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Optimization of Physics-Informed Neural Networks for Solving the Nolinear Schrödinger Equation
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 investigated. Estimates of the convergence domain of the method in terms of fibre length and pulse energy are obtained. It is shown that the application sinusoidal activation function, as well as the weighting of the loss function terms are able to extend the convergence region of PINN with respect to fibre length and pulse energy. A generalization of the method (meta-PINN) is derived, allowing to solve the equation at its various parameters by using the pre-trained neural network.
Ивченко В. С., Иевлева В. А., Matienko D. et al., Журнал технической физики 2026 № 9 С. 1738–1749
Задача о возбуждении бегущих фонон-поляритонных волн на поверхности полярного кристалла падающей извне световой волной (с частотой, близкой к частоте решеточных колебаний) решена теоретически только для бесконечной открытой поверхности кристалла. В случаях, когда часть поверхности покрыта металлической маской, препятствующей проникновению возбуждающего излучения к атомам среды, и эта маска имеет произвольную форму, общепризнанного решения неоднородной задачи нет. ...
Added: October 20, 2026
Logvenkov S. A., Известия РАН. Механика жидкости и газа 2026 № 3 С. 59–75
The problem of the evolution of cell volume fraction in a spherical aggregate composed of cells,
extracellular matrix, and fluid is considered. The aggregate is surrounded by extracellular matrix. The
problem formulation employs a multiphase model of a biological continuum, previously developed by the
author, consisting of two actively interacting solid phases and a fluid. The propagation of ...
Added: October 20, 2026
Lavrukhina E. A., Krasavin D. P., Krishtopenko S. S. et al., Physical Review B: Condensed Matter and Materials Physics 2026 Vol. 114 No. 22 Article 225414
We study coherent electric manipulation of magnetic field induced localized states at a double kink of a helical edge in a HgTe/CdHgTe quantum well. An in-plane magnetic field opens a gap in the one-dimensional (1D) edge spectrum, while changes in the edge orientation generate localized in-gap states at the kinks. We show that, for suitable ...
Added: October 19, 2026
Lev Pyatko, Sergey Aksenov, Regular and Chaotic Dynamics 2026 Vol. 31 No. 5 P. 794–813
In the circular restricted three-body problem, families of periodic and quasi-periodic orbits exist in the vicinity of the libration points and are of significant interest for practical applications. This work presents a neural network-based algorithm for orbit construction and station-keeping, applicable to both periodic and quasi-periodic orbits near collinear libration points. The method employs a ...
Added: October 19, 2026
Vorontsova T., М.: Академия, 2025.
The textbook has been prepared in accordance with the requirements of the federal state educational standards for secondary vocational education and is intended for studying the professional modules “Information Security in Information and Telecommunication Systems and Networks Using Software and Hardware‑Software Tools, Including Cryptographic Protection Tools” and “Information Security in Automated Systems Using Software and ...
Added: October 19, 2026
Смерчанский П. С., Koledov V. V., Kamantsev A. P. et al., Physics of Metals and Metallography 2026 Vol. 127 No. 6-7 P. 689–693
Heusler alloys of the Ni2MnX family, where X = Ga, In, Sn, …, which have been shown to exhibit
giant magnetocaloric effect (MCE) and magnetically controlled shape memory effect due to thermoelastic
magnetostructural phase transition (MSPT), continue to attract attention. However, these functional properties are fully manifested in strong magnetic fields of at least several T. Currently, ...
Added: October 19, 2026
Naumov A., Рубцов А. С., Samsonov S. et al., Успехи математических наук 2026 Т. 81 № 4 (490) С. 161–162
Краткое сообщение рассматривает Моментные оценки для стохастической аппроксимации ...
Added: October 17, 2026
Roman Avdeev, Yulia Zaitseva, Mediterranean Journal of Mathematics 2026 Vol. 23 No. 7 Article 224
We provide an infinite series of commutative finite-dimensional Gorenstein local algebras A_n for n ≥ 2. We give an elementary proof that the maximal ideal of every algebra A_n possesses a one-dimensional subspace that is different from the socle and invariant under the automorphism group of A_n. The latter implies that the algebras A_n fail ...
Added: October 17, 2026
Gordin V. A., Efremenko D., Boundary-Layer Meteorology 2026 Vol. 192 No. 51
An inverse problem of reconstructing the turbulent exchange tensor from large archives of observed wind profiles within the Åkerblom–Ekman (A-E) model framework is investigated using high-vertical-resolution radiosonde observations. The reconstructed tensor provides improved agreement between modeled and observed wind profiles compared to classical formulations based on real turbulent exchange coefficient. Instead of the classical A-E ...
Added: October 16, 2026
Kuznetsov A. P., Sedova Y. V., Stankevich N., Chaos, Solitons and Fractals 2026 Vol. 213 No. 12 Article 119309
We analyze the interaction of a quasi-periodic subsystem, in which two-, three-, and four- frequency quasi-periodic oscillations are possible, with a chaotic subsystem. A discrete version is obtained via the Euler scheme from the corresponding flow model. The dynamics of individual subsystems are discussed, including quasi-periodic bifurcations of invariant tori and the occur rence of ...
Added: October 16, 2026
Aleksei Samarin, Nazarenko A., Nazarenko D. et al., Machine Learning and Knowledge Extraction 2026 Vol. 8 No. 10 Article 330
Automated microscopic image analysis is essential for quantitative microbiology, yet manual acquisition and generic recognition models struggle with morphological variability and scene artifacts. We address both ends of this pipeline. First, we present a low-cost, open-source acquisition system, based on an Arduino UNO R3 microcontroller and NEMA 17 stepper motors, that automates focusing, magnification, and ...
Added: October 14, 2026
Тукачев Н. В., Bataev V., Abramenkov A. et al., Computational and Theoretical Chemistry 2016 No. 1080 P. 23–32
Electronic state calculations, such as equilibrium geometry parameters, harmonic vibrational frequencies and potential barriers to conformational transitions (as well as conformer energy differences in excited states), using ab initio methods, such as MP2, CCSD(T), CASSCF, CASPT2 and MRCI, were carried out on the formamide molecule in the ground (S0) and the lowest excited singlet (S1) ...
Added: October 14, 2026
Тукачев Н. В., Bataev V. А., Godunov I. А., Journal of Quantitative Spectroscopy and Radiative Transfer 2016 Vol. 177 P. 291–300
For conformers of the N-methylformamide (HCONHCH3) molecule, calculations of equilibrium geometry parameters, harmonic vibration frequencies, energy differences and potential barriers to conformational transitions were performed in the ground (S0) and lowest excited singlet (S1) and triplet (T1) electronic states. In the S0 state, the molecule exists in trans and cis stable conformations (having Cs symmetry). ...
Added: October 14, 2026
Тукачев Н. В., Bataev V. А., Godunov I. А., Journal of Quantitative Spectroscopy and Radiative Transfer 2017 Vol. 192 P. 30–41
For acetamide molecule (CH3CONH2) in the ground (S0) and lowest excited singlet (S1) and triplet (T1) electronic states calculations of equilibrium geometry parameters, harmonic vibrational frequencies and barriers to conformational transitions (also conformer energy differences in excited states) using following ab initio methods: MP2, CCSD(T), CASSCF, CASPT2 and MRCI were performed. One-, two- and three-dimensional ...
Added: October 14, 2026
Тукачев Н. В., Bataev V. A., Godunov I. A., Computational and Theoretical Chemistry 2017 Vol. 1113 P. 82–93
Equilibrium geometry parameters, harmonic vibrational frequencies and barriers to conformational transitions and conformer energy differences for N-methylacetamide (CH3CONHCH3) molecule in S0, S1 and T1 electronic states were calculated in MP2 (S0) and CASPT2 (S1, T1) levels of theory. It is known that there are two planar (or effectively planar) conformers of N-methylacetamide in the ground ...
Added: October 14, 2026
Тукачев Н. В., Maslennikov D., Sosorev A. et al., The Journal of Physical Chemistry Letters 2019 Vol. 10 No. 12 P. 3232–3239
Conformational space of polyphenylenevinylene oligomers is systematically investigated computationally at energies relevant for room temperature dynamics in a solvent and in a solid state. Our calculations show that optimal oligomer structures are essentially planar. However, lack of a deep minimum at the planar geometry allows for large molecular deformations even at very low temperatures. At ...
Added: October 14, 2026
Buzaev F., Andrei Ermakov, Ivanova M. et al., , in: AI & PDE: ICLR 2026 Workshop on AI and Partial Differential Equations.: [б.и.], 2026.
Transformer-based physics-informed neural networks (PINNs) have recently improved PDE solving by modeling spatiotemporal interactions with self-attention, yet most variants still rely on absolute coordinate embeddings. We ask whether relative positional structure - a key inductive bias in modern Transformers can be made coordinate-aware and yield an accuracy boost with minimal overhead for PDE PINNs. Building ...
Added: June 24, 2026
Khassan Y., Efremenko D., Buzaev F. et al., , in: AI & PDE: ICLR 2026 Workshop on AI and Partial Differential Equations.: [б.и.], 2026.
Singularities in the source functions of partial differential equations (PDEs) pose significant challenges for physics-informed neural networks (PINNs), often leading to numerical instability and requiring a large number of sampling points to achieve accurate solutions, which increases computational costs. In this paper, we propose a novel sampling strategy that uses diffusion models for generative sampling ...
Added: June 24, 2026
Bugaev E., Buzaev F., Efremenko D. et al., , in: AI & PDE: ICLR 2026 Workshop on AI and Partial Differential Equations.: [б.и.], 2026.
This study introduces enhancements to physics-constrained neural networks (PCNNs) that improve the accuracy and stability of hybrid short-term weather forecasting models. Building on the WeatherGFT architecture, three innovations are proposed. First, an upgraded numerical solver, combining a fifth-order weighted essentially non-oscillatory scheme (WENO-5), a beta-plane approximation, and subgrid-scale viscosity, permits a fourfold increase in the ...
Added: June 24, 2026
Buzaev F., Чупров И. А., Efremenko D. et al., Doklady Mathematics 2025
Single-mode optical fibers (SMFs) have become the foundation of modern communication systems. However, their capacity is expected to reach its theoretical limit in the near future. The use of multimode fibers (MMF) is seen as one of the most promising solutions to address this capacity deficit. The multimode nonlinear Schrödinger equation (MMNLSE) describing light propagation ...
Added: April 28, 2025
F. A. Buzaev, D. S. Efremenko, I. A. Chuprov et al., Doklady Mathematics 2025 Vol. 110 P. S8–S14
The accuracy of solving partial differential equations using physics-informed neural networks (PINNs) significantly depends on their architecture and the choice of hyperparameters. However, manually searching for the optimal configuration can be difficult due to the high computational complexity. In this paper, we propose an approach for optimizing the PINN architecture using a differential evolution algorithm. ...
Added: April 28, 2025
Slunyaev A., Physica D: Nonlinear Phenomena 2025 Vol. 474 Article 134575
We reveal and discuss the self-similar structure of breather solutions of the cubic nonlinear Schrödinger
equation which describe the modulational instability of infinitesimal perturbations of plane waves. All the time
of the evolution, the breather solutions are represented by fully coherent perturbations with self-similar shapes.
The evolving modulations are characterized by constant values of the similarity parameter of ...
Added: February 19, 2025
Slunyaev A., Rozental R., Ginzburg N. et al., Chaos, Solitons and Fractals 2024 Vol. 183 Article 114884
Within the framework of numerical simulations, we study the gyrotron dynamics under conditions of a significant
excess of the operating current over the starting value, when the generation of electromagnetic pulses with
anomalously large amplitudes (“rogue waves”) can be realized. The averaged shape of high-power pulses is
shown to be very close to the celebrated Peregrine breather. At ...
Added: November 22, 2024
Чупров И. А., Гао Ц., Efremenko D. et al., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2023 Т. 514 № 2 С. 28–38
Физико-информированные нейронные сети (Physics Informed Neural Networks – PINN) являются перспективным методом решения уравнений в частных производных с помощью машинного обучения. В работе рассмотрено применение PINN к нелинейному уравнению Шредингера для описания ...
Added: December 19, 2023