Related papers: An efficient, partitioned ensemble algorithm for s…
A numerical algorithm for solving mantle convection problems with strongly variable viscosity is presented. Equations for conservation of mass and momentum for highly viscous and incompressible fluids are solved iteratively by a multigrid…
We introduce a nonlinear stochastic model reduction technique for high-dimensional stochastic dynamical systems that have a low-dimensional invariant effective manifold with slow dynamics, and high-dimensional, large fast modes. Given only…
We propose a general algorithm to enumerate all solutions of a zero-dimensional polynomial system with respect to a given cost function. The algorithm is developed and is used to study a polynomial system obtained by discretizing the steady…
The discovery of dynamical models from data represents a crucial step in advancing our understanding of physical systems. Library-based sparse regression has emerged as a powerful method for inferring governing equations directly from…
We consider an incompressible magnetohydrodynamics (MHD) model in which the classical first-order time derivatives in the momentum and magnetic induction equations are replaced by variable-order Caputo time-fractional derivatives. This…
Astrophysical plasmas in relativistic spacetimes, such as black hole accretion flows, are often weakly collisional and require kinetic modeling to capture non-local transport and particle acceleration. However, the extreme scale separation…
Numerical simulation of multi-component flow systems characterized by the simultaneous presence of pressure-velocity coupling and pressure-density coupling dominated regions remains a significant challenge in computational fluid dynamics.…
We present a principled and efficient planning algorithm for collaborative multiagent dynamical systems. All computation, during both the planning and the execution phases, is distributed among the agents; each agent only needs to model and…
Accurate and efficient prediction of multi-scale flows remains a formidable challenge. Constructing theoretical models and numerical methods often involves the design and optimization of parameters. While gradient descent methods have been…
This paper addresses the problem of planning under uncertainty in large Markov Decision Processes (MDPs). Factored MDPs represent a complex state space using state variables and the transition model using a dynamic Bayesian network. This…
This work proposes multi-agent systems setting for concurrent engineering system design optimization and gradually paves the way towards examining graph theoretic constructs in the context of multidisciplinary design optimization problem.…
The Lattice Boltzmann Method algorithm is simplified by assuming constant numerical viscosity (the relaxation time is fixed at $\tau=1$). This leads to the removal of the distribution function from the computer memory. To test the solver…
This paper presents and analyzes two robust, efficient, and optimally accurate fully discrete finite element algorithms for computing the parameterized Navier-Stokes Equations (NSEs) flow ensemble. The timestepping algorithms are…
Modeling and predicting the dynamics of complex multiscale systems remains a significant challenge due to their inherent nonlinearities and sensitivity to initial conditions, as well as limitations of traditional machine learning methods…
Numerical investigation of compressible flows faces two main challenges. In order to accurately describe the flow characteristics, high-resolution nonlinear numerical schemes are needed to capture discontinuities and resolve wide…
Finding a reduction of complex, high-dimensional dynamics to its essential, low-dimensional "heart" remains a challenging yet necessary prerequisite for designing efficient numerical approaches. Machine learning methods have the potential…
We present a formulation and numerical algorithm to extend the scheme for grey radiation magneto-hydrodynamics (MHD) developed by Jiang (2021) to include the frequency dependence via the multi-group approach. The entire frequency space can…
We present a hybrid continuum-atomistic scheme which combines molecular dynamics (MD) simulations with on-the-fly machine learning techniques for the accurate and efficient prediction of multiscale fluidic systems. By using a Gaussian…
Magnetohydrodynamics (MHD)---the study of electrically conducting fluids---can be harnessed to produce efficient, low-emissions power generation. Today, computational modeling assists engineers in studying candidate designs for such…
An efficient numerical method is developed using the matrix product formalism for computing the properties at finite energy densities in one-dimensional (1D) many-body localized (MBL) systems. Arguing that any efficient (possibly quantum)…