Related papers: From Massively Parallel Algorithms and Fluctuating…
We present a low-space overhead simulation algorithm based on the truncated Dyson series for time-dependent quantum dynamics. This algorithm is applied to simulating time-independent Hamiltonians by transitioning to the interaction picture,…
Estimation of stochastic processes evolving in a random environment is of crucial importance for example to predict aircraft trajectories evolving in an unknown atmosphere. For fixed parameter, interacting particle systems are a convenient…
Simulating the time-evolution of quantum mechanical systems is BQP-hard and expected to be one of the foremost applications of quantum computers. We consider classical algorithms for the approximation of Hamiltonian dynamics using…
Numerical diffusion is introduced by any numerical scheme as soon as small scales fluctuations, generated during the dynamical evolution of a collisionless plasma, become comparable to the grid size. Here we investigate the role of…
We analyze a stochastic approximation algorithm for decision-dependent problems, wherein the data distribution used by the algorithm evolves along the iterate sequence. The primary examples of such problems appear in performative prediction…
The numerical simulation of multiphase flows involving dispersed components with large scale disparities, such as the collisions between millimeter-sized bubbles and micron-sized mineral particles in flotation, poses a significant…
We study the asymptotic limit of the Cahn-Hilliard equation on an evolving surface with prescribed velocity. The method of formally matched asymptotic expansions is extended to account for the movement of the domain. We consider various…
We provide a framework which admits a number of ``marginal'' sequential Monte Carlo (SMC) algorithms as particular cases -- including the marginal particle filter [Klaas et al., 2005, in: Proceedings of Uncertainty in Artificial…
We present a new time-stepping algorithm for nonlinear PDEs that exhibit scale separation in time. Our scheme combines asymptotic techniques (which are inexpensive but can have insufficient accuracy) with parallel-in-time methods (which,…
It was previously shown that the superdroplet algorithm for modeling the collision-coalescence process can faithfully represent mean droplet growth in turbulent clouds. But an open question is how accurately the superdroplet algorithm…
This paper introduces a new asymptotic regime for simplifying stochastic models having non-stationary effects, such as those that arise in the presence of time-of-day effects. This regime describes an operating environment within which the…
We study maximum-likelihood-type estimation for diffusion processes when the coefficients are nonrandom and observation occurs in nonsynchronous manner. The problem of nonsynchronous observations is important when we consider the analysis…
We review the derivation of the Kac master equation model for random collisions of particles, its relationship to the Poisson process, and existing algorithms for simulating values from the marginal distribution of velocity for a single…
We show that a scaling approach successfully characterizes clustering and intermittency in space and time, in systems of noninteracting particles driven by fluctuating surfaces. We study both the steady state and the approach to it, for…
We consider the polynuclear growth (PNG) model in 1+1 dimension with flat initial condition and no extra constraints. The joint distributions of surface height at finitely many points at a fixed time moment are given as marginals of a…
The asymptotic behavior of stochastic gradient algorithms is studied. Relying on results from differential geometry (Lojasiewicz gradient inequality), the single limit-point convergence of the algorithm iterates is demonstrated and…
We consider the spherically symmetric, asymptotically flat, non-vacuum Einstein equations, using as matter model a collisionless gas as described by the Vlasov equation. We find explicit conditions on the initial data which guarantee the…
In this work we analyse asymptotically flat, spherically symmetric spacetimes in which an event horizon is present without any trapped surfaces. We identify two types of such spacetimes, each related to the asymptotic behaviour (in time) of…
We introduce a scalable approach to Gaussian process inference that combines spatio-temporal filtering with natural gradient variational inference, resulting in a non-conjugate GP method for multivariate data that scales linearly with…
This study investigates the dynamics of alternating minimization applied to a bilinear regression task with normally distributed covariates, under the asymptotic system size limit where the number of parameters and observations diverge at…