Related papers: The Numerical Flow Iteration for the Vlasov-Poisso…
In this paper we present a numerical scheme for nonlinear continuity equations, which is based on the gradient flow formulation of an energy functional with respect to the quadratic transportation distance. It can be applied to a large…
A Fourier-based Library of Unbounded Poisson Solvers (FLUPS) for 2D and 3D homogeneous distributed grids is presented. It is designed to handle every possible combination of periodic, symmetric, semi-unbounded and fully unbounded boundary…
An efficient solver for the three dimensional free-space Poisson equation is presented. The underlying numerical method is based on finite Fourier series approximation. While the error of all involved approximations can be fully controlled,…
This paper proposes a new non-oscillatory {\em energy-splitting} conservative algorithm for computing multi-fluid flows in the Eulerian framework. In comparison with existing multi-fluid algorithms in literatures, it is shown that the mass…
Quantum power flow (QPF) provides inspiring directions for tackling power flow's computational burdens leveraging quantum computing. However, existing QPF methods are mainly based on noise-sensitive quantum algorithms, whose practical…
Inverse problems of partial differential equations are ubiquitous across various scientific disciplines and can be formulated as statistical inference problems using Bayes' theorem. To address large-scale problems, it is crucial to develop…
It is nontrivial to store rapidly growing big data nowadays, which demands high-performance lossless compression techniques. Likelihood-based generative models have witnessed their success on lossless compression, where flow based models…
In this paper we present a novel particle method for the Vlasov--Poisson equation. Unlike in conventional particle methods, the particles are not interpreted as point charges, but as point values of the distribution function. In between the…
The particle-in-cell numerical method of plasma physics balances a trade-off between computational cost and intrinsic noise. Inference on data produced by these simulations generally consists of binning the data to recover the particle…
This work deals with the numerical solution of the Vlasov equation. This equation gives a kinetic description of the evolution of a plasma, and is coupled with Poisson's equation for the computation of the self-consistent electric field.…
We formulate a steady-state network flow problem for non-ideal gas that relates injection rates and nodal pressures in the network to flows in pipes. For this problem, we present and prove a theorem on uniqueness of generalized solution for…
We consider numerical methods for linear parabolic equations in one spatial dimension having piecewise constant diffusion coefficients defined by a one parameter family of interface conditions at the discontinuity. We construct immersed…
It was estimated that the world produced $59 ZB$ ($5.9 \times 10^{13} GB$) of data in 2020, resulting in the enormous costs of both data storage and transmission. Fortunately, recent advances in deep generative models have spearheaded a new…
Real-time high-accuracy optical flow estimation is critical for a variety of real-world robotic applications. However, current learning-based methods often struggle to balance accuracy and computational efficiency: methods that achieve high…
The kinetic analyses of many-particle soft matter often employ many simulation studies of various physical phenomena which supplement the experimental limitations or compliment the theoretical findings of the study. Such simulations are…
We present a novel numerical method to solve the incompressible Navier-Stokes equations for two-phase flows with phase change, using a one-fluid approach. Separate phases are tracked using a geometric Volume-Of-Fluid (VOF) method with…
Real-world data with underlying structure, such as pictures of faces, are hypothesized to lie on a low-dimensional manifold. This manifold hypothesis has motivated state-of-the-art generative algorithms that learn low-dimensional data…
This paper presents a new resolution strategy for multi-scale streamer discharge simulations based on a second order time adaptive integration and space adaptive multiresolution. A classical fluid model is used to describe plasma…
Inferring dynamical models from data continues to be a significant challenge in computational biology, especially given the stochastic nature of many biological processes. We explore a common scenario in omics, where statistically…
The nonuniform fast Fourier transform (NUFFT) enables spectral methods for problems with irregularly spaced samples, with applications in medical imaging, molecular dynamics, and kinetic plasma simulations. Existing implementations are…