default.
• W3048778144 hasFunder F4320306084 @default.
• W3048778144 hasFunder F4320332180 @default.
• W3048778144 hasFunder F4320338281 @default.
• W3048778144 hasLocation W30487781441 @default.
• W3048778144 hasLocation W30487781442 @default.
• W3048778144 hasLocation W30487781443 @default.
• W3048778144 hasLocation W30487781444 @default.
• W3048778144 hasOpenAccess W3048778144 @default.
• W3048778144 hasPrimaryLocation W30487781441 @default.
• W3048778144 hasRelatedWork W109107975 @default.
• W3048778144 hasRelatedWork W2002742428 @default.
• W3048778144 hasRelatedWork W2016551852 @default.
• W3048778144 hasRelatedWork W2049083434 @default.
• W3048778144 hasRelatedWork W2063058192 @default.
• W3048778144 hasRelatedWork W2317381076 @default.
• W3048778144 hasRelatedWork W2401850100 @default.
• W3048778144 hasRelatedWork W2551281655 @default.
• W3048778144 hasRelatedWork W2935109770 @default.
• W3048778144 hasRelatedWork W3100471806 @default.
• W3048778144 hasVolume "422" @default.
• W3048778144 isParatext "false" @default.
• W3048778144 isRetracted "false" @default.
• W3048778144 magId "3048778144" @default.

• next