Related papers: RAM: Rapid Advection Algorithm on Arbitrary Meshes
Ray tracing is an efficient channel modeling method. However, the traditional ray tracing method has high computation complexity. To solve this problem, an improved bounding volume hierarchies (BVH) algorithm is proposed in this paper.…
The nonconvex and nonsmooth finite-sum optimization problem with linear constraint has attracted much attention in the fields of artificial intelligence, computer, and mathematics, due to its wide applications in machine learning and the…
This work introduces a novel adaptive mesh refinement (AMR) method that utilizes dominant balance analysis (DBA) for efficient and accurate grid adaptation in computational fluid dynamics (CFD) simulations. The proposed method leverages a…
Designing effective optimisation strategies for unsteady flows in the presence of complex dynamics is challenging. Gradient-based optimisation algorithms that rely on gradient information obtained from adjoint equations are efficient for…
Anderson mixing (AM) is an acceleration method for fixed-point iterations. Despite its success and wide usage in scientific computing, the convergence theory of AM remains unclear, and its applications to machine learning problems are not…
We present a numerical implementation of radiative transfer based on an explicitly photon-conserving advection scheme, where radiative fluxes over the cell interfaces of a structured or unstructured mesh are calculated with a second-order…
The problem of the resolution of turbulent flows in adaptive mesh refinement (AMR) simulations is investigated by means of 3D hydrodynamical simulations in an idealised setup, representing a moving subcluster during a merger event. AMR…
The efficiency of sampling-based motion planning brings wide application in autonomous mobile robots. The conventional rapidly exploring random tree (RRT) algorithm and its variants have gained significant successes, but there are still…
Adaptive importance sampling for stochastic optimization is a promising approach that offers improved convergence through variance reduction. In this work, we propose a new framework for variance reduction that enables the use of mixtures…
We propose an exact polynomial algorithm for a resource allocation problem with convex costs and constraints on partial sums of resource consumptions, in the presence of either continuous or integer variables. No assumption of strict…
This work presents a high-order finite-difference adaptive mesh refinement (AMR) framework for robust simulation of shock-turbulence interaction problems. A staggered-grid arrangement, in which solution points are stored at cell centers…
We introduce Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments. The method is straightforward to implement, is computationally efficient, has…
We present a forward semi-Lagrangian numerical method for systems of transport equations able to advect smooth and discontinuous fields with high-order accuracy. The numerical scheme is composed of an integration of the transport equations…
We propose a dynamic computational time model to accelerate the average processing time for recurrent visual attention (RAM). Rather than attention with a fixed number of steps for each input image, the model learns to decide when to stop…
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…
This work is devoted to the numerical approximation of high-dimensional advection-diffusion equations. It is well-known that classical methods, such as the finite volume method, suffer from the curse of dimensionality, and that their time…
In this paper, we propose a regularized auxiliary variable (RAV) approach and construct accurate and robust time-discrete schemes for a large class of gradient flows. By introducing an auxiliary variable $r=0$ and constructing an auxiliary…
For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…
We present a class of high order finite volume schemes for the solution of non-conservative hyperbolic systems that combines the one-step ADER-WENO finite volume approach with space-time adaptive mesh refinement (AMR). The resulting…
The advent of robust, reliable and accurate higher order Godunov schemes for many of the systems of equations of interest in computational astrophysics has made it important to understand how to solve them in multi-scale fashion. This is so…