相关论文: L1-ROC and R2-ROC: L1- and R2-based Reduced Over-C…

Deep surrogate models for parametric partial differential equations (PDEs) can deliver high-fidelity approximations but remain prohibitively data-hungry: training often requires thousands of fine-grid simulations, each incurring substantial…

Reduced basis approximations of Optimal Control Problems (OCPs) governed by steady partial differential equations (PDEs) with random parametric inputs are analyzed and constructed. Such approximations are based on a Reduced Order Model,…

In the present paper we consider a 2-D shallow-water equations (SWE) model on a $\beta$-plane solved using an alternating direction fully implicit (ADI) finite-difference scheme on a rectangular domain. The scheme was shown to be…

In analyzing and assessing the condition of dynamical systems, it is necessary to account for nonlinearity. Recent advances in computation have rendered previously computationally infeasible analyses readily executable on common computer…

In this work, we propose an optimization framework for estimating a sparse robust one-dimensional subspace. Our objective is to minimize both the representation error and the penalty, in terms of the l1-norm criterion. Given that the…

We consider the numerical solution of partial differential equations with coefficients that are strongly heterogeneous in space. We provide an overview of higher-order localized orthogonal decomposition (LOD) methods for the elliptic…

Iterative steady-state solvers are widely used in computational fluid dynamics. Unfortunately, it is difficult to obtain steady-state solution for unstable problem caused by physical instability and numerical instability. Optimization is a…

A bottleneck for computational lithography and optical metrology are long computational times for near field simulations. For design, optimization, and inverse scatterometry usually the same basic layout has to be simulated multiple times…

Multiple binary responses arise in many modern data-analytic problems. Although fitting separate logistic regressions for each response is computationally attractive, it ignores shared structure and can be statistically inefficient,…

This paper investigates compact large language model (LLM) deployment and world-model-assisted inference offloading in mobile edge computing (MEC) networks. We first propose an edge compact LLM deployment (ECLD) framework that jointly…

We present a new parallel computational framework for the efficient solution of a class of $L^2$/$L^1$-regularized optimal control problems governed by semi-linear elliptic partial differential equations (PDEs). The main difficulty in…

The two-layer quasi-geostrophic equations (2QGE) serve as a simplified model for simulating wind-driven, stratified ocean flows. However, their numerical simulation remains computationally expensive due to the need for high-resolution…

Many applications in computational physics involve approximating problems with microstructure, characterized by multiple spatial scales in their data. However, these numerical solutions are often computationally expensive due to the need to…

Data-driven black-box model-based optimization (MBO) problems arise in a great number of practical application scenarios, where the goal is to find a design over the whole space maximizing a black-box target function based on a static…

Optimization modeling and solving are fundamental to the application of Operations Research (OR) in real-world decision making, yet the process of translating natural language problem descriptions into formal models and solver code remains…

Robust optimization is a framework for modeling optimization problems involving data uncertainty and during the last decades has been an area of active research. If we focus on linear programming (LP) problems with i) uncertain data, ii)…

This work is concerned with linear matrix equations that arise from the space-time discretization of time-dependent linear partial differential equations (PDEs). Such matrix equations have been considered, for example, in the context of…

We present a new surrogate modeling technique for efficient approximation of input-output maps governed by parametrized PDEs. The model is hierarchical as it is built on a full order model (FOM), reduced order model (ROM) and…

This paper investigates a joint beamforming and resource allocation problem in downlink reconfigurable intelligent surface (RIS)-assisted orthogonal frequency division multiplexing (OFDM) systems to minimize the average delay, where data…

Mechanical systems are often characterized only by their response to certain loads known from experiments or simulations. The obtained data can be used for various purposes: system analysis, design of mathematical models, or construction of…