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Author (up) Ferrer-Sanchez, A.; Martin-Guerrero, J.; Ruiz de Austri, R.; Torres-Forne, A.; Font, J.A. url  doi
openurl 
  Title Gradient-annihilated PINNs for solving Riemann problems: Application to relativistic hydrodynamics Type Journal Article
  Year 2024 Publication Computer Methods in Applied Mechanics and Engineering Abbreviated Journal Comput. Meth. Appl. Mech. Eng.  
  Volume 424 Issue Pages 116906 - 18pp  
  Keywords Riemann problem; Euler equations; Machine learning; Neural networks; Relativistic hydrodynamics  
  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 forces 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. The performance of our methodology 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 the 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 corresponding error obtained with a second-order, central, shock-capturing scheme. In all problems investigated, the accuracy reached by the GA-PINN model is comparable to that obtained with a shock-capturing scheme, achieving a performance superior to that of the baseline PINN algorithm in general. 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 variables, 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 methodology discussed in this paper could be a valuable tool to model relativistic flows in astrophysics and particle physics, characterized by the prevalence of discontinuous solutions.  
  Address [Ferrer-Sanchez, Antonio; Martin-Guerrero, JoseD.] ETSE UV, Elect Engn Dept, IDAL, Avgda Univ S-N, Valencia 46100, Spain, Email: Antonio.Ferrer-Sanchez@uv.es  
  Corporate Author Thesis  
  Publisher Elsevier Science Sa Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0045-7825 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:001221797400001 Approved no  
  Is ISI yes International Collaboration no  
  Call Number IFIC @ pastor @ Serial 6126  
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