Related papers: BEKAN: Boundary condition-guaranteed evolutionary …
Kolmogorov-Arnold Networks (KANs) represent an innovation in neural network architectures, offering a compelling alternative to Multi-Layer Perceptrons (MLPs) in models such as Convolutional Neural Networks (CNNs), Recurrent Neural Networks…
Nonlinear partial differential equations (PDEs) are used to model dynamical processes in a large number of scientific fields, ranging from finance to biology. In many applications standard local models are not sufficient to accurately…
We propose PO-CKAN, a physics-informed deep operator framework based on Chunkwise Rational Kolmogorov--Arnold Networks (KANs), for approximating the solution operators of partial differential equations. This framework leverages a Deep…
Kolmogorov-Arnold Networks (KANs) have inspired numerous works exploring their applications across a wide range of scientific problems, with the potential to replace Multilayer Perceptrons (MLPs). While many KANs are designed using basis…
Recent years have witnessed growing interests in solving partial differential equations by deep neural networks, especially in the high-dimensional case. Unlike classical numerical methods, such as finite difference method and finite…
Kolmogorov-Arnold Networks (KANs) relocate learnable nonlinearities from nodes to edges, demonstrating remarkable capabilities in scientific machine learning and interpretable modeling. However, current KAN implementations suffer from…
Neural operators have emerged as powerful surrogates for the solution of partial differential equations (PDEs), yet their ability to handle general, highly variable boundary conditions (BCs) remains limited. Existing approaches often fail…
We introduce Geometric Kolmogorov--Arnold Networks (GeoKANs), a family of geometry-aware KAN-type models in which approximation is carried out in learned, geometry-adapted coordinates rather than in fixed Euclidean input coordinates. GeoKAN…
In this work, we employ physics-informed neural operators to map pressure profiles from an input function space to the corresponding bubble radius responses. Our approach employs a two-step DeepONet architecture. To address the intrinsic…
Physics-Informed Neural Networks (PINNs) and more recently Physics-Informed Kolmogorov-Arnold Networks (PIKANs) have emerged as promising approaches for solving partial differential equations (PDEs) without reliance on extensive labeled…
To address the issue of interpretability in multilayer perceptrons (MLPs), Kolmogorov-Arnold Networks (KANs) are introduced in 2024. However, optimizing KAN structures is labor-intensive, typically requiring manual intervention and…
This work extends the paradigm of evolutional deep neural networks (EDNNs) to solving parametric time-dependent partial differential equations (PDEs) on domains with geometric structure. By introducing positional embeddings based on…
Solving partial differential equations (PDEs) is essential in scientific forecasting and fluid dynamics. Traditional approaches often incur expensive computational costs and trade-offs in efficiency and accuracy. Recent deep neural networks…
Deep Reinforcement Learning (DRL), a subset of machine learning focused on sequential decision-making, has emerged as a powerful approach for tackling financial trading problems. In finance, DRL is commonly used either to generate discrete…
Function approximation is a critical task in various fields. However, existing neural network approaches struggle with locally complex or discontinuous functions due to their reliance on a single global model covering the entire problem…
Kolmogorov-Arnold Networks (KANs) are a class of neural networks that have received increased attention in recent literature. In contrast to MLPs, KANs leverage parameterized, trainable activation functions and offer several benefits…
In this paper, we present Convolutional Kolmogorov-Arnold Networks, a novel architecture that integrates the learnable spline-based activation functions of Kolmogorov-Arnold Networks (KANs) into convolutional layers. By replacing…
The aim of this work is to consider multiscale algorithms for solving PDEs with Galerkin methods on bounded domains. We provide results on convergence and condition numbers. We show how to handle PDEs with Dirichlet boundary conditions. We…
For linear partial differential equations with known fundamental solutions, this work introduces a novel operator learning framework that relies exclusively on domain boundary data, including solution values and normal derivatives, rather…
Recent advancements in neural network design have given rise to the development of Kolmogorov-Arnold Networks (KANs), which enhance speed, interpretability, and precision. This paper presents the Fractional Kolmogorov-Arnold Network (fKAN),…