Related papers: Predictor-corrector method based on dynamic mode d…

Momentum plays a crucial role in stochastic gradient-based optimization algorithms for accelerating or improving training deep neural networks (DNNs). In deep learning practice, the momentum is usually weighted by a well-calibrated…

Dynamic Mode Decomposition (DMD) is a powerful, data-driven method for diagnosing complex dynamics. Various DMD algorithms allow one to fit data with a low-rank model that decomposes it into a sum of coherent spatiotemporal patterns.…

Time-dependent density functional theory (TDDFT) is a widely used method to investigate electron dynamics under various external perturbations such as laser fields. In this work, we present a novel approach to accelerate real time TDDFT…

Coherent electronic transport through a molecular device is studied using non-equilibrium Green's function (NEGF) formalism. Such device is made of a carbon nanowire which is connected to ferromagnetic electrodes. The molecule itself is…

The dynamic mode decomposition (DMD) has become a leading tool for data-driven modeling of dynamical systems, providing a regression framework for fitting linear dynamical models to time-series measurement data. We present a simple…

We discuss a tensor network method for constructing the adiabatic gauge potential -- the generator of adiabatic transformations -- as a matrix product operator, which allows us to adiabatically transport matrix product states. Adiabatic…

Recent advances in deep learning have allowed neural networks (NNs) to successfully replace traditional numerical solvers in many applications, thus enabling impressive computing gains. One such application is time domain simulation, which…

Numerically solving a large parametric nonlinear dynamical system is challenging due to its high complexity and the high computational costs. In recent years, machine-learning-aided surrogates are being actively researched. However, many…

Diffusion transformers have demonstrated remarkable generation quality, albeit requiring longer training iterations and numerous inference steps. In each denoising step, diffusion transformers encode the noisy inputs to extract the…

This work aims to introduce a heuristic timestep-adaptive algorithm for Computational Fluid Dynamics (CFD) and Fluid-Structure Interaction (FSI) problems where the flow is dominated by the pressure. In such scenarios, many time-adaptive…

In the realm of quantum chemistry, the accurate prediction of electronic structure and properties of nanostructures remains a formidable challenge. Density Functional Theory (DFT) and Density Matrix Renormalization Group (DMRG) have emerged…

We present a new rank-adaptive tensor method to compute the numerical solution of high-dimensional nonlinear PDEs. The method combines functional tensor train (FTT) series expansions, operator splitting time integration, and a new…

A key challenge for molecular dynamics simulations is efficient exploration of free energy landscapes over relevant collective variables (CV). Common methods for enhancing sampling become prohibitively inefficient beyond only a few CVs; in…

In the framework of the quantum theory of many-particle systems, we study the compatibility of approximated Non-Equilibrium Green Functions (NEGFs) and of approximated solutions of the Dyson equation with a modified continuity equation of…

We propose a scheme for calculation of linear optical response of current-carrying molecular junctions for the case when electronic tunneling through the junction is much faster than characteristic time of external laser field. We discuss…

Parametric partial differential equations (PDEs) are fundamental for modeling a wide range of physical and engineering systems influenced by uncertain or varying parameters. Traditional neural network-based solvers, such as Physics-Informed…

We propose a non-linear, hybrid quantum-classical scheme for simulating non-equilibrium dynamics of strongly correlated fermions described by the Hubbard model in a Bethe lattice in the thermodynamic limit. Our scheme implements…

Maximizing the Kullback-Leibler divergence (KLD) is a fundamental problem in waveform design for active sensing and hypothesis testing, as it directly relates to the error exponent of detection probability. However, the associated…

Detecting and preventing falls in humans is a critical component of assistive robotic systems. While significant progress has been made in detecting falls, the prediction of falls before they happen, and analysis of the transient state…

This study proposes a novel approach for dynamic load balancing in Software-Defined Networks (SDNs) using a Transformer-based Deep Q-Network (DQN). Traditional load balancing mechanisms, such as Round Robin (RR) and Weighted Round Robin…