Related papers: KANHedge: Efficient Hedging of High-Dimensional Op…

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.…

Cyber-security systems often operate in resource-constrained environments, such as edge environments and real-time monitoring systems, where model size and inference time are crucial. A light-weight intrusion detection framework is proposed…

We propose a quantum machine learning framework for approximating solutions to high-dimensional parabolic partial differential equations (PDEs) that can be reformulated as backward stochastic differential equations (BSDEs). In contrast to…

Because of its strong predictive skills, deep learning has emerged as an essential tool in many industries, including healthcare. Traditional deep learning models, on the other hand, frequently lack interpretability and omit to take…

Score prediction is crucial in evaluating realistic image sharpness based on collected informative features. Recently, Kolmogorov-Arnold networks (KANs) have been developed and witnessed remarkable success in data fitting. This study…

We present a new framework for computing fine-scale solutions of multiscale Partial Differential Equations (PDEs) using operator learning tools. Obtaining fine-scale solutions of multiscale PDEs can be challenging, but there are many…

Kolmogorov--Arnold networks (KANs) have demonstrated their potential as an alternative to multi-layer perceptions (MLPs) in various domains, especially for science-related tasks. However, transfer learning of KANs remains a relatively…

We propose \textit{DeepMartingale}, a deep-learning framework for the dual formulation of discrete-monitoring optimal stopping problems under continuous-time models. Leveraging a martingale representation, our method implements a…

Artificial intelligence is continuously seeking novel challenges and benchmarks to effectively measure performance and to advance the state-of-the-art. In this paper we introduce KANDY, a benchmarking framework that can be used to generate…

Inferring parameters of high-dimensional partial differential equations (PDEs) poses significant computational and inferential challenges, primarily due to the curse of dimensionality and the inherent limitations of traditional numerical…

Algebraic multigrid (AMG) methods are among the most efficient solvers for linear systems of equations and they are widely used for the solution of problems stemming from the discretization of Partial Differential Equations (PDEs). The most…

We report two methods for solving FBSDEs of path dependent types of high dimensions. Specifically, we propose a deep learning framework for solving such problems using path signatures as underlying features. Our two methods…

This study explores the application of Kolmogorov-Arnold Networks (KANs) in predicting nuclear binding energies, leveraging their ability to decompose complex multi-parameter systems into simpler univariate functions. By utilizing data from…

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…

Data science has emerged as fourth paradigm of scientific exploration. However many machine learning models operate as black boxes offering limited insight into the reasoning behind their predictions. This lack of transparency is one of the…

Nonlinear programming (NLP) plays a critical role in domains such as power energy systems, chemical engineering, communication networks, and financial engineering. However, solving large-scale, nonconvex NLP problems remains a significant…

We introduce the first method of uncertainty quantification in the domain of Kolmogorov-Arnold Networks, specifically focusing on (Higher Order) ReLUKANs to enhance computational efficiency given the computational demands of Bayesian…

We propose new machine learning schemes for solving high dimensional nonlinear partial differential equations (PDEs). Relying on the classical backward stochastic differential equation (BSDE) representation of PDEs, our algorithms estimate…

Microbial Fuel Cells (MFCs) offer a promising pathway for sustainable energy generation by converting organic matter into electricity through microbial processes. A key factor influencing MFC performance is the anode structure, where design…