左のテーブル Abstract and 1. Introduction 抽象と1 導入 1.1 入門コメント 1.2 ニューラルネットワークの基本 1.3.Direct PINN methods entropyについて 4.紙の組織化 
 
 
 
 
 
 
 
 
 
 
 
 
 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-diffusive neural network solver for one-dimensional scalar HCL 結論と参照 5.結論 この論文では、非散布性ニューラルネットワークの方法を使用してハイパーボリック保存法を解決するためのオリジナルな方法を提案しました。 DLs と DLs が定義するサブドメインで保存法を解決し、その解決がスムーズな場所で ニューラルネットワークを使用して DLs と各サブドメインの保存法の解決に近づきました ネットワークは、保存法、境界および初期条件およびRankine-Hugoniot 条件の残留を測定する機能損失を最小限に抑えることによって訓練されています このアプローチは、HCL の弱い公式を使用することなくショック波の計算を可能にします 他の機能は、ソリューションと DLs を近づけるために使用できますが、ニューラルネットワークは興味深い機能を提供します。実際には、それらは、衍生物の近似エラーを回避し、アルゴリズムの実装を容易に グローバル損失機能アプローチが近づくのが遅い場合、急速に近づき、恥ずかしく平行(Schwarz)ドメイン分解方法が使用されることがあります。 将来の仕事では、この方法論をより高い次元の問題に適用する予定です。 CRediT authorship contribution statement 著者は同様に貢献した。 Declaration of competing interest 著者は、この論文で報告された仕事に影響を与える可能性のある競合する財務的利益や個人的な関係が知られていないことを宣言する。 Data availability この記事で説明された研究のためのデータは使用されていません。 参照 [1] J.-M. Ghidaglia and F. Pascal. The normal flow method at the boundary for multidimensional finite volume approximations in CFD. Eur. J. Mech. B Fluids, 24(1):1-17, 2005. [2] E. Godlewski and P.-A. Raviart. 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Geuzaine. A non-overlapping domain decomposition method with high-order transmission conditions and cross-point treatment for Helmholtz problems. Comput. Methods Appl. Mech. Engrg., 368:113162, 23, 2020. [34] I. Badia, B. Caudron, X. Antoine, and C. Geuzaine. A well conditioned weak coupling of boundary element and high-order finite element methods for time-harmonic electromagnetic scattering by inhomogeneous objects. SIAM J. Sci. Comput., 44(3):B640–B667, 2022. [35] X. Antoine and C. Besse. Unconditionally stable discretization schemes of non-reflecting boundary conditions for the one-dimensional Schrodinger equation. J. Comput. Phys., 188(1):157–175, 2003. [36] R. Gorenflo. Fractional calculus: Some numerical methods. In CISM Courses and Lectures, volume 378. Springer, 1997. [37] X. Antoine, E. Lorin, and Q. Tang. A friendly review to absorbing boundary conditions and perfectly matched layers for classical and relativistic quantum wave equations. 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 著者: (1) Emmanuel LORIN, School of Mathematics and Statistics, Carleton University, Ottawa, Canada, K1S 5B6 and Centre de Recherches Mathematiques, Universit ́e de Montr ́eal, Montreal, Canada, H3T 1J4 (elorin@math.carleton.ca) (2)アリアン・ノブルジ(Arian NOVRUZI)は、カナダのオタワ大学数学および統計学部(Ottawa University, ON K1N 6N5, Canada)の著者(novruzi@uottawa.ca)。 Authors: (1) Emmanuel LORIN, School of Mathematics and Statistics, Carleton University, Ottawa, Canada, K1S 5B6 and Centre de Recherches Mathematiques, Universit ́e de Montr ́eal, Montreal, Canada, H3T 1J4 (elorin@math.carleton.ca) (2)アリアン・ノブルジ(Arian NOVRUZI)は、カナダのオタワ大学数学および統計学部(Ottawa University, ON K1N 6N5, Canada)の著者(novruzi@uottawa.ca)。 
 
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A Non-Diffusive Neural Network Method for Solving Hyperbolic Conservation Laws ハイパーボリック保存法則

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