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In this paper we compute families of reduced order models that match a prescribed set of moments of a highly dimensional linear time-invariant system. First, we fully parametrize the models in the interpolation points and in the free…
In order to extract the best possible performance from asynchronous stochastic gradient descent one must increase the mini-batch size and scale the learning rate accordingly. In order to achieve further speedup we introduce a technique that…
Density-based topology optimization has become a powerful method for automatically generating optimized designs in a wide variety of applications. However, it comes with a large computational cost when solving the physical model requires…
Distributed optimization is essential for training large models on large datasets. Multiple approaches have been proposed to reduce the communication overhead in distributed training, such as synchronizing only after performing multiple…
Several applications exist in which lattice Boltzmann methods (LBM) are used to compute stationary states of fluid motions, particularly those driven or modulated by external forces. Standard LBM, being explicit time-marching in nature,…
Linear stationary reaction-convection-diffusion equations with Dirichlet boundary conditions are approximated using a simple finite difference method corresponding to central differences and the addition of a high-order stabilization term…
We focus on reducing the computational costs associated with the hydrodynamic stability of solutions of the incompressible Navier-Stokes equations for a Newtonian and viscous fluid in contraction-expansion channels. In particular, we are…
A double-distribution-function based lattice Boltzmann method (DDF-LBM) is proposed for the simulation of polyatomic gases in the supersonic regime. The model relies on an extended equilibrium state that is constructed to reproduce the…
We propose an accelerated computational fluid dynamics framework based on a hybrid Fourier Neural Operator-Lattice Boltzmann Method (FNO-LBM) for steady and unsteady weakly compressible flows. FNO-based initialization significantly…
The parametric behavior of regular periodic arrays of rising bubbles is investigated with the aid of 2-dimensional BGK Lattice-Boltzmann (LB) simulators. The Recursive Projection Method is implemented and coupled to the LB simulators,…
The high-order hybridizable discontinuous Galerkin (HDG) method combining with an implicit iterative scheme is used to find the steady-state solution of the Boltzmann equation with full collision integral on two-dimensional triangular…
In analyzing and assessing the condition of dynamical systems, it is necessary to account for nonlinearity. Recent advances in computation have rendered previously computationally infeasible analyses readily executable on common computer…
This work explores the capability of simulating complex fluid flows by directly solving the Boltzmann equation. Due to the high-dimensionality of the governing equation, the substantial computational cost of solving the Boltzmann equation…
The present paper addresses the numerical solution of turbulent flows with high-order discontinuous Galerkin methods for discretizing the incompressible Navier-Stokes equations. The efficiency of high-order methods when applied to…
We propose an arbitrarily high-order accurate, fully well-balanced numerical method for the one-dimensional blood flow model. The developed method employs a continuous solution representation, combining conservative and primitive…
Simulation-based optimization of acoustic liner design in a turbofan engine nacelle for noise reduction purposes can dramatically reduce the cost and time needed for experimental designs. Because uncertainties are inevitable in the design…
In this paper, we propose an acceleration framework for a class of iterative methods using the Reduced Order Method (ROM). Assuming that the underlying iterative scheme generates a rich basis for the solution space, we construct the next…
Asynchronous algorithms have attracted much attention recently due to the crucial demands on solving large-scale optimization problems. However, the accelerated versions of asynchronous algorithms are rarely studied. In this paper, we…
We propose a study of structured non-convex non-concave min-max problems which goes beyond standard first-order approaches. Inspired by the tight understanding established in recent works [Adil et al., 2022, Lin and Jordan, 2022b], we…
We study the iterative methods for large moment systems derived from the linearized Boltzmann equation. By Fourier analysis, it is shown that the direct application of the block symmetric Gauss-Seidel (BSGS) method has slower convergence…