Related papers: AI paradigm for solving differential equations: fi…

Delay-Differential Equations (DDEs) are the most common representation for systems with delay. However, the DDE representation is limited. In network models with delay, the delayed channels are low-dimensional and accounting for this…

Massive MIMO systems are seen by many researchers as a paramount technology toward next generation networks. This technology consists of hundreds of antennas that are capable of sending and receiving simultaneously a huge amount of data.…

In this article, we introduce an original hybrid quantum-classical algorithm based on a variational quantum algorithm for solving systems of differential equations. The algorithm relies on a spectral decomposition of the trial functions…

Sphere packing, Hilbert's eighteenth problem, asks for the densest arrangement of congruent spheres in n-dimensional Euclidean space. Although relevant to areas such as cryptography, crystallography, and medical imaging, the problem remains…

As AI models expand in size, it has become increasingly challenging to deploy federated learning (FL) on resource-constrained edge devices. To tackle this issue, split federated learning (SFL) has emerged as an FL framework with reduced…

Large Language Models (LLMs), as the foundational architecture for next-generation interactive AI applications, not only power intelligent dialogue systems but also drive the evolution of embodied intelligence on edge devices, including…

Physics-informed (PI) methodologies have surged to become a pillar route to solve Differential Equations (DEs), sustained by the growth of machine learning methods in scientific contexts. The main proposition of PI is to minimise…

We propose a machine learning framework to accelerate numerical computations of time-dependent ODEs and PDEs. Our method is based on recasting (generalizations of) existing numerical methods as artificial neural networks, with a set of…

Stochastic differential equations provide a rich class of flexible generative models, capable of describing a wide range of spatio-temporal processes. A host of recent work looks to learn data-representing SDEs, using neural networks and…

Diffusion-based generative models have achieved remarkable performance across various domains, yet their practical deployment is often limited by high sampling costs. While prior work focuses on training objectives or individual solvers,…

Fourier neural operators (FNOs) are a recently introduced neural network architecture for learning solution operators of partial differential equations (PDEs), which have been shown to perform significantly better than comparable deep…

A new numerical method for solving a scalar ordinary differential equation with a given initial condition is introduced. The method is using a numerical integration procedure for an equivalent integral equation and is called in this paper…

Recent advances in selected CI, including the adaptive sampling configuration interaction (ASCI) algorithm and its heat bath extension, have made the ASCI approach competitive with the most accurate techniques available, and hence an…

Several neural network approaches for solving differential equations employ trial solutions with a feedforward neural network. There are different means to incorporate the trial solution in the construction, for instance one may include…

As data-driven and AI-based decision making gains widespread adoption across disciplines, it is crucial that both data privacy and decision fairness are appropriately addressed. Although differential privacy (DP) provides a robust framework…

Improved local numerical solution for the ADER-DG numerical method with a local DG predictor for solving the initial value problem for a first-order ODE system is proposed. The improved local numerical solution demonstrates convergence…

Recent progress in scientific machine learning (SciML) has opened up the possibility of training novel neural network architectures that solve complex partial differential equations (PDEs). Several (nearly data free) approaches have been…

Efficient differential equation solvers have significantly reduced the sampling time of diffusion models (DMs) while retaining high sampling quality. Among these solvers, exponential integrators (EI) have gained prominence by demonstrating…

Adaptive gradient methods have shown excellent performances for solving many machine learning problems. Although multiple adaptive gradient methods were recently studied, they mainly focus on either empirical or theoretical aspects and also…

Learning dynamics governed by differential equations is crucial for predicting and controlling the systems in science and engineering. Neural Ordinary Differential Equation (NODE), a deep learning model integrated with differential…