Related papers: PO-CKAN:Physics Informed Deep Operator Kolmogorov …

Physics-Informed Neural Networks (PINNs) seek to solve partial differential equations (PDEs) with deep learning. Mainstream approaches that deploy fully-connected multi-layer deep learning architectures require prolonged training to achieve…

Deep neural networks achieve state-of-the-art performance in estimating heterogeneous treatment effects, but their opacity limits trust and adoption in sensitive domains such as medicine, economics, and public policy. Building on…

Solving partial differential equations (PDEs) by neural networks as well as Kolmogorov-Arnold Networks (KANs), including physics-informed neural networks (PINNs), physics-informed KANs (PIKANs), and neural operators, are known to exhibit…

This paper proposes a Physics-Informed Kolmogorov-Arnold Network for analyzing elasticity problems in multi-material electronic packaging structures. The method replaces traditional Multi-Layer Perceptrons with Kolmogorov-Arnold Networks…

Partial differential equations (PDEs) serve as the cornerstone of mathematical physics. In recent years, Physics-Informed Neural Networks (PINNs) have significantly reduced the dependence on large datasets by embedding physical laws…

Physics-informed holomorphic neural networks (PIHNNs) have recently emerged as efficient surrogate models for solving differential problems. By embedding the underlying problem structure into the network, PIHNNs require training only to…

Physics-Informed Neural Operators provide efficient, high-fidelity simulations for systems governed by partial differential equations (PDEs). However, most existing studies focus only on multi-scale, multi-physics systems within a single…

We introduce Kolmogorov--Arnold Neural Operator (KANO), a dual-domain neural operator jointly parameterized by both spectral and spatial bases with intrinsic symbolic interpretability. We theoretically demonstrate that KANO overcomes the…

Kolmogorov-Arnold Networks (KANs) have recently emerged as a powerful alternative to traditional multilayer perceptrons. However, their reliance on predefined, bounded grids restricts their ability to approximate functions on unbounded…

Physics-informed neural networks (PINNs) are effective in solving integer-order partial differential equations (PDEs) based on scattered and noisy data. PINNs employ standard feedforward neural networks (NNs) with the PDEs explicitly…

Solving parametric Partial Differential Equations (PDEs) for a broad range of parameters is a critical challenge in scientific computing. To this end, neural operators, which \textcolor{black}{predicts the PDE solution with variable PDE…

Multi-Layer Perceptrons (MLPs) rely on pre-defined, fixed activation functions, imposing a static inductive bias that forces the network to approximate complex topologies solely through increased depth and width. Kolmogorov-Arnold Networks…

This study evaluates the applicability of Kolmogorov-Arnold Networks (KAN) in fraud detection, finding that their effectiveness is context-dependent. We propose a quick decision rule using Principal Component Analysis (PCA) to assess the…

The Kolmogorov-Arnold Network (KAN) has emerged as a promising neural network architecture for small-scale AI+Science applications. However, it suffers from inflexibility in modeling ridge functions, which is widely used in representing the…

The prediction of quantum dynamical responses lies at the heart of modern physics. Yet, modeling these time-dependent behaviors remains a formidable challenge because quantum systems evolve in high-dimensional Hilbert spaces, often…

Partial differential equations (PDEs) play a fundamental role in modeling and simulating problems across a wide range of disciplines. Recent advances in deep learning have shown the great potential of physics-informed neural networks…

Medical image segmentation demands models that achieve high accuracy while maintaining computational efficiency and clinical interpretability. While recent Kolmogorov-Arnold Networks (KANs) offer powerful adaptive non-linearities, their…

Recent work provides promising evidence that Physics-Informed Neural Networks (PINN) can efficiently solve partial differential equations (PDE). However, previous works have failed to provide guarantees on the worst-case residual error of a…

The Kolmogorov-Arnold Network (KAN) is a novel multi-layer network model recognized for its efficiency in neuromorphic computing, where synapses between neurons are trained linearly. Computations in KAN are performed by generating a…

Deep Operator Networks (DeepONets) and their physics-informed variants have shown significant promise in learning mappings between function spaces of partial differential equations, enhancing the generalization of traditional neural…