Related papers: Kolmogorov Arnold Informed neural network: A physi…

The physics informed neural network (PINN) is evolving as a viable method to solve partial differential equations. In the recent past PINNs have been successfully tested and validated to find solutions to both linear and non-linear partial…

The physics informed neural network (PINN) is a promising method for solving time-evolution partial differential equations (PDEs). However, the standard PINN method may fail to solve the PDEs with strongly nonlinear characteristics or those…

Partial differential equations (PDEs) form a central component of scientific computing. Among recent advances in deep learning, evolutionary neural networks have been developed to successively capture the temporal dynamics of time-dependent…

Physics-informed neural networks (PINNs) constitute a flexible deep learning approach for solving partial differential equations (PDEs), which model phenomena ranging from heat conduction to quantum mechanical systems. Despite their…

Kolmogorov-Arnold Networks (KANs) were proposed as an alternative to traditional neural network architectures based on multilayer perceptrons (MLP-NNs). The potential advantages of KANs over MLP-NNs, including significantly enhanced…

Physics informed neural network (PINN) based solution methods for differential equations have recently shown success in a variety of scientific computing applications. Several authors have reported difficulties, however, when using PINNs to…

Physics-informed neural networks (PINNs) have emerged as promising surrogate modes for solving partial differential equations (PDEs). Their effectiveness lies in the ability to capture solution-related features through neural networks.…

Physics-informed neural networks (PINNs) and their variants have been very popular in recent years as algorithms for the numerical simulation of both forward and inverse problems for partial differential equations. This article aims to…

Physics-Informed Neural Networks (PINNs) provide a learning-based framework for solving partial differential equations (PDEs) by embedding governing physical laws into neural network training. In practice, however, their performance is…

Deep learning has achieved remarkable success in diverse applications; however, its use in solving partial differential equations (PDEs) has emerged only recently. Here, we present an overview of physics-informed neural networks (PINNs),…

Finding solutions to partial differential equations (PDEs) is an important and essential component in many scientific and engineering discoveries. One of the common approaches empowered by deep learning is Physics-informed Neural Networks…

Complex physical systems are often described by partial differential equations (PDEs) that depend on parameters such as the Reynolds number in fluid mechanics. In applications such as design optimization or uncertainty quantification,…

Engineering components must meet increasing technological demands in ever shorter development cycles. To face these challenges, a holistic approach is essential that allows for the concurrent development of part design, material system and…

In various engineering and applied science applications, repetitive numerical simulations of partial differential equations (PDEs) for varying input parameters are often required (e.g., aircraft shape optimization over many design…

Physics-informed neural networks (PINNs) are a promising approach that combines the power of neural networks with the interpretability of physical modeling. PINNs have shown good practical performance in solving partial differential…

PINNs enhance scientific computing by incorporating physical laws into neural network structures, leading to significant advancements in scientific computing. However, PINNs struggle with multi-scale and high-frequency problems due to…

Kolmogorov-Arnold Networks (KANs) shift neural computation from linear layers to learnable nonlinear edge functions, but implementing these nonlinearities efficiently in hardware remains an open challenge. Here we introduce a physical…

Kolmogorov-Arnold Networks represent a recent advancement in machine learning, with the potential to outperform traditional perceptron-based neural networks across various domains as well as provide more interpretability with the use of…

Physics-informed neural networks (PINNs) have been proven as a promising way for solving various partial differential equations, especially high-dimensional ones and those with irregular boundaries. However, their capabilities in real…

Physics-Informed Neural Networks (PINNs) have become a promising research direction in the field of solving Partial Differential Equations (PDEs). Dealing with singular perturbation problems continues to be a difficult challenge in the…