Related papers: Comparison study for Level set and Direct Lagrangi…
This paper proposes a novel class of data-driven acceleration methods for steady-state flow field solvers. The core innovation lies in predicting and assigning the asymptotic limit value for each parameter during iterations based on its own…
We propose a deep learning strategy to estimate the mean curvature of two-dimensional implicit interfaces in the level-set method. Our approach is based on fitting feed-forward neural networks to synthetic data sets constructed from…
In this paper, we propose an optimally structured gradient coding scheme to mitigate the straggler problem in distributed learning. Conventional gradient coding methods often assume homogeneous straggler models or rely on excessive data…
We investigate the motion of closed smooth curves that evolve in space $\mathbb{R}^3$. The governing evolutionary equation for the evolution of the curve is accompanied by a parabolic equation for the scalar quantity evaluated over the…
The linear transport equation allows to advect level-set functions to represent moving sharp interfaces in multiphase flows as zero level-sets. A recent development in computational fluid dynamics is to modify the linear transport equation…
We examine Lagrangian techniques for computing underapproximations of finite-time horizon, stochastic reach-avoid level-sets for discrete-time, nonlinear systems. We use the concept of reachability of a target tube in the control literature…
We study the application of the Augmented Lagrangian Method to the solution of linear ill-posed problems. Previously, linear convergence rates with respect to the Bregman distance have been derived under the classical assumption of a…
We investigate a family of approximate multi-step proximal point methods, accelerated by implicit linear discretizations of gradient flow. The resulting methods are multi-step proximal point methods, with similar computational cost in each…
We consider stochastic gradient methods under the interpolation regime where a perfect fit can be obtained (minimum loss at each observation). While previous work highlighted the implicit regularization of such algorithms, we consider an…
We propose and analyze a two-level method for mimetic finite difference approximations of second order elliptic boundary value problems. We prove that the two-level algorithm is uniformly convergent, i.e., the number of iterations needed to…
In this article we investigate a system of geometric evolution equations describing a curvature driven motion of a family of 3D curves in the normal and binormal directions. Evolving curves may be subject of mutual interactions having both…
We develop a general mathematical framework to analyze scaling regimes and derive explicit analytic solutions for gradient flow (GF) in large learning problems. Our key innovation is a formal power series expansion of the loss evolution,…
As one of the most popular interface-capturing methods, the level-set method is inherently non-conservative, and its evolution usually leads to unphysical mass gain/loss. In this paper, a novel conservative level set method is developed for…
We propose an algorithm to estimate the path-gradient of both the reverse and forward Kullback-Leibler divergence for an arbitrary manifestly invertible normalizing flow. The resulting path-gradient estimators are straightforward to…
In many engineering systems operating with a working fluid, the best efficiency is reached close to a condition of flow separation, which makes its prediction very crucial in industry. Providing that wall-based quantities can be measured,…
In this paper, a parametric level set method for reconstruction of obstacles in general inverse problems is considered. General evolution equations for the reconstruction of unknown obstacles are derived in terms of the underlying level set…
In this paper, we propose novel algorithms integrated projection-free techniques with accelerated gradient flows to minimize bending energies for nonlinear plates with non-convex metric constraints. We discuss the stability and constraint…
In this paper, we study the convergence analysis for a robust stochastic structure-preserving Lagrangian numerical scheme in computing effective diffusivity of time-dependent chaotic flows, which are modeled by stochastic differential…
The role of Regge calculus as a tool for numerical relativity is discussed, and a parallelizable implicit evolution scheme described. Because of the structure of the Regge equations, it is possible to advance the vertices of a triangulated…
The advantage of particle Lagrangian methods in computational fluid dynamics is that advection is accurately modeled. However, this complicates the calculation of space derivatives. If a mesh is employed, it must be updated at each time…