Heng Wu^1,2, Junjie Wang^1,2, Benzhuo Lu^1,2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.148, No.2, 2026, DOI:10.32604/cmes.2026.084608 - 28 August 2026

Abstract Neural operator learning directly constructs the mapping relationship from the equation parameter space to the solution space, enabling efficient direct inference in practical applications without the need for repeated solution of partial differential equations (PDEs)—an advantage that is difficult to achieve with traditional numerical methods. In this work, we investigate a two-path formulation that combines affine and nonlinear computational components within such operator mappings to improve learning efficiency. This yields a novel network structure, namely the Linear–Nonlinear Fusion Neural Operator (LNF-NO), which models operator mappings via the multiplicative fusion of a linear component and a… More >

Ali Raza^1,*, Umar Shafique¹, Marek Lampart¹, Dumitru Baleanu², Emad Fadhal³, Hadil Alhazmi⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.148, No.1, 2026, DOI:10.32604/cmes.2026.084939 - 27 July 2026

Abstract Kawasaki disease (KD) is an acute, self-limited pediatric vasculitis of unknown etiology and is one of the leading causes of acquired coronary artery complications in children. Endothelial dysfunction, vascular endothelial growth factor (VEGF) activity, adhesion molecule/chemokine activation, and inflammatory cytokine responses play important roles in its pathogenesis. This paper presents a delay differential equation model with stochastic perturbations to study lesion-level inflammatory mechanisms involved in Kawasaki disease pathogenesis. The model describes interactions among healthy endothelial cells, vascular endothelial growth factor (VEGF), adhesion molecules/chemokines, and inflammatory cytokine activity. Mathematically, endothelial-cell injury promotes VEGF production, VEGF contributes… More >

Anton Surkov, Vera Ignatenko^*, Sergei Koltcov

CMC-Computers, Materials & Continua, Vol.88, No.3, 2026, DOI:10.32604/cmc.2026.083643 - 23 July 2026

Abstract Large language models have recently demonstrated promising capabilities in mathematical reasoning; however, their performance on tasks requiring strict symbolic manipulation, such as solving differential equations, remains limited, especially for compact models. In this work, we investigate whether activation steering combined with reinforcement learning can improve the quality of solutions generated by pretrained language models without modifying their weights. In particular, we focus on relatively small-scale models, which exhibit limited baseline performance on symbolic mathematical tasks, and study whether their capabilities can be enhanced through activation-level interventions. The proposed approach introduces trainable steering vectors that are… More >

Nikita Sakovich¹, Dmitry Aksenov¹, Ekaterina Pleshakova^1,*, Sergey Gataullin^1,2

CMC-Computers, Materials & Continua, Vol.88, No.3, 2026, DOI:10.32604/cmc.2026.081449 - 23 July 2026

Abstract Neural operators provide a data-driven framework for learning mappings between function spaces and have shown strong performance in scientific computing and surrogate modeling. Existing architectures, however, typically rely on a single representation of the input function—either purely pointwise, as in DeepONet, or purely spectral, as in Fourier Neural Operators—which limits their ability to simultaneously capture local variability and global structure. In this work, we propose NOASLRR, a neural operator that integrates three complementary branches within a unified DeepONet-style formulation: a pointwise MLP embedding, a spectral branch based on Chebyshev polynomial coefficients, and a low-rank linear… More >

Mohamed R. Aboelmagd^1,*, Ali Selim^1,2,*, Mamdouh Abdel-Akher¹

Energy Engineering, Vol.123, No.8, 2026, DOI:10.32604/ee.2026.079171 - 12 July 2026

Abstract To enable the integration of photovoltaic (PV) power into electrical grids, accurate predictions are vital. This study applies the Multistage Attention Neural Ordinary Differential Equation (MANODE) model, which combines Long Short-Term Memory (LSTM) networks, Temporal Convolutional Networks (TCN), and a two-stage attention mechanism to capture complex spatiotemporal patterns for PV power forecasting. The improved MANODE model is evaluated on three real-world datasets from PV stations in Egypt. Each dataset contains 12 feature parameters and spans an entire year. Comprehensive comparisons are conducted between the improved MANODE model and other neural network models, including one-layer and More >

Thao Nguyen-Trang^1,2,*, Hiep Ha-Hoang³

CMES-Computer Modeling in Engineering & Sciences, Vol.147, No.2, 2026, DOI:10.32604/cmes.2026.080808 - 27 May 2026

Abstract Solving differential equations (DEs), including ordinary differential equations (ODEs) and partial differential equations (PDEs), is fundamental to scientific computing and engineering. The development of deep learning has led to Physics-Informed Neural Networks (PINNs), in which physical laws are embedded directly into the loss function. However, PINNs inherit the intrinsic instability of deep neural networks (DNNs) and lack an effective mechanism for Uncertainty Quantification (UQ). This paper proposes a stochastic ensemble framework to address these limitations. The proposed method is a double-stochastic ensemble framework that combines bagging (via bootstrap resampling and randomized collocation points) with Monte… More >

Hongsheng Su, Zhensheng Teng^*, Zihan Zhou

Energy Engineering, Vol.123, No.2, 2026, DOI:10.32604/ee.2025.069495 - 27 January 2026

Abstract Addressing the limitations of inadequate stochastic disturbance characterization during wind turbine degradation processes that result in constrained modeling accuracy, replacement-based maintenance practices that deviate from actual operational conditions, and static maintenance strategies that fail to adapt to accelerated deterioration trends leading to suboptimal remaining useful life utilization, this study proposes a Time-Based Incomplete Maintenance (TBIM) strategy incorporating reliability constraints through stochastic differential equations (SDE). By quantifying stochastic interference via Brownian motion terms and characterizing nonlinear degradation features through state influence rate functions, a high-precision SDE degradation model is constructed, achieving 16% residual reduction compared to… More >

Ndolane Sene^1,*, Ameth Ndiaye²

CMES-Computer Modeling in Engineering & Sciences, Vol.145, No.3, pp. 2849-2852, 2025, DOI:10.32604/cmes.2025.075915 - 23 December 2025

Abstract This article has no abstract. More >

Inga Telksniene¹, Tadas Telksnys², Romas Marcinkevičius³, Zenonas Navickas², Raimondas Čiegis¹, Minvydas Ragulskis^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.145, No.2, pp. 2131-2156, 2025, DOI:10.32604/cmes.2025.072938 - 26 November 2025

Abstract Fractional differential equations (FDEs) provide a powerful tool for modeling systems with memory and non-local effects, but understanding their underlying structure remains a significant challenge. While numerous numerical and semi-analytical methods exist to find solutions, new approaches are needed to analyze the intrinsic properties of the FDEs themselves. This paper introduces a novel computational framework for the structural analysis of FDEs involving iterated Caputo derivatives. The methodology is based on a transformation that recasts the original FDE into an equivalent higher-order form, represented as the sum of a closed-form, integer-order component G(y) and a residual… More >

Hongwei Ma¹, Yingqian Tian^2,*, Fuzhang Wang^3,*, Quanfu Lou⁴, Lijuan Yu⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.144, No.3, pp. 3419-3432, 2025, DOI:10.32604/cmes.2025.070791 - 30 September 2025

Abstract This study introduces a novel single-layer meshless method, the space-time collocation method based on multiquadric-radial basis functions (MQ-RBF), for solving the Benjamin-Bona-Mahony-Burgers (BBMB) equation. By reconstructing the time variable as a space variable, this method establishes a combined space-time structure that can eliminate the two-step computational process required in traditional grid methods. By introducing shape parameter-optimized MQ-RBF, high-precision discretization of the nonlinear, dispersive, and dissipative terms in the BBMB equation is achieved. The numerical experiment section validates the effectiveness of the proposed method through three benchmark examples. This method shows significant advantages in computational efficiency, More >