Related papers: On developing piecewise rational mapping with fine…
Optimization under uncertainty and risk is indispensable in many practical situations. Our paper addresses stability of optimization problems using composite risk functionals which are subjected to measure perturbations. Our main focus is…
A new second-order numerical scheme based on an operator splitting is proposed for the Godunov-Peshkov-Romenski model of continuum mechanics. The homogeneous part of the system is solved with a finite volume method based on a WENO…
This paper explores recent progress related to constraint maps. Building on the exposition in [14], our goal is to provide a clear and accessible account of some of the more intricate arguments behind the main results in this work. Along…
Motivation: Sequence mapping is the cornerstone of modern genomics. However, most existing sequence mapping algorithms are insufficiently general. Results: We introduce context schemes: a method that allows the unambiguous recognition of a…
Software development projects management is a complex endeavor because it requires dealing with numerous unforeseen events that constantly arise along the way and that go against the expectations that had been established at the beginning.…
In this paper, we combine the nonlinear HWENO reconstruction in \cite{newhwenozq} and the fixed-point iteration with Gauss-Seidel fast sweeping strategy, to solve the static Hamilton-Jacobi equations in a novel HWENO framework recently…
Deep learning based localization and mapping approaches have recently emerged as a new research direction and receive significant attentions from both industry and academia. Instead of creating hand-designed algorithms based on physical…
We consider compact finite-difference schemes of the 4th approximation order for an initial-boundary value problem (IBVP) for the $n$-dimensional non-homogeneous wave equation, $n\geq 1$. Their construction is accomplished by both the…
To solve large-scale or high-resolution topology optimization problem, a novel algorithm is developed based on modified bi-directional evolutionary structure optimization (BESO) and extended finite element method (XFEM). Within XFEM, a set…
Current autonomous driving systems often favor end-to-end frameworks, which take sensor inputs like images and learn to map them into trajectory space via neural networks. Previous work has demonstrated that models can achieve better…
We consider a many-parametric piecewise mapping with discontinuity. That is a one dimensional model of singular dynamic system. The stability boundary are calculated analytically and numerically. New typical features of stable cycle…
Nowadays the number of available processing cores within computing nodes which are used in recent clustered environments, are growing up with a rapid rate. Despite this trend, the number of available network interfaces in such computing…
This paper develops high-order accurate, well-balanced (WB), and positivity-preserving (PP) finite volume schemes for shallow water equations on adaptive moving structured meshes. The mesh movement poses new challenges in maintaining the WB…
Multicriteria adjustable robust optimization (MARO) problems arise in a wide variety of practical settings, for example, in the design of a building's energy supply. However, no general approaches, neither for the characterization of…
We propose a novel method for planning shortest length piecewise-linear motions through complex environments punctured with static, moving, or even morphing obstacles. Using a moment optimization approach, we formulate a hierarchy of…
Multispecies kinematic flow models are defined by systems of N strongly coupled, nonlinear first-order conservation laws, where the solution is a vector of N partial volume fractions or densities. These models arise in various applications…
Safety alignment of large language models remains brittle under domain shift and noisy preference supervision. Most existing robust alignment methods focus on uncertainty in alignment data, while overlooking optimization-induced fragility…
The aim of this study is to develop a novel WENO scheme that improves the performance of the well-known fifth-order WENO methods. The approximation space consists of exponential polynomials with a tension parameter that may be optimized to…
The weighted essentially non-oscillatory (WENO) methods are popular and effective spatial discretization methods for nonlinear hyperbolic partial differential equations. Although these methods are formally first-order accurate when a shock…
In [1], we have presented the theoretical background for finding the Elementary Invariants for a 3D system of first order rational differential equations (1ODEs). We have also provided an algorithm to find such Invariants. Here we introduce…