Related papers: Scalable Bayesian Physics-Informed Kolmogorov-Arno…

This work investigates Kolmogorov-Arnold network-based wavefunction ansatz as viable representations for quantum Monte Carlo simulations. Through systematic analysis of one-dimensional model systems, we evaluate their computational…

Kolmogorov-Arnold Networks (KANs) were recently introduced as an alternative representation model to MLP. Herein, we employ KANs to construct physics-informed machine learning models (PIKANs) and deep operator models (DeepOKANs) for solving…

The recently proposed Kolmogorov-Arnold network (KAN) is a promising alternative to multi-layer perceptrons (MLPs) for data-driven modeling. While original KAN layers were only capable of representing the addition operator, the…

DreamerV3 is a state-of-the-art online model-based reinforcement learning (MBRL) algorithm known for remarkable sample efficiency. Concurrently, Kolmogorov-Arnold Networks (KANs) have emerged as a promising alternative to Multi-Layer…

Kolmogorov-Arnold Networks (KANs) are a recent neural network architecture offering an alternative to Multilayer Perceptrons (MLPs) with improved explainability and expressibility. However, KANs are significantly slower than MLPs due to the…

Physics-Informed Neural Networks (PINNs) have emerged as a powerful mesh-free framework for solving ordinary and partial differential equations by embedding the governing physical laws directly into the loss function. However, their…

To address the challenge of tractability for optimizing mathematical models in science and engineering, surrogate models are often employed. Recently, a new class of machine learning models named Kolmogorov Arnold Networks (KANs) have been…

High-dimensional linear mappings, or linear layers, dominate both the parameter count and the computational cost of most modern deep-learning models. We introduce a general-purpose drop-in replacement, lookup multivariate Kolmogorov-Arnold…

A problem of considerable importance within the field of uncertainty quantification (UQ) is the development of efficient methods for the construction of accurate surrogate models. Such efforts are particularly important to applications…

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…

Uncertainty quantification (UQ) is important to machine learning (ML) force fields to assess the level of confidence during prediction, as ML models are not inherently physical and can therefore yield catastrophically incorrect predictions.…

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…

The high dimensionality of kinetic equations with stochastic parameters poses major computational challenges for uncertainty quantification (UQ). Traditional Monte Carlo (MC) sampling methods, while widely used, suffer from slow convergence…

In recent years, operator learning, particularly the DeepONet, has received much attention for efficiently learning complex mappings between input and output functions across diverse fields. However, in practical scenarios with limited and…

Nuclear mass prediction is one of the core issues in nuclear physics research, yet it faces the challenge of small-sample datasets with high complexity. This study introduces the Kolmogorov-Arnold Network (KAN) into the refinement of…

Reconstructing time-resolved flow fields from temporally sparse velocimetry measurements is critical for characterizing many complex thermal-fluid systems. We introduce a machine learning framework for uncertainty-aware flow reconstruction…

The Kolmogorov-Arnold network (KAN) is a regression model that is based on a representation of an arbitrary continuous multivariate function by a composition of functions of a single variable. Experimentally-obtained datasets for regression…

The Kolmogorov-Arnold Network (KAN) has recently gained attention as an alternative to traditional multi-layer perceptrons (MLPs), offering improved accuracy and interpretability by employing learnable activation functions on edges. In this…

We propose a Kolmogorov-Arnold Representation-based Hamiltonian Neural Network (KAR-HNN) that replaces the Multilayer Perceptrons (MLPs) with univariate transformations. While Hamiltonian Neural Networks (HNNs) ensure energy conservation by…

Kolmogorov Arnold Networks (KANs), built upon the Kolmogorov Arnold representation theorem (KAR), have demonstrated promising capabilities in expressing complex functions with fewer neurons. This is achieved by implementing learnable…