FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W3201527904> ?p ?o ?g. }

• W3201527904 abstract "Recent research works for solving partial differential equations (PDEs) with deep neural networks (DNNs) have demonstrated that spatiotemporal function approximators defined by auto-differentiation are effective for approximating nonlinear problems, e.g. the Burger's equation, heat conduction equations, Allen-Cahn and other reaction-diffusion equations, and Navier-Stokes equation. Meanwhile, researchers apply automatic differentiation in physics-informed neural network (PINN) to solve nonlinear hyperbolic systems based on conservation laws with highly discontinuous transition, such as Riemann problem, by inverse problem formulation in data-driven approach. However, it remains a challenge for forward methods using DNNs without knowing part of the solution to resolve discontinuities in nonlinear conservation laws. In this study, we incorporate 1st order numerical schemes into DNNs to set up the loss functional approximator instead of auto-differentiation from traditional deep learning framework, e.g. TensorFlow package, which improves the effectiveness of capturing discontinuities in Riemann problems. In particular, the 2-Coarse-Grid neural network (2CGNN) and 2-Diffusion-Coefficient neural network (2DCNN) are introduced in this work. We use 2 solutions of a conservation law from a converging sequence, computed from a low-cost numerical scheme, and in a domain of dependence of a space-time grid point as the input for a neural network to predict its high-fidelity solution at the grid point. Despite smeared input solutions, they output sharp approximations to solutions containing shocks and contacts and are efficient to use once trained." @default.
• W3201527904 created "2021-09-27" @default.
• W3201527904 creator A5005085650 @default.
• W3201527904 creator A5030732775 @default.
• W3201527904 creator A5041825125 @default.
• W3201527904 date "2021-09-20" @default.
• W3201527904 modified "2023-09-26" @default.
• W3201527904 title "Neural Networks with Inputs Based on Domain of Dependence and A Converging Sequence for Solving Conservation Laws, Part I: 1D Riemann Problems" @default.
• W3201527904 cites W1969188355 @default.
• W3201527904 cites W1973481688 @default.
• W3201527904 cites W1998229174 @default.
• W3201527904 cites W2002775473 @default.
• W3201527904 cites W2039150507 @default.
• W3201527904 cites W2045849310 @default.
• W3201527904 cites W2080202186 @default.
• W3201527904 cites W2108543964 @default.
• W3201527904 cites W2112548197 @default.
• W3201527904 cites W2163554784 @default.
• W3201527904 cites W2163605009 @default.
• W3201527904 cites W2185627778 @default.
• W3201527904 cites W2254050631 @default.
• W3201527904 cites W2271840356 @default.
• W3201527904 cites W2503167201 @default.
• W3201527904 cites W2605147767 @default.
• W3201527904 cites W2618462867 @default.
• W3201527904 cites W2626778328 @default.
• W3201527904 cites W2811395263 @default.
• W3201527904 cites W2899283552 @default.
• W3201527904 cites W2943124479 @default.
• W3201527904 cites W2961184445 @default.
• W3201527904 cites W2962727772 @default.
• W3201527904 cites W2964608097 @default.
• W3201527904 cites W2971949107 @default.
• W3201527904 cites W2978957278 @default.
• W3201527904 cites W2993063996 @default.
• W3201527904 cites W2998366519 @default.
• W3201527904 cites W3003922491 @default.
• W3201527904 cites W3008747420 @default.
• W3201527904 cites W3010839048 @default.
• W3201527904 cites W3093127984 @default.
• W3201527904 cites W3093784762 @default.
• W3201527904 cites W3099057226 @default.
• W3201527904 cites W3104873019 @default.
• W3201527904 cites W3105648287 @default.
• W3201527904 cites W3111914315 @default.
• W3201527904 cites W3124907191 @default.
• W3201527904 cites W3126940265 @default.
• W3201527904 cites W3135839834 @default.
• W3201527904 cites W3146803896 @default.
• W3201527904 cites W3153200540 @default.
• W3201527904 cites W3163993681 @default.
• W3201527904 cites W3181235980 @default.
• W3201527904 cites W3184123732 @default.
• W3201527904 doi "https://doi.org/10.48550/arxiv.2109.09316" @default.
• W3201527904 hasPublicationYear "2021" @default.
• W3201527904 type Work @default.
• W3201527904 sameAs 3201527904 @default.
• W3201527904 citedByCount "0" @default.
• W3201527904 crossrefType "posted-content" @default.
• W3201527904 hasAuthorship W3201527904A5005085650 @default.
• W3201527904 hasAuthorship W3201527904A5030732775 @default.
• W3201527904 hasAuthorship W3201527904A5041825125 @default.
• W3201527904 hasBestOaLocation W32015279041 @default.
• W3201527904 hasConcept C121332964 @default.
• W3201527904 hasConcept C126255220 @default.
• W3201527904 hasConcept C134306372 @default.
• W3201527904 hasConcept C154945302 @default.
• W3201527904 hasConcept C15627037 @default.
• W3201527904 hasConcept C158622935 @default.
• W3201527904 hasConcept C187691185 @default.
• W3201527904 hasConcept C199479865 @default.
• W3201527904 hasConcept C2524010 @default.
• W3201527904 hasConcept C2778112365 @default.
• W3201527904 hasConcept C28826006 @default.
• W3201527904 hasConcept C33923547 @default.
• W3201527904 hasConcept C3445786 @default.
• W3201527904 hasConcept C41008148 @default.
• W3201527904 hasConcept C50644808 @default.
• W3201527904 hasConcept C54355233 @default.
• W3201527904 hasConcept C62520636 @default.
• W3201527904 hasConcept C86803240 @default.
• W3201527904 hasConcept C93779851 @default.
• W3201527904 hasConceptScore W3201527904C121332964 @default.
• W3201527904 hasConceptScore W3201527904C126255220 @default.
• W3201527904 hasConceptScore W3201527904C134306372 @default.
• W3201527904 hasConceptScore W3201527904C154945302 @default.
• W3201527904 hasConceptScore W3201527904C15627037 @default.
• W3201527904 hasConceptScore W3201527904C158622935 @default.
• W3201527904 hasConceptScore W3201527904C187691185 @default.
• W3201527904 hasConceptScore W3201527904C199479865 @default.
• W3201527904 hasConceptScore W3201527904C2524010 @default.
• W3201527904 hasConceptScore W3201527904C2778112365 @default.
• W3201527904 hasConceptScore W3201527904C28826006 @default.
• W3201527904 hasConceptScore W3201527904C33923547 @default.
• W3201527904 hasConceptScore W3201527904C3445786 @default.
• W3201527904 hasConceptScore W3201527904C41008148 @default.
• W3201527904 hasConceptScore W3201527904C50644808 @default.
• W3201527904 hasConceptScore W3201527904C54355233 @default.
• W3201527904 hasConceptScore W3201527904C62520636 @default.
• W3201527904 hasConceptScore W3201527904C86803240 @default.

• next