Related papers: A novel parallelizable convergence accelerating me…
Reliable tracking of moving boundaries is important for the simulation of compressible fluid flows and there are a lot of contributions in literature. We recognize from the classical piston problem, a typical moving boundary problem in gas…
Massively parallel hardware (GPUs) and long sequence data have made parallel algorithms essential for machine learning at scale. Yet dynamical systems, like recurrent neural networks and Markov chain Monte Carlo, were thought to suffer from…
In this paper we study the asymptotic behavior of a very fast diffusion PDE in 1D with periodic boundary conditions. This equation is motivated by the gradient flow approach to the problem of quantization of measures introduced in…
Many machine learning models, including those with non-smooth regularizers, can be formulated as consensus optimization problems, which can be solved by the alternating direction method of multipliers (ADMM). Many recent efforts have been…
Asynchronous distributed stochastic gradient descent methods have trouble converging because of stale gradients. A gradient update sent to a parameter server by a client is stale if the parameters used to calculate that gradient have since…
We show that asymptotically, completely asynchronous stochastic gradient procedures achieve optimal (even to constant factors) convergence rates for the solution of convex optimization problems under nearly the same conditions required for…
The recent evolution of software and hardware technologies is leading to a renewed computational interest in Particle-In-Cell (PIC) methods such as the Material Point Method (MPM). Indeed, provided some critical aspects are properly…
We analyse and improve the volume-penalty method, a simple and versatile way to model objects in fluid flows. The volume-penalty method is a kind of fictitious-domain method that approximates no-slip boundary conditions with rapid linear…
This paper presents convergence acceleration, a method for computing efficiently the limit of numerical sequences as a typical application of streams and higher-order functions.
Interactions between an evolving solid and inviscid flow can result in substantial computational complexity, particularly in circumstances involving varied boundary conditions between the solid and fluid phases. Examples of such…
Diffusion models have garnered significant interest from the community for their great generative ability across various applications. However, their typical multi-step sequential-denoising nature gives rise to high cumulative latency,…
In order to prevent velocity, pressure, and temperature spikes at material discontinuities occurring when the interface-capturing schemes inconsistently simulate compressible multi-material flows(when the specific heats ratio is…
Estimation of unsteady flow fields around flight vehicles may improve flow interactions and lead to enhanced vehicle performance. Although flow-field representations can be very high-dimensional, their dynamics can have low-order…
A hybrid sharp-interface immersed-boundary/front-tracking (IB/FT) method is developed for interface-resolved simulation of evaporating droplets in incompressible multiphase flows. A one-field formulation is used to solve the flow, species…
High-fidelity flow simulations are indispensable when analyzing systems exhibiting multiphase flow phenomena. The accuracy of multiphase flow simulations is strongly contingent upon the finest mesh resolution used to represent the…
We present a multi-block finite-difference solver for massively parallel Direct Numerical Simulations (DNS) of incompressible flows. The algorithm combines the versatility of a multi-block solver with the method of eigenfunctions…
Generative models like Flow Matching have achieved state-of-the-art performance but are often hindered by a computationally expensive iterative sampling process. To address this, recent work has focused on few-step or one-step generation by…
We are concerned with the simulation and optimization of large-scale gas pipeline systems in an error-controlled environment. The gas flow dynamics is locally approximated by sufficiently accurate physical models taken from a hierarchy of…
This paper investigates the asymptotic behavior of solutions to the steady pressure-free Prandtl system. By employing a modified von Mises transformation, we rigorously prove the far-field convergence of Prandtl solutions to Blasius flow. A…
Flow matching (FM) is a general framework for defining probability paths via Ordinary Differential Equations (ODEs) to transform between noise and data samples. Recent approaches attempt to straighten these flow trajectories to generate…