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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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Elsevier Science Sa |
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English |
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Series Volume |
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Edition |
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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 |
Babiano, V.; Caballero, L.; Calvo, D.; Ladarescu, I.; Olleros, P.; Domingo-Pardo, C. |
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Title |
gamma-Ray position reconstruction in large monolithic LaCl3(Ce) crystals with SiPM readout |
Type |
Journal Article |
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Year |
2019 |
Publication |
Nuclear Instruments & Methods in Physics Research A |
Abbreviated Journal |
Nucl. Instrum. Methods Phys. Res. A |
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Volume |
931 |
Issue |
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Pages |
1-22 |
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Keywords |
Gamma-ray; Position-sensitive detectors; Monolithic crystals; Spatial resolution; Neural networks |
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Abstract |
We report on the spatial response characterization of large LaCl3(Ce) monolithic crystals optically coupled to 8 x 8 pixel silicon photomultiplier (SiPM) sensors. A systematic study has been carried out for 511 keV gamma-rays using three different crystal thicknesses of 10 mm, 20 mm and 30 mm, all of them with planar geometry and a base size of 50 x 50 mm(2). In this work we investigate and compare two different approaches for the determination of the main gamma-ray hit location. On one hand, methods based on the fit of an analytical model for the scintillation light distribution provide the best results in terms of linearity and field of view, with spatial resolutions close to similar to 1 mm FWHM. On the other hand, position reconstruction techniques based on neural networks provide similar linearity and field-of-view, becoming the attainable spatial resolution similar to 3 mm FWHM. For the third space coordinate z or depth-of-interaction we have implemented an inverse linear calibration approach based on the cross-section of the measured scintillation-light distribution at a certain height. The detectors characterized in this work are intended for the development of so-called Total Energy Detectors with Compton imaging capability (i-TED), aimed at enhanced sensitivity and selectivity measurements of neutron capture cross sections via the time-of-flight (TOF) technique. |
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Address |
[Babiano, V; Caballero, L.; Calvo, D.; Ladarescu, I; Olleros, P.; Domingo-Pardo, C.] Univ Valencia, Inst Fis Corpuscular, CSIC, Valencia, Spain, Email: domingo@ific.uv.es |
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Publisher |
Elsevier Science Bv |
Place of Publication |
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Editor |
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Language |
English |
Summary Language |
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Original Title |
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Series Editor |
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Abbreviated Series Title |
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Series Volume |
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Edition |
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ISSN |
0168-9002 |
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Conference |
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Notes |
WOS:000466151600001 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
no |
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Call Number |
IFIC @ pastor @ |
Serial |
4015 |
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