Matches in SemOpenAlex for { <https://semopenalex.org/work/W4376988377> ?p ?o ?g. }
Showing items 1 to 71 of
71
with 100 items per page.
- W4376988377 abstract "We present a novel methodology based on Physics-Informed Neural Networks (PINNs) for solving systems of partial differential equations admitting discontinuous solutions. Our method, called Gradient-Annihilated PINNs (GA-PINNs), introduces a modified loss function that requires the model to partially ignore high-gradients in the physical variables, achieved by introducing a suitable weighting function. The method relies on a set of hyperparameters that control how gradients are treated in the physical loss and how the activation functions of the neural model are dynamically accounted for. The performance of our GA-PINN model is demonstrated by solving Riemann problems in special relativistic hydrodynamics, extending earlier studies with PINNs in the context of the classical Euler equations. The solutions obtained with our GA-PINN model correctly describe the propagation speeds of discontinuities and sharply capture the associated jumps. We use the relative $l^{2}$ error to compare our results with the exact solution of special relativistic Riemann problems, used as the reference ``ground truth'', and with the error obtained with a second-order, central, shock-capturing scheme. In all problems investigated, the accuracy reached by our GA-PINN model is comparable to that obtained with a shock-capturing scheme and significantly higher than that achieved by a baseline PINN algorithm. An additional benefit worth stressing is that our PINN-based approach sidesteps the costly recovery of the primitive variables from the state vector of conserved ones, a well-known drawback of grid-based solutions of the relativistic hydrodynamics equations. Due to its inherent generality and its ability to handle steep gradients, the GA-PINN method discussed could be a valuable tool to model relativistic flows in astrophysics and particle physics, characterized by the prevalence of discontinuous solutions." @default.
- W4376988377 created "2023-05-18" @default.
- W4376988377 creator A5002567561 @default.
- W4376988377 creator A5044341859 @default.
- W4376988377 creator A5081768850 @default.
- W4376988377 creator A5086082507 @default.
- W4376988377 creator A5088679659 @default.
- W4376988377 date "2023-05-15" @default.
- W4376988377 modified "2023-09-26" @default.
- W4376988377 title "Gradient-Annihilated PINNs for Solving Riemann Problems: Application to Relativistic Hydrodynamics" @default.
- W4376988377 doi "https://doi.org/10.48550/arxiv.2305.08448" @default.
- W4376988377 hasPublicationYear "2023" @default.
- W4376988377 type Work @default.
- W4376988377 citedByCount "0" @default.
- W4376988377 crossrefType "posted-content" @default.
- W4376988377 hasAuthorship W4376988377A5002567561 @default.
- W4376988377 hasAuthorship W4376988377A5044341859 @default.
- W4376988377 hasAuthorship W4376988377A5081768850 @default.
- W4376988377 hasAuthorship W4376988377A5086082507 @default.
- W4376988377 hasAuthorship W4376988377A5088679659 @default.
- W4376988377 hasBestOaLocation W43769883771 @default.
- W4376988377 hasConcept C121332964 @default.
- W4376988377 hasConcept C134306372 @default.
- W4376988377 hasConcept C151730666 @default.
- W4376988377 hasConcept C15627037 @default.
- W4376988377 hasConcept C183115368 @default.
- W4376988377 hasConcept C199479865 @default.
- W4376988377 hasConcept C24890656 @default.
- W4376988377 hasConcept C2779343474 @default.
- W4376988377 hasConcept C28826006 @default.
- W4376988377 hasConcept C33923547 @default.
- W4376988377 hasConcept C34862557 @default.
- W4376988377 hasConcept C38409319 @default.
- W4376988377 hasConcept C40709475 @default.
- W4376988377 hasConcept C41008148 @default.
- W4376988377 hasConcept C62884695 @default.
- W4376988377 hasConcept C86803240 @default.
- W4376988377 hasConcept C93779851 @default.
- W4376988377 hasConceptScore W4376988377C121332964 @default.
- W4376988377 hasConceptScore W4376988377C134306372 @default.
- W4376988377 hasConceptScore W4376988377C151730666 @default.
- W4376988377 hasConceptScore W4376988377C15627037 @default.
- W4376988377 hasConceptScore W4376988377C183115368 @default.
- W4376988377 hasConceptScore W4376988377C199479865 @default.
- W4376988377 hasConceptScore W4376988377C24890656 @default.
- W4376988377 hasConceptScore W4376988377C2779343474 @default.
- W4376988377 hasConceptScore W4376988377C28826006 @default.
- W4376988377 hasConceptScore W4376988377C33923547 @default.
- W4376988377 hasConceptScore W4376988377C34862557 @default.
- W4376988377 hasConceptScore W4376988377C38409319 @default.
- W4376988377 hasConceptScore W4376988377C40709475 @default.
- W4376988377 hasConceptScore W4376988377C41008148 @default.
- W4376988377 hasConceptScore W4376988377C62884695 @default.
- W4376988377 hasConceptScore W4376988377C86803240 @default.
- W4376988377 hasConceptScore W4376988377C93779851 @default.
- W4376988377 hasLocation W43769883771 @default.
- W4376988377 hasOpenAccess W4376988377 @default.
- W4376988377 hasPrimaryLocation W43769883771 @default.
- W4376988377 hasRelatedWork W1577037560 @default.
- W4376988377 hasRelatedWork W1663225052 @default.
- W4376988377 hasRelatedWork W2046932560 @default.
- W4376988377 hasRelatedWork W2091352395 @default.
- W4376988377 hasRelatedWork W2106787187 @default.
- W4376988377 hasRelatedWork W2113315237 @default.
- W4376988377 hasRelatedWork W3090723141 @default.
- W4376988377 hasRelatedWork W4312365456 @default.
- W4376988377 hasRelatedWork W65282041 @default.
- W4376988377 hasRelatedWork W1821327223 @default.
- W4376988377 isParatext "false" @default.
- W4376988377 isRetracted "false" @default.
- W4376988377 workType "article" @default.