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## Оптимизация физико-информированных нейронных сетей для решения нелинейного уравнения Шредингера

Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика). 2023. Т. 514. № 2. С. 28-38.

Чупров И. А., Гао Ц., Efremenko D., Казаков Е., Buzaev F., Земляков В. В.

Buzaev F., Чупров И. А., Efremenko D., Doklady Mathematics 2023 Vol. 108 No. S2 P. S186-S195

Physics Informed Neural Networks (PINN) is a promising method for solving partial differential equations using machine learning. In this paper we consider the application of PINN to the nonlinear Schrödinger equation to describe the propagation of signal in an optical fibre. The factors determining the convergence of PINN from the physical point of view are ...

Added: April 3, 2024

Buzaev F., Gao J., Ivan Chuprov et al., Machine Learning 2024 Vol. 113 No. 6 P. 3675 -3692

Physics-informed neural networks (PINN) has emerged as a promising approach for solving partial differential equations (PDEs). However, the training process for PINN can be computationally expensive, limiting its practical applications. To address this issue, we investigate several acceleration techniques for PINN that combine Fourier neural operators, separable PINN, and first-order PINN. We also propose novel ...

Added: December 19, 2023

Slunyaev A., Степанянц Ю. А., Physics of Fluids 2022 Vol. 34 No. 7 Article 077121

We study the nonlinear modulation property of flexural-gravity waves on a water surface covered by a compressed ice sheet of given thickness and density in a basin of a constant depth. For weakly nonlinear perturbations, we derive the nonlinear Schrodinger equation and investigate the conditions when a quasi-sinusoidal wave becomes unstable with respect to amplitude modulation. The ...

Added: October 13, 2022

Agalarov A. M., Gadzhimuradov T. A., Potapov A. A. et al., Modeling and Analysis of Information Systems 2018 Vol. 25 No. 1 P. 133-139

The multi-component extension problem of the (2 + 1)D-gauge topological Jackiw–Pi model describing the nonlinear quantum dynamics of charged particles in multi-layer Hall systems is considered. By applying the dimensional reduction (2 + 1)D → (1 + 1)D to Lagrangians with the Chern–Simons topologic fields , multi-component nonlinear Schrodinger equations for particles are constructed with ...

Added: December 20, 2022

Slunyaev A., Studies in Applied Mathematics 2019 Vol. 142 P. 385-413

Conditions of optimal (synchronized) collisions of any number of solitons and breathers are studied within the framework of the Gardner equation (GE) with positive cubic nonlinearity, which in the limits of small and large
amplitudes tends to other long-wave models, the classic and the modified Korteweg–de Vries equations. The local
solution for an isolated soliton or breather within the GE is obtained. ...

Added: March 11, 2019

Chabchoub A., Slunyaev A., Hoffmann N. et al., Frontiers in Physics 2021 Vol. 9 Article 633549

Solitons are coherent structures that describe the nonlinear evolution of wave localizations in hydrodynamics, optics, plasma and Bose-Einstein condensates. While the Peregrine breather is known to amplify a single localized perturbation of a carrier wave of finite amplitude by a factor of three, there is a counterpart solution on zero background known as the degenerate ...

Added: August 25, 2021

Serkhacheva N., Gainanova, A., Kuz’micheva G. et al., International Journal of Polymer Analysis and Characterization 2015 Vol. 20 No. 8 P. 743-753

This study produced for the first time composites based on polystyrene microspheres with nano-sized titania synthesized by sulfate and sol-gel methods, as well as commercial Hombifine N, Hombikat UV100, and Degussa P25. The starting samples and the composites were characterized by X-ray diffraction, scanning electron microscopy, nitrogen adsorption capacity, and IR spectroscopy. The highest content ...

Added: December 2, 2015

Захарова Т. В., Yuzhakov T., ООО «Макс Пресс», 2019

В настоящий сборник вошли тезисы докладов секции Вычислительной математики и кибернетики конференции «Ломоносовские чтения‑2019», проводимой Московским государственным университетом имени М. В. Ломоносова в 2019 году. ...

Added: December 13, 2023

Prudnikov V., Prudnikov P., Malyarenko P. et al., Journal of Experimental and Theoretical Physics 2020 Vol. 130 No. 2 P. 258-273

The influence of various initial magnetizations m0 and structural defects on the nonequilibrium critical behavior of the two-dimensional Ising model is numerically simulated by Monte Carlo methods. Based on analysis of the time dependence of magnetization and the two-time dependences of autocorrelation function and dynamic susceptibility, we revealed the influence of logarithmic corrections and the ...

Added: June 29, 2020

Зайцев В. И., Щавелин В. М., М. : ВИНИТИ РАН, 1985

Added: November 30, 2020

Aaij R., Abdelmotteleb A. S., Abellan Beteta C. et al., Physical Review Letters 2023 Vol. 131 No. 7 Article 071901

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.131.071901 ...

Added: December 4, 2023

Пенза : ПГУ, 2015

В сборник трудов включены доклады юбилейного ХХ-го Международного симпозиума «Надежность и качество», проходившего с 25 по 31 мая 2015 г. в городе Пензе.
Рассмотрены актуальные проблемы теории и практики повышения надежности и качества; эффективности внедрения инновационных и информационных технологий в фундаментальных научных и прикладных исследованиях, образовательных и коммуникативных системах и средах, экономике и юриспруденции; методов и ...

Added: May 31, 2015

Zelenyi L., Malova H., Grigorenko E. et al., 2019 Vol. 61 P. 1-12

In this article we aim to highlight the problems related to the structure and stability of the
comparatively thin current sheets that were relatively recently discovered by space missions in
the magnetospheres of the Earth and planets, as well as in the solar wind. These magnetoplasma
structures are universal in collisionless cosmic plasmas and can play a key ...

Added: March 22, 2019

Маршалко Г. Б., Денисенко Д. В., Рудской В. И. et al., Journal of Experimental and Theoretical Physics 2019 Vol. 128 No. 4 P. 552-559

Following the approach proposed in [3], we estimate resources of a quantum computer required for solving the key search problem of block cipher algorithms Kuznechik and Magma, defined by the national standard GOST R 34.12-2015, with the use of Grover’s quantum algorithm. ...

Added: October 7, 2022

Молотков С. Н., Арбеков И. М., Журнал экспериментальной и теоретической физики 2017 Т. 152 № 1 С. 62-78

The proof of the security of quantum key distribution is a rather complex problem. Security is
defined in terms different from the requirements imposed on keys in classical cryptography. In quantum
cryptography, the security of keys is expressed in terms of the closeness of the quantum state of an eavesdropper
after key distribution to an ideal quantum state ...

Added: March 2, 2018

Aaij R., Abdelmotteleb A. S., Abellan Beteta C. et al., Journal of High Energy Physics 2023 No. 6 Article 22

https://link.springer.com/article/10.1007/JHEP06(2023)022#Abs1 ...

Added: December 4, 2023

Aaij R., Abdelmotteleb A. S., Abellan Beteta C. et al., Chinese Physics C 2023 Vol. 47 No. 9 Article 093001

https://iopscience.iop.org/article/10.1088/1674-1137/ace9c8#artAbst ...

Added: December 4, 2023

Morozov I., Norman G. E., Insepov Z. et al., Physical Review Special Topics - Accelerators and Beams 2012 Vol. 15 P. 053501

This paper describes the surface environment of the dense plasma arcs that damage rf accelerators, tokamaks, and other high gradient structures. We simulate the dense, nonideal plasma sheath near a metallic surface using molecular dynamics (MD) to evaluate sheaths in the non-Debye region for high density, low temperature plasmas. We use direct two-component MD simulations ...

Added: October 28, 2013

Aaij R., Abdelmotteleb A. S., Abellan Beteta C. et al., Journal of High Energy Physics 2023 Vol. 2023 No. 08 Article 93

https://link.springer.com/article/10.1007/JHEP08(2023)093#Abs1 ...

Added: November 30, 2023

Dmitriev A., Kornilov V., Dmitriev V. et al., Frontiers in Physics 2022 Vol. 10 No. 839383 Article 839383

The sandpile cellular automata, despite the simplicity of their basic rules, are adequate mathematical models of real-world systems, primarily open nonlinear systems capable to self-organize into the critical state. Such systems surround us everywhere. Starting from processes at microscopic distances in the human brain and ending with large-scale water flows in the oceans. The detection ...

Added: March 14, 2022

Faizullina Kamilla, Pchelintsev Ilya, Burovskiy E., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2021 Vol. 104 Article 054501

We study a lattice model of a single magnetic polymer chain, where Ising spins are located on the sites of a lattice self-avoiding walk in $d=2$. We consider the regime where both conformations and magnetic degrees of freedom are dynamic, thus the Ising model is defined on a dynamic lattice and conformations generate an annealed disorder. Using Monte Carlo ...

Added: November 5, 2021

Roman Moskalenko, Evgeni Burovski, Shchur L., Journal of Physics: Conference Series 2021 Vol. 1740 Article 012057

We consider a spatially distributed evolutionary game based on the Prisoner’s
Dilemma with agents arranged on a three-dimensional simple cubic lattice. Comparing to twodimensional arrangements, we find that the larger number of neighbors favors the formation of
spatial chaos: the steady state of the game is chaotic unless the payoff parameter is small. ...

Added: January 23, 2021

Aaij R., Abdelmotteleb A. S., Abellán Beteta C. et al., Physical Review Letters 2022 Vol. 129 No. 9 Article 091801

The first study of the angular distribution of μþμ− pairs produced in the forward rapidity region via the Drell-Yan reaction pp → γ=Z þ X → lþl− þ X is presented, using data collected with the LHCb detector at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 5.1 fb−1. The coefficients ...

Added: December 29, 2022

Aaij R., Abdelmotteleb A. S., Abellán Beteta C. et al., Nature Communications 2022 No. 13 Article 3351

Quantum chromodynamics, the theory of the strong force, describes interactions of coloured quarks and gluons and the formation of hadronic matter. Conventional hadronic matter consists of baryons and mesons made of three quarks and quark-antiquark pairs, respectively. Particles with an alternative quark content are known as exotic states. Here a study is reported of an ...

Added: December 31, 2022