Related papers: A note on statistical consistency of numerical int…
We introduce a data assimilation strategy aimed at accurately capturing key non-Gaussian structures in probability distributions using a small ensemble size. A major challenge in statistical forecasting of nonlinearly coupled multiscale…
Stochastic averaging allows for the reduction of the dimension and complexity of stochastic dynamical systems with multiple time scales, replacing fast variables with statistically equivalent stochastic processes in order to analyze…
Within the framework of weighted integrable Hamiltonian systems, we study the long-time behavior of the associated statistical ensembles. We construct an action-dependent angular conjugacy that rectifies the nonuniform angular flow into a…
By a high-order numerical homogenization method, a heterogeneous multiscale scheme was developed in Jin & Li (2022) for evolving differential equations containing two time scales. In this paper, we further explore the technique to propose…
We propose a novel numerical homogenization method based on the edge multiscale approach for solving indefinite time-harmonic Maxwell equations in heterogeneous media with large wavenumber. Numerical methods for these equations in…
Viewing optimization methods as numerical integrators for ordinary differential equations (ODEs) provides a thought-provoking modern framework for studying accelerated first-order optimizers. In this literature, acceleration is often…
Multiscale dynamics are ubiquitous in applications of modern science. Because of time scale separation between relatively small set of slowly evolving variables and (typically) much larger set of rapidly changing variables, direct numerical…
We propose an algorithm for approximating the solution of a strongly oscillating SDE, that is, a system in which some ergodic state variables evolve quickly with respect to the other variables. The algorithm profits from homogenization…
We construct a novel estimator for the diffusion coefficient of the limiting homogenized equation, when observing the slow dynamics of a multiscale model, in the case when the slow dynamics are of bounded variation. Previous research…
The Lie-Trotter formula, together with its higher-order generalizations, provides a direct approach to decomposing the exponential of a sum of operators. Despite significant effort, the error scaling of such product formulas remains poorly…
Mobile sensing enabled by GPS or smart phones has become an increasingly important source of traffic data. For sufficient coverage of the traffic stream, it is important to maintain a reasonable penetration rate of probe vehicles. From the…
The efficient management of large-scale queueing networks is critical for a variety of sectors, including healthcare, logistics, and customer service, where system performance has profound implications for operational effectiveness and cost…
A framework for deriving probabilistic data-driven closure models is proposed for coarse-grained numerical simulations of turbulence in statistically stationary state. The approach unites the ideal large-eddy simulation model and data…
In the Monte Carlo (MC) method statistical noise is usually present. Statistical noise may become dominant in the calculation of a distribution, usually by iteration, but is less Important in calculating integrals. The subject of the…
The dispersion of solute in porous media shows a non-linear increase in the transition from diffusion to advection dominated dispersion as the flow velocity is raised. In the past, the behavior in this intermediate regime has been explained…
A multi-scale method for the hyperbolic systems governing sediment transport in subcritical case is developed. The scale separation of this problem is due to the fact that the sediment transport is much slower than flow velocity. We first…
Existing statistical methods for the analysis of micro-randomized trials (MRTs) are designed to estimate causal excursion effects using data from a single MRT. In practice, however, researchers can often find previous MRTs that employ…
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…
A stochastic Forward-Backward algorithm with a constant step is studied. At each time step, this algorithm involves an independent copy of a couple of random maximal monotone operators. Defining a mean operator as a selection integral, the…
High-dimensional limit theorems have been shown useful to derive tuning rules for finding the optimal scaling in random-walk Metropolis algorithms. The assumptions under which weak convergence results are proved are however restrictive: the…