相关论文: Fast numerical evaluation of time-derivative nonad…
We analyze rigorously error estimates and compare numerically spatial/temporal resolution of various numerical methods for the discretization of the Dirac equation in the nonrelativistic limit regime, involving a small dimensionless…
Excited-state molecular dynamics (ESMD) simulations near conical intersections (CIs) pose significant challenges when using machine learning potentials (MLPs). Although MLPs have gained recognition for their integration into mixed…
In empirical studies with time-to-event outcomes, investigators often leverage observational data to conduct causal inference on the effect of exposure when randomized controlled trial data is unavailable. Model misspecification and lack of…
The nonlinear gyrokinetic equations describe plasma turbulence in laboratory and astrophysical plasmas. To solve these equations, massively parallel codes have been developed and run on present-day supercomputers. This paper describes…
We study the numerical anisotropy existent in compact difference schemes as applied to hyperbolic partial differential equations, and propose an approach to reduce this error and to improve the stability restrictions based on a previous…
The paper presents a numerical technique for computing directly the Takens-Bogdanov points in the nonlinear system of differential equations with one constant delay and two parameters. By representing the delay differential equations as…
We introduce a quantum algorithm for simulating the time-dependent Dirac equation in 3+1 dimensions using discrete-time quantum walks. Thus far, promising quantum algorithms have been proposed to simulate quantum dynamics in…
We present a new approach to parallelization of the first-order backward difference discretization (BDF1) of the time derivative in partial differential equations, such as the nonlinear heat and viscous Burgers equations. The time…
Nonadiabatic couplings (NACs) play a crucial role in modeling photochemical and photophysical processes with methods such as the widely used fewest-switches surface hopping (FSSH). There is therefore a strong incentive to machine learn NACs…
Applying time-dependent driving is a basic way of quantum control. Driven systems show various dynamics as its time scale is changed due to the different amount of nonadiabatic transitions. The fast-forward scaling theory enables us to…
In recent years, deep learning has become a part of our everyday life and is revolutionizing quantum chemistry as well. In this work, we show how deep learning can be used to advance the research field of photochemistry by learning all…
We propose a novel approach to symbolic timing analysis for digital integrated circuits based on recently developed analytic delay formulas for 2-input NOR, NAND, and Muller-C gates by Ferdowsi et al. (NAHS 2025). Given a fixed order of the…
Trajectory-based mixed quantum-classical approaches to coupled electron-nuclear dynamics suffer from well-studied problems such as the lack of (or incorrect account for) decoherence in the trajectory surface hopping method and the inability…
A study is conducted to evaluate four derivative estimation methods when solving a large sparse nonlinear programming problem that arises from the approximation of an optimal control problem using a direct collocation method. In particular,…
In this paper we develop the theory of discrete averaging designed to study discrete time dynamical systems defined by iterates of a map. The discrete averaging uses weighted averages over a segment of trajectory to find an autonomous…
The proposal of the optical scheme for holonomic quantum computation is evaluated based on dynamical resolution to the system beyond adiabatic limitation. The time-dependent Schr\"{o}dinger equation is exactly solved by virtue of the…
We study a wave equation with a nonlocal time fractional damping term that models the effects of acoustic attenuation characterized by a frequency dependence power law. First we prove existence of a unique solution to this equation with…
The article proposes formulating and codifying a set of applied numerical methods, coined as Deep Learning Discrete Calculus (DLDC), that uses the knowledge from discrete numerical methods to interpret the deep learning algorithms through…
This paper presents a review of the current state-of-the-art of numerical methods for nonlinear Dirac (NLD) equation. Several methods are extendedly proposed for the (1+1)-dimensional NLD equation with the scalar and vector self-interaction…
The computational demand posed by applying multi-Slater determinant trials in phaseless auxiliary-field quantum Monte Carlo methods (MSD-AFQMC) is particularly significant for molecules exhibiting strong correlations. Here, we propose using…