Tabel van links Abstract and 1. Introduction Abstract and 1. Introduction 1.1. Introductory remarks 1.2. Basics of neural networks 1.3. About the entropy of direct PINN methods 1.4. Organization of the paper 
 
 
 
 
 
 
 
 
 
 
 
 
 Non-diffusive neural network solver for one dimensional scalar HCLs 2.1. One shock wave 2.2. Arbitrary number of shock waves 2.3. Shock wave generation 2.4. Shock wave interaction 2.5. Non-diffusive neural network solver for one dimensional systems of CLs 2.6. Efficient initial wave decomposition 
 
 
 
 Gradient descent algorithm and efficient implementation 3.1. Classical gradient descent algorithm for HCLs 3.2. Gradient descent and domain decomposition methods 
 
 
 
 
 
 
 
 
 Numerics 4.1. Practical implementations 4.2. Basic tests and convergence for 1 and 2 shock wave problems 4.3. Shock wave generation 4.4. Shock-Shock interaction 4.5. Entropy solution 4.6. Domain decomposition 4.7. Nonlinear systems 
 
 Conclusion and References Non-diffusiewe neurale netwerk oplosmiddel vir een-dimensionele skalar HCLs Conclusion and References 5 Konklusie In hierdie artikel het ons 'n oorspronklike metode voorgestel vir die oplos van hiperboliese bewaringswette met behulp van 'n nie-diffusiewe neurale netwerkmetode. die DL's en die bewaringswetgewing op te los in die subdomeine wat die DL's definieer, en waar die oplossing glad is. Ons het neurale netwerke gebruik om die DL's en die oplossing van bewaringswetgewing in elke van die subdomeine te benader. Die netwerke word opgelei deur 'n funksionele verlies te verminder wat die (norm van die) oorblywings van bewaringswetgewing, grense en aanvanklike toestande en Rankine-Hugoniot-omstandighede meet. Hierdie benadering laat 'n berekening van skokgolwe toe sonder om 'n swak formulering van HCL te gebruik. Ander funksies kan gebruik word om die oplossing en die DL's te benader, maar neurale netwerke bied interessante funksies. Inderdaad, hulle toela Wanneer die globale verlies funksioneel benadering is stadig om te convergeer, kan 'n vinnig converge en verontrustend parallel (Schwarz) domein ontbindingsmetode gebruik word. In a future work, we plan to apply to this methodology to higher dimensional problems. CRediT authorship contribution statement Die skrywers het gelykgemaak. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Data availability Geen data is gebruik vir die navorsing beskryf in hierdie artikel. Verwysings [1] J.-M. Ghidaglia and F. Pascal. The normal flux method at the boundary for multidimensional finite volume approximations in CFD. Eur. J. Mech. B Fluids, 24(1):1–17, 2005. [2] E. Godlewski en P.-A. Raviart. Hyperbolieke stelsels van bewaringswette, volume 3/4 van Math'ematiques & Applications (Paris) [Matematiese en toepassings]. [3] D. 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 Die skrywers: (1) Emmanuel LORIN, Skool van Wiskunde en Statistiek, Carleton Universiteit, Ottawa, Kanada, K1S 5B6 en Centre de Recherches Mathematiques, Universit ́e de Montr ́eal, Montreal, Kanada, H3T 1J4 (elorin@math.carleton.ca); (2) Arian NOVRUZI, korrespondent van die Departement van Wiskunde en Statistiek, Universiteit van Ottawa, Ottawa, ON K1N 6N5, Kanada (novruzi@uottawa.ca). Authors: (1) Emmanuel LORIN, Skool van Wiskunde en Statistiek, Carleton Universiteit, Ottawa, Kanada, K1S 5B6 en Centre de Recherches Mathematiques, Universit ́e de Montr ́eal, Montreal, Kanada, H3T 1J4 (elorin@math.carleton.ca); (2) Arian NOVRUZI, korrespondent van die Departement van Wiskunde en Statistiek, Universiteit van Ottawa, Ottawa, ON K1N 6N5, Kanada (novruzi@uottawa.ca). 
 
 Hierdie artikel is beskikbaar onder CC by 4.0 Deed (Attribution 4.0 International) lisensie. Hierdie artikel is beskikbaar onder CC by 4.0 Deed (Attribution 4.0 International) lisensie. available on arxiv

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