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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 |
Type |
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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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 |
Balibrea-Correa, J.; Lerendegui-Marco, J.; Babiano-Suarez, V.; Caballero, L.; Calvo, D.; Ladarescu, I.; Olleros-Rodriguez, P.; Domingo-Pardo, C. |
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Title |
Machine Learning aided 3D-position reconstruction in large LaCl3 crystals |
Type |
Journal Article |
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Year |
2021 |
Publication |
Nuclear Instruments & Methods in Physics Research A |
Abbreviated Journal |
Nucl. Instrum. Methods Phys. Res. A |
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Volume |
1001 |
Issue |
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Pages |
165249 - 17pp |
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Keywords |
Gamma-ray; Position sensitive detectors; Monolithic crystals; Compton imaging; Machine Learning; Convolutional Neural Networks; Total Energy Detector; Neutron capture cross-section |
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Abstract |
We investigate five different models to reconstruct the 3D gamma-ray hit coordinates in five large LaCl3(Ce) monolithic crystals optically coupled to pixelated silicon photomultipliers. These scintillators have a base surface of 50 x 50 mm(2) and five different thicknesses, from 10 mm to 30 mm. Four of these models are analytical prescriptions and one is based on a Convolutional Neural Network. Average resolutions close to 1-2 mm fwhm are obtained in the transverse crystal plane for crystal thicknesses between 10 mm and 20 mm using analytical models. For thicker crystals average resolutions of about 3-5 mm fwhm are obtained. Depth of interaction resolutions between 1 mm and 4 mm are achieved depending on the distance of the interaction point to the photosensor surface. We propose a Machine Learning algorithm to correct for linearity distortions and pin-cushion effects. The latter allows one to keep a large field of view of about 70%-80% of the crystal surface, regardless of crystal thickness. This work is aimed at optimizing the performance of the so-called Total Energy Detector with Compton imaging capability (i-TED) for time-of-flight neutron capture cross-section measurements. |
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Address |
[Balibrea-Correa, J.; Lerendegui-Marco, J.; Babiano-Suarez, V.; Caballero, L.; Calvo, D.; Ladarescu, I.; Olleros-Rodriguez, P.; Domingo-Pardo, C.] Univ Valencia, CSIC, Inst Fis Corpuscular, Valencia, Spain, Email: javier.balibrea@ific.uv.es |
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Publisher |
Elsevier |
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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:000641308300007 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
no |
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Call Number |
IFIC @ pastor @ |
Serial |
4803 |
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