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Scaling transformation of the multimode nonlinear Schrödinger equation for physics-informed neural networks
Чупров И. А., Efremenko D., Gao J., Anisimov P., Zemlyakov V.
Single-mode optical fibers (SMFs) have become the backbone of modern communication systems. However, their throughput is expected to reach its theoretical limit in the nearest future. Utilization of multimode fibers (MMFs) is considered as one of the most promising solutions rectifying this capacity crunch. Nevertheless, differential equations describing light propagation in MMFs are a way more sophisticated than those for SMFs, which makes numerical modelling of MMF-based systems computationally demanding and impractical for the most part of realistic scenarios. Physics-informed neural networks (PINNs) are known to outperform conventional numerical approaches in various domains and have been successfully applied to the nonlinear Schrödinger equation (NLSE) describing light propagation in SMFs. A comprehensive study on application of PINN to the multimode NLSE (MMNLSE) is still lacking though. To the best of our knowledge, this paper is the first to deploy the paradigm of PINN for MMNLSE and to demonstrate that a straightforward implementation of PINNs by analogy with NLSE does not work out. We pinpoint all issues hindering PINN convergence and introduce a novel scaling transformation for the zero-order dispersion coefficient that makes PINN capture all relevant physical effects. Our simulations reveal good agreement with the split-step Fourier (SSF) method and extend numerically attainable propagation lengths up to several hundred meters. All major limitations are also highlighted.
Priority areas:
IT and mathematics
Language:
English
Snegirev A., Sychev S., Futures 2026 Vol. 183 P. 1–22
This study addresses the systemic identification and categorization of risks associated with AI development, arising from tensions between technological evolution and institutional, infrastructural, and economic contexts. Drawing on a constructionist methodology, we interpret technological risks as constitutive elements of expert communities' images of the future. Through in-depth interviews with 100 AI experts, proportionally representing corporate, ...
Added: September 23, 2026
Parshakov P., Paklina S., International Journal of Human-Computer Interaction 2026 P. 1–17
This study examines how emotional tone shapes user preference in human–large language model (LLM) interaction. Drawing on the Computers as Social Actors framework, we treat conversational AI as a social communicator whose affective cues influence user judgments. Using large-scale pairwise preference data from LMSYS Chatbot Arena, we model emotional tone through the Valence–Arousal–Dominance framework and ...
Added: September 23, 2026
Andrabi U., Wadood E., Ojha S. K. et al., IEEE Access 2026 Vol. 14 P. 103358–103375
The emergence of 5G networks, aimed at accommodating diverse service requirements such as enhanced Mobile Broadband (eMBB), Ultra-Reliable Low-Latency Communication (URLLC), and massive Machine-Type Communication (mMTC), has presented significant challenges in radio resource management and network slicing. In dynamic heterogeneous network systems, traditional heuristics and mathematical programming methods find it challenging to attain scalable multi-objective ...
Added: September 23, 2026
Paklina S., Parshakov P., Elena Rapoport, Scientometrics 2026 P. 1–26
Generative artificial intelligence has become a routine part of academic writing. While much of the debate has focused on questions of integrity and authorship, less attention has been paid to how AI-assisted writing may affect research evaluation itself. This paper asks a straightforward but important question: does the use of LLMs in academic writing change ...
Added: September 23, 2026
Kryzhanovskaya N., Makhov I., Dragunova A., St. Petersburg Polytechnical University Journal: Physics and Mathematics 2026 Vol. 19 No. 1.1 P. 98–104
The planar microcavity structure was grown using molecular-beam epitaxy.
Single-mode lasing was observed at a wavelength of 960 nm for pillars with a diameter of
15 μm. At 300 K, the lasing threshold was approximately 30 mW. Increasing the pump
power to 2.7 times the threshold power resulted in a mode energy shift of approximately
1 meV. This shift ...
Added: September 23, 2026
Kertesz-Farkas A., Acquaye F. L., Journal of Proteome Research 2026 Vol. 25 P. 3764–3768
Ultimately, most tandem mass spectrometry (MS/MS) proteomics experiments aim to not just detect but also quantify the proteins in a given complex sample. Here, we describe an extension to the Crux MS/MS analysis toolkit to enable label-free quantification of peptides. We demonstrate that Crux’s new quantification command, which is modeled after the algorithms implemented in ...
Added: September 23, 2026
Andreeva S., Gavrilov A. A., Dzhikirba K. R. et al., Physical Review B: Condensed Matter and Materials Physics 2026 Vol. 114 Article 134515
We examine plasma excitations with linear dispersion in a system of superconducting electrons in thin
NbN disks. Using frequency-domain terahertz spectroscopy, we study the evolution of plasmons up to critical
temperature Tc. The observed excitations tend to shift to the lower frequencies while temperature is increasing
and the spectral features vanish at T > Tc. We study the ...
Added: September 23, 2026
Образцова А. А., Ivanov K., Moiseev E. et al., Journal of Physics D: Applied Physics 2026 Vol. 59 No. 30 P. 305103
We demonstrate a thermo-optically tunable microlaser based on an InGaAs/GaAs quantum-dot (QD) active region employing a deformed limaçon-shaped cavity. The asymmetric geometry effectively lifts the degeneracy of high-Q whispering-gallery modes, enabling single-mode lasing. A side-mode suppression ratio exceeds 25 dB over a wide current range. Under continuous-wave electrical pumping, the device achieves a peak output power ...
Added: September 23, 2026
Budkov Y., Journal of Chemical Physics 2026 Vol. 165 No. 12 Article 124105
Exact theories of electrolyte structure must satisfy the nonlocal constraints imposed by electrostatic screening, yet these constraints are most commonly formulated only for homogeneous bulk systems and at the level of two-point correlations. Here, we develop a unified field-theoretic framework that extends them to general inhomogeneous ionic fluids and nonlinear charge correlations. Using a standard ...
Added: September 22, 2026
Боровицкая И. В., Пименов В. Н., Коршунов С. Н. et al., Перспективные материалы 2026 № 10 С. 37–54
Проведено сравнение, обобщение и систематизация механизмов эрозии и разрушения
поверхности малоактивируемых материалов, перспективных для использования в
качестве материалов вакуумной камеры термоядерных реакторов: ванадия, его сплава
V – 10 Ti – 6 Cr – 0,05 Zr – 0,1 Si и вольфрама при последовательном воздействии на
них ионных и тепловых потоков. Тепловые потоки имитировали с помощью мощного
импульсного лазерного излучения (ЛИ), создаваемого ...
Added: September 22, 2026
Iontsev M.A., Mukhin S. I., Fistul M. V., Physical Review B: Condensed Matter and Materials Physics 2016 Vol. 94 No. 17 P. 174–510
We report a theoretical study of the ac response of superconducting quantum metamaterials (SQMs), i.e., an array of qubits (two-level systems) embedded in a low-dissipative resonator. By making use of a particular example of a SQM, namely the array of charge qubits capacitively coupled to the resonator, we obtain a second-order phase transition between an ...
Added: September 22, 2026
Maddalena L., Yildiz B., Del Vecchio Blanco F. et al., Risk Analysis 2026 Vol. 46 No. 4 P. 1–26
Heated tobacco products (HTPs) are marketed as alternatives to conventional cigarettes with a potential reduced risk profile. Yet, their actual impact on cancer and noncancer disease risk remains uncertain and requires rigorous quantitative assessment. In this study, we develop a unified and transparent computational framework for toxicological risk assessment of HTPs, integrating chemical emissions data ...
Added: September 22, 2026
Дильмухаметова Алия Мидхатовна, Напалков В. В., Муллабаева А. У., Уфимский математический журнал 2010 Т. 2 № 1 С. 52–58
В данной статье введены обобщённые пространства Фока и рассмотрены основные свойства этих пространств. Найдена операция, сопряженная к операции умножения на переменную в обобщенном пространстве Фока. Также определены собственные функции сопряженного оператора. Изучены обобщенное преобразование Лапласа и задача построения базиса для введенных пространств. ...
Added: September 21, 2026
Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Pattern Recognition and Image Analysis 2024 Vol. 34 No. 3 P. 855–862
Tasks related to the automation of medical data processing are becoming more urgent. Particular attention is paid to systems for monitoring and analyzing human physiological parameters. Such systems often use specialized sensors to capture biomedical images, such as infrared cameras. This article describes our study of the problem of segmenting the eye pupil and iris ...
Added: September 21, 2026
Shabanov N., Kuricheva O., Kurbatova J. et al., / Series Working Papers SSRN "Department of Economics Ca’ Foscari University of Venice". 2026.
The carbon balance of an ecosystem is the difference between Gross Primary Productivity (GPP) and Ecosystem Respiration (Reco) as expressed by Net Ecosystem Exchange (NEE). While remote sensing retrievals of GPP have reached maturity, Reco estimation remains underexplored and ultimately cast bias on NEE. Here we present an end-to-end multi-scale analysis of the mechanism of ...
Added: August 21, 2026
Ponomarenko A., / Series Computer Science "arxiv.org". 2025.
This paper addresses the challenge of merging hierarchical navigable small world (HNSW) graphs, a critical operation for distributed systems, incremental indexing, and database compaction. We propose three algorithms for this task: Naive Graph Merge (NGM), Intra Graph Traversal Merge (IGTM), and Cross Graph Traversal Merge (CGTM). These algorithms differ in their approach to vertex selection ...
Added: July 30, 2026
Buzaev F., Efremenko D., Bugaev E. et al., , in: AI & PDE: ICLR 2026 Workshop on AI and Partial Differential Equations.: [б.и.], 2026.
Physics-Informed Neural Networks (PINNs) solve Partial Differential Equations (PDEs) by embedding physical laws into neural network training. However, their performance suffers from unstable convergence, training plateaus, and strong sensitivity to architectural and optimization hyperparameters due to the highly non-convex and multi-term structure of the physics-informed loss. In this setting, the outer-loop hyperparameter search is a ...
Added: June 23, 2026
Piontkovski D., / Series arXiv "math". 2026.
A noncommutative projective variety is defined, following Artin and Zhang, by a graded coherent algebra 𝐴. The category of coherent sheaves is then the quotient qgr(𝐴) of the category of finitely presented graded modules by the subcategory of torsion modules. We consider the categorical and polynomial entropies of the Serre twist, that is, of the ...
Added: June 23, 2026
Piontkovski D., / Series arXiv "math". 2025.
If a symmetric multilinear algebra is weakly nil, then it is Engel. This result may be regarded as an infinite-dimensional analogue of the well-known Jacobian theorem, which states that if a polynomial mapping has a polynomial inverse, then its Jacobian matrix is invertible. This refines a theorem of Gerstenhaber and partially answers a question posed ...
Added: June 23, 2026
Shipilov F., Barnyakov A., Ivanov A. et al., / Series Physics "arxiv.org". 2026.
A fast simulation of the detector response is a vital task in high-energy physics (HEP). Traditional Monte-Carlo methods form the backbone of modern particle physics simulation software but are computationally expensive. We present a machine-learning-based approach to fast simulation of the Focusing Aerogel Ring Imaging Cherenkov (FARICH) detector response. Given a particle track and momentum, ...
Added: May 19, 2026
Derkacheva A., Sakirkina M., Kraev G. et al., /. 2026.
Comprehensive data on natural hazards and their consequences are crucial for effective for risk assessment, adaptation planning, and emergency response. However, many countries face challenges with fragmented, inconsistent, and inaccessible data, particularly regarding local-scale events. To address this data gap in Russia, we developed an end-to-end processing pipeline that scrapes news from various online sources, ...
Added: April 28, 2026
Pilé I., Deng Y., Shchur L., / Series arXiv "math". 2026. No. 2604.10254.
We investigate the spatial overlap of successive spin configurations in Markov chain Monte Carlo simulations using the local Metropolis algorithm and the Svendsen-Wang and Wolff cluster algorithms. We examine the dynamics of these algorithms for two models in different universality classes: the Ising model and the Potts model with three components. The overlap of two ...
Added: April 20, 2026
Gabdullin N., Androsov I., / Series Computer Science "arxiv.org". 2026.
Label prediction in neural networks (NNs) has O(n) complexity proportional to the number of classes. This holds true for classification using fully connected layers and cosine similarity with some set of class prototypes. In this paper we show that if NN latent space (LS) geometry is known and possesses specific properties, label prediction complexity can ...
Added: April 2, 2026
Sorokin K., Beketov M., Онучин А. et al., / arxiv.org. Серия cs.SI "Social and Information Networks ". 2025.
Community detection in complex networks is a fundamental problem, open to new approaches in various scientific settings. We introduce a novel community detection method, based on Ricci flow on graphs. Our technique iteratively updates edge weights (their metric lengths) according to their (combinatorial) Foster version of Ricci curvature computed from effective resistance distance between the ...
Added: January 15, 2026