相关论文: ARC-STAR: Auditable Post-Hoc Correction for PDE Fo…

The Deferred Correction (DeC) is an iterative procedure, characterized by increasing accuracy at each iteration, which can be used to design numerical methods for systems of ODEs. The main advantage of such framework is the automatic way of…

This work unifies pseudo-time and inexact regularization techniques for nonmonotone classes of partial differential equations, into a regularized pseudo-time framework. Convergence of the residual at the predicted rate is investigated…

The (modern) arbitrary derivative (ADER) approach is a popular technique for the numerical solution of differential problems based on iteratively solving an implicit discretization of their weak formulation. In this work, focusing on an ODE…

Efficient and stable solution of partial differential equations (PDEs) is central to scientific and engineering applications, yet existing numerical solvers rely heavily on matrix based discretizations, while learning based methods require…

We propose a new paradigm for designing efficient p-adaptive arbitrary high order methods. We consider arbitrary high order iterative schemes that gain one order of accuracy at each iteration and we modify them in order to match the…

In this note, we extend the analysis for the residual-based a posteriori error estimators in the energy norm defined for the algebraic flux correction (AFC) schemes [Jha20.CAMWA] to the newly proposed algebraic stabilization schemes…

Despite advances in test-time scaling and diffusion finetuning, guidance for Auto-Regressive Diffusion Models (ARDMs) remains underexplored. We introduce an amortized framework that augments a pretrained ARDM with an offline-trained…

We propose and analyze reliable and efficient a posteriori error estimators for an optimal control problem that involves a nondifferentiable cost functional, the Poisson problem as state equation and control constraints. To approximate the…

Advection-Diffusion-Reaction (ADR) Partial Differential Equations (PDEs) appear in a wide spectrum of applications such as chemical reactors, concentration flows, and biological systems. A large number of these applications require the…

We present a trust-region-based adaptive finite-element algorithm for numerically solving a class of nonsmooth PDE-constrained optimization problems that includes problems with sparsifying regularizers and convex constraints. In particular,…

The Stefan PDE system is a representative model for thermal phase change phenomena, such as melting and solidification, arising in numerous science and engineering processes. The mathematical description is given by a Partial Differential…

Adaptive cubic regularization (ARC) methods for unconstrained optimization compute steps from linear systems involving a shifted Hessian in the spirit of the Levenberg-Marquardt and trust-region methods. The standard approach consists in…

Adaptive atomistic/continuum (a/c) coupling method is an important method for the simulation of material and atomistic systems with defects to achieve the balance of accuracy and efficiency. Residual based a posteriori error estimator is…

This paper presents a novel dynamic post-shielding framework that enforces the full class of $\omega$-regular correctness properties over pre-computed probabilistic policies. This constitutes a paradigm shift from the predominant setting of…

Deploying Automatic Speech Recognition (ASR) models on memory-constrained edge devices requires aggressive low-bit weight quantization. Layer-wise post-training quantization is practical and effective, but it suffers from cross-layer error…

In modern electronic manufacturing, defect detection on Printed Circuit Boards (PCBs) plays a critical role in ensuring product yield and maintaining the reliability of downstream assembly processes. However, existing methods often suffer…

We introduce the notion of heterogeneous calibration that applies a post-hoc model-agnostic transformation to model outputs for improving AUC performance on binary classification tasks. We consider overconfident models, whose performance is…

Numerical methods for approximately solving partial differential equations (PDE) are at the core of scientific computing. Often, this requires high-resolution or adaptive discretization grids to capture relevant spatio-temporal features in…

This paper is concerned with the recovery of (approximate) solutions to parabolic problems from incomplete and possibly inconsistent observational data, given on a time-space cylinder that is a strict subset of the computational domain…

Modern robotic systems, deployed across domains from industrial automation to domestic assistance, face a critical challenge: executing tasks with precision and adaptability in dynamic, unpredictable environments. To address this, we…