相关论文: PO-CKAN:Physics Informed Deep Operator Kolmogorov …

Efforts to improve Kolmogorov--Arnold networks (KANs) with architectural enhancements have been stymied by the complexity those enhancements bring, undermining the interpretability that makes KANs attractive in the first place. Here we…

Symbolic discovery of governing equations is a long-standing goal in scientific machine learning, yet a fundamental trade-off persists between interpretability and scalable learning. Classical symbolic regression methods yield explicit…

Symbolic neural networks, such as Kolmogorov-Arnold Networks (KAN), offer a promising approach for integrating prior knowledge with data-driven methods, making them valuable for addressing inverse problems in scientific and engineering…

Physics-informed neural networks (PINNs) offer a promising avenue for tackling both forward and inverse problems in partial differential equations (PDEs) by incorporating deep learning with fundamental physics principles. Despite their…

The predictive accuracy of operator learning frameworks depends on the quality and quantity of available training data (input-output function pairs), often requiring substantial amounts of high-fidelity data, which can be challenging to…

Operator learning has become a powerful tool in machine learning for modeling complex physical systems governed by partial differential equations (PDEs). Although Deep Operator Networks (DeepONet) show promise, they require extensive data…

Operator learning provides methods to approximate mappings between infinite-dimensional function spaces. Deep operator networks (DeepONets) are a notable architecture in this field. Recently, an extension of DeepONet based on model…

Physics-informed neural networks have shown significant potential in solving partial differential equations (PDEs) across diverse scientific fields. However, their performance often deteriorates when addressing PDEs with intricate and…

Deep operator networks (DeepONets) are receiving increased attention thanks to their demonstrated capability to approximate nonlinear operators between infinite-dimensional Banach spaces. However, despite their remarkable early promise,…

Physics-informed neural networks (PINNs) have been widely applied to solve partial differential equations (PDEs) by enforcing outputs and gradients of deep models to satisfy target equations. Due to the limitation of numerical computation,…

Accurately modeling and inferring solutions to time-dependent partial differential equations (PDEs) over extended horizons remains a core challenge in scientific machine learning. Traditional full rollout (FR) methods, which predict entire…

Neural operator learning methods have garnered significant attention in scientific computing for their ability to approximate infinite-dimensional operators. However, increasing their complexity often fails to substantially improve their…

Despite the great promise of the physics-informed neural networks (PINNs) in solving forward and inverse problems, several technical challenges are present as roadblocks for more complex and realistic applications. First, most existing…

Interpreting complex datasets remains a major challenge for scientists, particularly due to high dimensionality and collinearity among variables. We introduce a novel application of Kolmogorov-Arnold Networks (KANs) to enhance…

This paper introduces Quantum Orthogonal Separable Physics-Informed Neural Networks (QO-SPINNs), a novel architecture for solving Partial Differential Equations, integrating quantum computing principles to address the computational…

In this study, novel physics-informed neural network (PINN) methods for coupling neighboring support points and their derivative terms which are obtained by automatic differentiation (AD), are proposed to allow efficient training with…

In this work we propose CVKAN, a complex-valued Kolmogorov-Arnold Network (KAN), to join the intrinsic interpretability of KANs and the advantages of Complex-Valued Neural Networks (CVNNs). We show how to transfer a KAN and the necessary…

The Method of Moments (MoM) is constrained by the usage of static, geometry-defined basis functions, such as the Rao-Wilton-Glisson (RWG) basis. This letter reframes electromagnetic modeling around a learnable basis representation rather…

Semantic segmentation plays a crucial role in remote sensing applications, where the accurate extraction and representation of features are essential for high-quality results. Despite the widespread use of encoder-decoder architectures,…

To address the trade-off between computational efficiency and adherence to Kolmogorov-Arnold Network (KAN) principles, we propose TruKAN, a new architecture based on the KAN structure and learnable activation functions. TruKAN replaces the…