Related papers: EFKAN: A KAN-Integrated Neural Operator For Effici…

The recent development of Neural Operator (NeurOp) learning for solutions to the elastic wave equation shows promising results and provides the basis for fast large-scale simulations for different seismological applications. In this paper,…

The numerical approximation of the Boltzmann collision operator presents significant challenges arising from its high dimensionality, nonlinear structure, and nonlocal integral form. In this work, we propose a Fourier Neural Operator (FNO)…

Non-Terrestrial Networks (NTNs) are becoming a critical component of modern communication infrastructures, especially with the advent of Low Earth Orbit (LEO) satellite systems. Traditional centralized learning approaches face major…

We apply Fourier neural operators (FNOs), a state-of-the-art operator learning technique, to forecast the temporal evolution of experimentally measured velocity fields. FNOs are a recently developed machine learning method capable of…

Kolmogorov-Arnold Networks (KANs) have garnered attention for replacing fixed activation functions with learnable univariate functions, but they exhibit practical limitations, including high computational costs and performance deficits in…

Microstructural evolution, particularly grain growth, plays a critical role in shaping the physical, optical, and electronic properties of materials. Traditional phase-field modeling accurately simulates these phenomena but is…

Multilayer Perceptron (MLP), as a simple yet powerful model, continues to be widely used in classification and regression tasks. However, traditional MLPs often struggle to efficiently capture nonlinear relationships in load data when…

Partial differential equations (PDEs) govern a wide variety of dynamical processes in science and engineering, yet obtaining their numerical solutions often requires high-resolution discretizations and repeated evaluations of complex…

Learning accurate and stable time-advancement operators for nonlinear partial differential equations (PDEs) remains challenging, particularly for chaotic, stiff, and long-horizon dynamical systems. While neural operator methods such as the…

Neural operators are a new type of models that can map between function spaces, allowing trained models to emulate the solution operators of partial differential equations (PDEs). This paper proposes a multigrid Fourier neural operator…

Kolmogorov-Arnold networks (KANs) as an alternative to multi-layer perceptrons (MLPs) are a recent development demonstrating strong potential for data-driven modeling. This work applies KANs as the backbone of a neural ordinary differential…

Predicting the microstructural and morphological evolution of materials through phase-field modelling is computationally intensive, particularly for high-throughput parametric studies. While neural operators such as the Fourier neural…

Inspired by the Kolmogorov-Arnold representation theorem and Kurkova's principle of using approximate representations, we propose the Kurkova-Kolmogorov-Arnold Network (KKAN), a new two-block architecture that combines robust multi-layer…

Time-periodic quantum systems exhibit a rich variety of far-from-equilibrium phenomena and serve as ideal platforms for quantum engineering and control. However, simulating their dynamics with conventional numerical methods remains…

High-fidelity simulations of laser welding capture complex thermo-fluid phenomena, including phase change, free-surface deformation, and keyhole dynamics, however their computational cost limits large-scale process exploration and real-time…

Background: Traumatic brain injury modeling requires integrating volumetric neuroimaging, demographic parameters, and acquisition metadata. Finite element solvers are too computationally expensive for clinical settings. Neural operators…

Neural networks (NN) have demonstrated remarkable capabilities in various tasks, but their computation-intensive nature demands faster and more energy-efficient hardware implementations. Optics-based platforms, using technologies such as…

Kolmogorov-Arnold Networks (KAN) are a new class of neural network architecture representing a promising alternative to the Multilayer Perceptron (MLP), demonstrating improved expressiveness and interpretability. However, KANs suffer from…

The Monte Carlo-type Neural Operator (MCNO) introduces a framework for learning solution operators of one-dimensional partial differential equations (PDEs) by directly learning the kernel function and approximating the associated integral…

Neural operators can learn nonlinear mappings between function spaces and offer a new simulation paradigm for real-time prediction of complex dynamics for realistic diverse applications as well as for system identification in science and…