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Author |
Ferrer-Sanchez, A.; Martin-Guerrero, J.; Ruiz de Austri, R.; Torres-Forne, A.; Font, J.A. |
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Title |
Gradient-annihilated PINNs for solving Riemann problems: Application to relativistic hydrodynamics |
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Journal Article |
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Year |
2024 |
Publication |
Computer Methods in Applied Mechanics and Engineering |
Abbreviated Journal |
Comput. Meth. Appl. Mech. Eng. |
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Volume |
424 |
Issue |
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Pages |
116906 - 18pp |
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Keywords |
Riemann problem; Euler equations; Machine learning; Neural networks; Relativistic hydrodynamics |
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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. |
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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 |
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Publisher |
Elsevier Science Sa |
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English |
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ISSN  |
0045-7825 |
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Notes |
WOS:001221797400001 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
no |
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Call Number |
IFIC @ pastor @ |
Serial |
6126 |
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Author |
Villanueva-Domingo, P.; Villaescusa-Navarro, F. |
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Title |
Removing Astrophysics in 21 cm Maps with Neural Networks |
Type |
Journal Article |
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Year |
2021 |
Publication |
Astrophysical Journal |
Abbreviated Journal |
Astrophys. J. |
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Volume |
907 |
Issue |
1 |
Pages |
44 - 14pp |
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Keywords |
Cosmology; Cold dark matter; Dark matter; Dark matter distribution; H I line emission; Intergalactic medium; Cosmological evolution; Convolutional neural networks; Large-scale structure of the universe |
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Abstract |
Measuring temperature fluctuations in the 21 cm signal from the epoch of reionization and the cosmic dawn is one of the most promising ways to study the universe at high redshifts. Unfortunately, the 21 cm signal is affected by both cosmology and astrophysics processes in a nontrivial manner. We run a suite of 1000 numerical simulations with different values of the main astrophysical parameters. From these simulations we produce tens of thousands of 21 cm maps at redshifts 10 <= z <= 20. We train a convolutional neural network to remove the effects of astrophysics from the 21 cm maps and output maps of the underlying matter field. We show that our model is able to generate 2D matter fields not only that resemble the true ones visually but whose statistical properties agree with the true ones within a few percent down to scales 2 Mpc(-1). We demonstrate that our neural network retains astrophysical information that can be used to constrain the value of the astrophysical parameters. Finally, we use saliency maps to try to understand which features of the 21 cm maps the network is using in order to determine the value of the astrophysical parameters. |
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Address |
[Villanueva-Domingo, Pablo] Univ Valencia, Inst Fis Corpuscular IFIC, CSIC, Apartado Correos 22085, E-46071 Valencia, Spain, Email: Pablo.Villanueva@ific.uv.es; |
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Publisher |
Iop Publishing Ltd |
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Language |
English |
Summary Language |
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ISSN |
0004-637x |
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Notes |
WOS:000612333400001 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
4698 |
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