相关论文: A Tutorial: Adaptive Runge-Kutta Integration for S…

Variational integrators are well-suited for simulation of mechanical systems because they preserve mechanical quantities about a system such as momentum, or its change if external forcing is involved, and holonomic constraints. While they…

Dynamic simulation of elastic bodies is a longstanding task in engineering and computer graphics. In graphics, numerical integrators like implicit Euler and BDF2 are preferred due to their stability at large time steps, but they tend to…

Variational integrators are derived for structure-preserving simulation of stochastic forced Hamiltonian systems. The derivation is based on a stochastic discrete Hamiltonian which approximates a type-II stochastic generating function for…

In this paper we review recent work on novel computing paradigms using coupled oscillatory dynamical systems. We explore systems of relaxation oscillators based on linear state transitioning devices, which switch between two discrete states…

In microscopic mechanical systems interactions between elastic structures are often mediated by the hydrodynamics of a solvent fluid. At microscopic scales the elastic structures are also subject to thermal fluctuations. Stochastic…

A harmonic oscillator linearly coupled with a linear chain of Ising spins is investigated. The $N$ spins in the chain interact with their nearest neighbours with a coupling constant proportional to the oscillator position and to $N^{-1/2}$,…

We present a new numerical multiscale integrator for stiff and highly oscillatory dynamical systems. The new algorithm can be seen as an improved version of the seamless Heterogeneous Multiscale Method by E, Ren, and Vanden-Eijnden and the…

Multiscale dynamical systems characterized by interacting fast and slow processes are ubiquitous across scientific domains, from climate dynamics to fluid mechanics. Accurate modeling of such systems requires capturing both the long-term…

A computational tool for coarse-graining nonlinear systems of ordinary differential equations in time is discussed. Three illustrative model examples are worked out that demonstrate the range of capability of the method. This includes the…

We consider the geometric numerical integration of Hamiltonian systems subject to both equality and "hard" inequality constraints. As in the standard geometric integration setting, we target long-term structure preservation. We…

Stiff ordinary differential equations (ODEs) are common in many science and engineering fields, but standard neural ODE approaches struggle to accurately learn these stiff systems, posing a significant barrier to widespread adoption of…

Variational integrators are derived for structure-preserving simulation of stochastic Hamiltonian systems with a certain type of multiplicative noise arising in geometric mechanics. The derivation is based on a stochastic discrete…

The popular method of Nose and Hoover to create canonically distributed positions and momenta in classical molecular dynamics simulations is generalized to a genuine quantum system of infinite dimensionality. We show that for the quantum…

In this paper, explicit stable integrators based on symplectic and contact geometries are proposed for a non-autonomous ordinarily differential equation (ODE) found in improving convergence rate of Nesterov's accelerated gradient method.…

The technique of continuous unitary transformations has recently been used to provide physical insight into a diverse array of quantum mechanical systems. However, the question of how to best numerically implement the flow equations has…

Oscillator Ising Machines (OIMs) and probabilistic bit (p-bit)-based computing platforms have emerged as promising paradigms for tackling complex combinatorial optimization problems. Although traditionally viewed as distinct approaches,…

We study dynamics of two coupled periodically driven oscillators. Important example of such a system is a dynamic vibration absorber which consists of a small mass attached to the primary vibrating system of a large mass. Periodic solutions…

Symplectic integrators are widely used for long-term integration of conservative astrophysical problems due to their ability to preserve the constants of motion; however, they cannot in general be applied in the presence of nonconservative…

Achieving stable hopping has been a hallmark challenge in the field of dynamic legged locomotion. Controlled hopping is notably difficult due to extended periods of underactuation combined with very short ground phases wherein ground…

This paper presents mathematical modeling and numerical analysis of bifurcation and synchronization phenomena in a system of coupled oscillators driven by a finite-power energy source and generating two-dimensional stick-slip…