Related papers: Physics-Informed Kolmogorov-Arnold Networks for mu…

Kolmogorov-Arnold Neural Networks (KANs) have gained significant attention in the machine learning community. However, their implementation often suffers from poor training stability and heavy trainable parameter. Furthermore, there is…

Partial Differential Equations (PDEs) are integral to modeling many scientific and engineering problems. Physics-informed Neural Networks (PINNs) have emerged as promising tools for solving PDEs by embedding governing equations into the…

Kolmogorov-Arnold Networks (KANs) have been recently proposed as a machine learning framework that is more interpretable and controllable than the multi-layer perceptron. Various network architectures have been proposed within the KAN…

Machine learning for scientific discovery is increasingly becoming popular because of its ability to extract and recognize the nonlinear characteristics from the data. The black-box nature of deep learning methods poses difficulties in…

Atmospheric correction is a critical preprocessing step in optical remote sensing, but repeated high-fidelity radiative transfer simulations remain computationally expensive for dense look-up-table generation, sensitivity analysis,…

This paper presents eXtended Physics-Informed Neural Network (X-PINN), a novel and robust framework for addressing fracture mechanics problems involving multiple cracks in fractured media. To address this, an energy-based loss function,…

The development of biophysical models for clinical applications is rapidly advancing in the research community, thanks to their predictive nature and their ability to assist the interpretation of clinical data. However, high-resolution and…

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…

Characterizing crystalline energy landscapes is essential to predicting thermodynamic stability, electronic structure, and functional behavior. While machine learning (ML) enables rapid property predictions, the "black-box" nature of most…

Physics-Informed Neural Networks (PINNs) are a new family of numerical methods, based on deep learning, for modeling boundary value problems. They offer an advantage over traditional numerical methods for high-dimensional, parametric, and…

Reinforcement learning (RL) has been increasingly applied to network control problems, such as load balancing. However, existing RL approaches often suffer from lack of interpretability and difficulty in extracting controller equations. In…

We present a data-driven framework for the multiscale modeling of anisotropic finite strain elasticity based on physics-augmented neural networks (PANNs). Our approach allows the efficient simulation of materials with complex underlying…

The Kolmogorov-Arnold representation theorem states that any continuous multivariable function can be exactly represented as a finite superposition of continuous single variable functions. Subsequent simplifications of this representation…

The curse of dimensionality poses a significant challenge to modern multilayer perceptron-based architectures, often causing performance stagnation and scalability issues. Addressing this limitation typically requires vast amounts of data.…

We develop the Randomized Neural Networks with Petrov-Galerkin Methods (RNN-PG methods) to solve linear elasticity problems. RNN-PG methods use Petrov-Galerkin variational framework, where the solution is approximated by randomized neural…

We introduce evolutionary Kolmogorov-Arnold Networks (EvoKAN), a novel framework for solving complex partial differential equations (PDEs). EvoKAN builds on Kolmogorov-Arnold Networks (KANs), where activation functions are spline based and…

Transformers stand as the cornerstone of mordern deep learning. Traditionally, these models rely on multi-layer perceptron (MLP) layers to mix the information between channels. In this paper, we introduce the Kolmogorov-Arnold Transformer…

Despite prior advances in PINNs, significant challenges remain in localized solid mechanics problems because of the limitations of single network formulations in simultaneous resolution of smooth global responses and near-tip singularities,…

The emergence of Kolmogorov-Arnold Networks (KANs) has sparked significant interest and debate within the scientific community. This paper explores the application of KANs in the domain of computer vision (CV). We examine the convolutional…

Kolmogorov-Arnold Networks (KANs), whose design is inspired-rather than dictated-by the Kolmogorov superposition theorem, have emerged as a structured alternative to MLPs. This review provides a systematic and comprehensive overview of the…