Related papers: High-order Moment Closure Models with Random Batch…
A new efficient ensemble prediction strategy is developed for a general turbulent model framework with emphasis on the nonlinear interactions between large and small scale variables. The high computational cost in running large ensemble…
Phase-averaged dilute bubbly flow models require high-order statistical moments of the bubble population. The method of classes, which directly evolve bins of bubbles in the probability space, are accurate but computationally expensive.…
We propose a Machine Learning (ML) non-Markovian closure modeling framework for accurate predictions of statistical responses of turbulent dynamical systems subjected to external forcings. One of the difficulties in this statistical closure…
The moments of spatial probabilistic systems are often given by an infinite hierarchy of coupled differential equations. Moment closure methods are used to approximate a subset of low order moments by terminating the hierarchy at some order…
Control of complex turbulent dynamical systems involving strong nonlinearity and high degrees of internal instability is an important topic in practice. Different from traditional methods for controlling individual trajectories, controlling…
Suitable reduced order models (ROMs) are computationally efficient tools in characterizing key dynamical and statistical features of nature. In this paper, a systematic multiscale stochastic ROM framework is developed for complex systems…
Turbulent dynamical systems characterized by both a high-dimensional phase space and a large number of instabilities are ubiquitous among many complex systems in science and engineering. The existence of a strange attractor in the turbulent…
The Random Batch Method (RBM) is an effective technique to reduce the computational complexity when solving certain stochastic differential problems (SDEs) involving interacting particles. It can transform the computational complexity from…
Controlling a large population, in the limit, a continuum, of structurally identical dynamical systems with parametric variations is a pervasive task in diverse applications in science and engineering. However, the severely underactuated…
Establishing appropriate mathematical models for complex systems in natural phenomena not only helps deepen our understanding of nature but can also be used for state estimation and prediction. However, the extreme complexity of natural…
The paper presents a Projection-Based Reduced-Order Model for simulations of high Reynolds turbulent flows. The PBROM are enhanced by incorporating various models of turbulent viscosity and residual closures to model the effects of…
We propose a statistical-stochastic surrogate modeling approach to predict the response of the mean and variance statistics under various initial conditions and external forcing perturbations. The proposed modeling framework extends the…
We present a new strategy for filtering high-dimensional multiscale systems characterized by high-order non-Gaussian statistics using observations from leading-order moments. A closed stochastic-statistical modeling framework suitable for…
We develop Random Batch Methods for interacting particle systems with large number of particles. These methods use small but random batches for particle interactions, thus the computational cost is reduced from $O(N^2)$ per time step to…
Moment-closure methods are popular tools to simplify the mathematical analysis of stochastic models defined on networks, in which high dimensional joint distributions are approximated (often by some heuristic argument) as functions of lower…
Maximum entropy methods, rooted in the inverse Ising/Potts problem from statistical physics, are widely used to model pairwise interactions in complex systems across disciplines such as bioinformatics and neuroscience. While successful,…
Nonequilibrium statistical models of point vortex systems are constructed using an optimal closure method, and these models are employed to approximate the relaxation toward equilibrium of systems governed by the two-dimensional Euler…
We model, simulate and control the guiding problem for a herd of evaders under the action of repulsive drivers. The problem is formulated in an optimal control framework, where the drivers (controls) aim to guide the evaders (states) to a…
In [Z. Hu, R. Li, and Z. Qiao. Acceleration for microflow simulations of high-order moment models by using lower-order model correction. J. Comput. Phys., 327:225-244, 2016], it has been successfully demonstrated that using lower-order…
Moment closure methods are widely used to analyze mathematical models. They are specifically geared toward derivation of approximations of moments of stochastic models, and of similar quantities in other models. The methods possess several…