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We propose a deterministic adjoint matching framework that formulates human preference alignment for flow-based generative models as an optimal control problem over velocity fields. One can directly regress the control toward a…

Artificial Intelligence · Computer Science 2026-05-08 Zhengyi Guo , Jiayuan Sheng , David D. Yao , Wenpin Tang

This paper develops a computational framework with unfitted meshes to solve linear piezoelectricity and flexoelectricity electromechanical boundary value problems including strain gradient elasticity at infinitesimal strains. The high-order…

Numerical Analysis · Mathematics 2020-10-08 David Codony , Onofre Marco , Sonia Fernández-Méndez , Irene Arias

In this paper, we examine a number of additive and multiplicative multilevel iterative methods and preconditioners in the setting of two-dimensional local mesh refinement. While standard multilevel methods are effective for uniform…

Numerical Analysis · Mathematics 2010-01-12 Burak Aksoylu , Stephen Bond , Michael Holst

We introduce a new "subpixel-smoothed projection" (SSP) formulation for differentiable binarization in topology optimization (TopOpt) as a drop-in replacement for previous projection schemes, which suffer from near-non-differentiability and…

Topology optimization (TO) in two dimensions often presents a trade-off between structural performance and manufacturability, with unpenalized (variable-thickness) methods yielding superior but complex designs, and penalized (SIMP) methods…

Computational Engineering, Finance, and Science · Computer Science 2025-07-28 Gabriel Stankiewicz , Chaitanya Dev , Paul Steinmann

An adaptive refinement strategy, based on an equilibrated flux a posteriori error estimator, is proposed in the context of defeaturing problems. Defeaturing consists of removing features from complex domains to simplify mesh generation and…

Numerical Analysis · Mathematics 2026-03-04 Annalisa Buffa , Denise Grappein , Rafael Vázquez

An adaptive parametric reduced-order modeling method based on interpolating poles of reduced-order models is proposed in this paper. To guarantee correct interpolation, a pole-matching process is conducted to determine which poles of two…

Numerical Analysis · Mathematics 2019-08-05 Yao Yue , Lihong Feng , Peter Benner

We consider a linear symmetric and elliptic PDE and a linear goal functional. We design and analyze a goal-oriented adaptive finite element method, which steers the adaptive mesh-refinement as well as the approximate solution of the arising…

Numerical Analysis · Mathematics 2024-01-12 Roland Becker , Gregor Gantner , Michael Innerberger , Dirk Praetorius

Bundle adjustment (BA) is a technique for refining sensor orientations of satellite images, while adjustment accuracy is correlated with feature matching results. Feature match-ing often contains high uncertainties in weak/repeat textures,…

Computer Vision and Pattern Recognition · Computer Science 2021-07-02 Xiao Ling , Xu Huang , Rongjun Qin

Basis splines enable a time-continuous feasibility check with a finite number of constraints. Constraints apply to the whole trajectory for motion planning applications that require a collision-free and dynamically feasible trajectory.…

Robotics · Computer Science 2023-10-06 Philip Dorpmüller , Thomas Schmitz , Naveen Bejagam , Torsten Bertram

Based on spline manifolds we introduce and study a mathematical framework for analysis-suitable unstructured B-spline spaces. In this setting the parameter domain has a manifold structure, which allows for the definition of function spaces…

Numerical Analysis · Mathematics 2015-07-31 Giancarlo Sangalli , Thomas Takacs , Rafael Vázquez

A general framework for goal-oriented a posteriori error estimation for finite volume methods is presented. The framework does not rely on recasting finite volume methods as special cases of finite element methods, but instead directly…

Numerical Analysis · Mathematics 2011-08-24 Qingshan Chen , Max Gunzburger

We investigate the application of a posteriori error estimates to a fractional optimal control problem with pointwise control constraints. Specifically, we address a problem in which the state equation is formulated as an integral form of…

Optimization and Control · Mathematics 2023-10-10 Fangyuan Wang , Qiming Wang , Zhaojie Zhou

Border basis schemes are open subschemes of Hilbert schemes parametrizing 0-dimensional subschemes of $\mathbb{P}^n$ of given length. They yield open coverings and are easy to describe and to compute with. Our topic is to find re-embeddings…

Algebraic Geometry · Mathematics 2023-11-28 Martin Kreuzer , Le Ngoc Long , Lorenzo Robbiano

This article firstly develops a proximal explicit approach for the generalized method of lines. In such a method, the domain of the PDE in question is discretized in lines and the equation solution is written on these lines as functions of…

Numerical Analysis · Mathematics 2019-05-08 Fabio Botelho

Given the spline representation of the boundary of a three dimensional domain, constructing a volumetric spline parameterization of the domain (i.e., a map from a unit cube to the domain) with the given boundary is a fundamental problem in…

Graphics · Computer Science 2020-01-08 Maodong Pan , Falai Chen , Weihua Tong

We investigate an optimization problem governed by an elliptic partial differential equation with uncertain parameters. We introduce a robust optimization framework that accounts for uncertain model parameters. The resulting non-linear…

Optimization and Control · Mathematics 2019-09-24 Alessandro Alla , Michael Hinze , Philip Kolvenbach , Oliver Lass , Stefan Ulbrich

We introduce a new numerical method to approximate the solution of a finite horizon deterministic optimal control problem. We exploit two Hamilton-Jacobi-Bellman PDE, arising by considering the dynamics in forward and backward time. This…

Optimization and Control · Mathematics 2023-04-21 Marianne Akian , Stéphane Gaubert , Shanqing Liu

This paper provides a normalized field product approach for topology optimization to achieve close-to-binary optimal designs. The method employs a parameter-free density measure that implicitly enforces a minimum length scale on the solid…

Computational Engineering, Finance, and Science · Computer Science 2024-12-25 Nikhil Singh , Prabhat Kumar , Anupam Saxena

In this paper, we propose a new horseshoe-type prior hierarchy for adaptively shrinking spline-based functional effects towards a predefined vector space of parametric functions. Instead of shrinking each spline coefficient towards zero, we…

Methodology · Statistics 2021-01-15 Paul Wiemann , Thomas Kneib