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Оптимизация физико-информированных нейронных сетей для решения нелинейного уравнения Шредингера
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
Mamedov I., Fofanov M., Lukianchenko P. et al., IEEE Access 2026 No. 14 P. 26662–26671
DreamBooth-style personalization, which often relies on one or a few images, can memorize context (background, pose, lighting) rather than learning the subject’s identity, thereby reducing fidelity and limiting prompt-driven edits. P-LoRA (Probability LoRA) is introduced as a training-time modification that biases diffusion timestep sampling and utilizes importance weights, ensuring that the overall objective remains unchanged. ...
Added: October 14, 2026
Springer, 2026.
This book highlights cutting-edge research in the field of network science, offering scientists, researchers, students and practitioners a unique update on the latest advances in theory and a multitude of applications. It presents the peer-reviewed proceedings of the XIV International Conference on Complex Networks and their Applications (COMPLEX NETWORKS 2025). The carefully selected papers cover ...
Added: October 13, 2026
Springer, 2026.
This book offers a comprehensive overview of the latest research, innovations, and practical applications in the field of sustainability, with a focus on construction materials and their use in building and civil engineering structures. As an outcome of the 3rd International Conference on Sustainability: Developments and Innovations (ICSDI 2026), this book presents a selection of ...
Added: October 13, 2026
Dmitriev A., Kornilov V., Batienkov R., Lecture Notes in Civil Engineering 2026 Vol. 886 P. 249–255
Numerous studies have provided compelling evidence that the probability distribution of avalanche sizes follows a power law, and that 1/f noise is present in the stochastic dynamics of landslides. We present a theoretical explanation of these phenomena within the framework of self-organized criticality theory, proposing a discrete-time model in the form of a sandpile cellular ...
Added: October 13, 2026
Dmitriev A., Shulman I., Lebedev A., Studies in Computational Intelligence 2026 Vol. 1265 P. 266–273
A discrete-time model is presented for the self-organization of the X/Twitter social network to the edge of a phase transition, characterized by avalanche-like propagation of information in the network. The model is based on the analogy between the critical dynamics of the X social network and sandpile cellular automata with Manna rule on the Chung-Lu ...
Added: October 13, 2026
Arutyunov K., Kharitonov I. A., Petrosyants K. O., JETP Letters 2026 Vol. 124 No. 6 P. 1–16
Superconducting properties of metallic micro- and nanowires can be entirely different from those of bulk superconductors. Of particular interest is the nonequilibrium current-induced state of a quasi-one-dimensional superconducting channel. The most interesting phenomenon here is the stepped I–V characteristic, explained by a process known as phase slip center activation. If the origin of such step-like ...
Added: October 13, 2026
Makarov D. M., Kalikin N., Fashchevsky K. A. et al., Electrochimica Acta 2026 Vol. 579 Article 150159
Machine learning (ML) has become a powerful tool for accelerating the development of carbon-based supercapacitors;
however, most published models assume that a single predictive framework can describe both conventional
porous carbons and hybrid carbon electrodes. Here, we test this assumption using a comprehensive
benchmark dataset and an extended literature-curated dataset enriched with synthesis- and electrolyte-related
descriptors. Three ML algorithms ...
Added: October 13, 2026
Lubashevsky I., Lubashevskiy V., Physica D: Nonlinear Phenomena 2026 Vol. 498 Article 135441
We develop a novel cloud-function formalism describing the dynamical relationship between sensory-information processing in large-scale brain networks (supraliminal processing) and the content of the mental representation of an observed object. The formalism combines elements of neural field theory for large-scale neural activity with the spatial characteristics of perceived objects and their embedding in the environment ...
Added: October 2, 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
Gromov E., Malomed B. A., Physics Letters A 2026 Vol. 567 Article 131219
We introduce an extended nonlinear Lugiato-Lefever equation (LLE) with the pseudo-stimulated-Raman-scattering (pseudo-SRS) cubic term, linear damping/gain, and spatial inhomogeneous (weekly or strongly localized) pump. The LLE is derived, in the extended adiabatic approximation, from the underlying Zakharov’s system (ZS), which includes a viscosity term acting on its low-frequency (LF) component and the pump supporting the ...
Added: November 28, 2025
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
V.P. Stepashkina, M.I. Hushchyn, Doklady Mathematics 2024 Vol. 110 No. 1 P. S95–S102
This paper presents the development and evaluation of methods for detecting cyberattacks on industrial systems using neural network approaches. The focus is on the task of detecting anomalies in multivariate time series, where the diversity and complexity of potential attack scenarios require the use of advanced models. To address these challenges, a transformer-based autoencoder architecture ...
Added: March 25, 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
Maria Lashina, Grishunin S., , in: Procedia Computer Science: Tenth International Conference on Information Technology and Quantitative Management (ITQM 2023)Vol. 221.: ScienceDirect, 2023. P. 442–449.
The study evaluates the effectiveness of combining different forecasting models to predict Russia's GDP growth rates for the upcoming quarter. The ensemble model utilized in this study consists of a dynamic factor model (DFM) and a neural network with long- and short-term memory (LSTM). The research compared the root-mean-squared errors (RMSE) of the ensemble model ...
Added: June 18, 2024
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
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
Rabchevskiy A., Ashikhmin E., Yasnitsky L., , in: Cyber-Physical Systems and Control II.: Springer, 2023. P. 535–544.
The problem of creating datasets for training and testing neural networks is described in the example of the task of social network management. A method of expert dataset synthesis based on experts’ knowledge of the subject area is proposed. The essence of the method lies in the fact that sets are generated randomly within the ...
Added: November 20, 2023