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High-dimensional PDEs have been a longstanding computational challenge. We propose to solve high-dimensional PDEs by approximating the solution with a deep neural network which is trained to satisfy the differential operator, initial…

Mathematical Finance · Quantitative Finance 2018-10-17 Justin Sirignano , Konstantinos Spiliopoulos

Estimating high-quality images while also quantifying their uncertainty are two desired features in an image reconstruction algorithm for solving ill-posed inverse problems. In this paper, we propose plug-and-play Monte Carlo (PMC) as a…

Image and Video Processing · Electrical Eng. & Systems 2024-08-29 Yu Sun , Zihui Wu , Yifan Chen , Berthy T. Feng , Katherine L. Bouman

High-order Discontinuous Galerkin Spectral Element Methods (DGSEM) provide excellent accuracy for complex flow simulations, but their computational cost increases sharply with higher polynomial orders. %that provide very accurate solutions.…

Fluid Dynamics · Physics 2025-12-11 Xukun Wang , Oscar A. Marino , Esteban Ferrer

In this paper we investigate the intrinsic sequential time complexity of universal elimination procedures for arbitrary continuous data structures encoding input and output objects of elimination theory (i.e. polynomial equation systems)…

Commutative Algebra · Mathematics 2007-05-23 David Castro , Marc Giusti , Joos Heintz , Guillermo Matera , Luis Miguel Pardo

Maximizing a non-negative, monontone, submodular function $f$ over $n$ elements under a cardinality constraint $k$ (SMCC) is a well-studied NP-hard problem. It has important applications in, e.g., machine learning and influence…

Data Structures and Algorithms · Computer Science 2024-02-05 Philip Cervenjak , Junhao Gan , Anthony Wirth

Submodular function minimization (SFM) and matroid intersection are fundamental discrete optimization problems with applications in many fields. It is well known that both of these can be solved making $\mathrm{poly}(N)$ queries to a…

Data Structures and Algorithms · Computer Science 2021-11-16 Deeparnab Chakrabarty , Yu Chen , Sanjeev Khanna

Polynomial optimization problems represent a wide class of optimization problems, with a large number of real-world applications. Current approaches for polynomial optimization, such as the sum of squares (SOS) method, rely on large-scale…

Optimization and Control · Mathematics 2025-07-04 Dimitris Bertsimas , Dick den Hertog , Thodoris Koukouvinos

In this paper, we consider a multi-stage dynamic assortment optimization problem with multi-nomial choice modeling (MNL) under resource knapsack constraints. Given the current resource inventory levels, the retailer makes an assortment…

Optimization and Control · Mathematics 2025-11-05 Xi Chen , Mo Liu , Yining Wang , Yuan Zhou

We consider the problems of Private and Secure Matrix Multiplication (PSMM) and Fully Private Matrix Multiplication (FPMM), for which matrices privately selected by a master node are multiplied at distributed worker nodes without revealing…

Information Theory · Computer Science 2022-06-24 Jinbao Zhu , Songze Li

We offer an improved method for using a nuclear-magnetic-resonance quantum computer (NMRQC) to solve the Deutsch-Jozsa problem. Two known obstacles to the application of the NMRQC are exponential diminishment of density-matrix elements with…

Quantum Physics · Physics 2009-11-06 John M. Myers , A. F. Fahmy , S. J. Glaser , R. Marx

In this paper we show a new way of constructing deterministic polynomial-time approximation algorithms for computing complex-valued evaluations of a large class of graph polynomials on bounded degree graphs. In particular, our approach…

Combinatorics · Mathematics 2018-01-11 Viresh Patel , Guus Regts

We report on the design and implementation of the AC/DC gradient descent solver for a class of optimization problems over normalized databases. AC/DC decomposes an optimization problem into a set of aggregates over the join of the database…

Databases · Computer Science 2018-06-18 Mahmoud Abo Khamis , Hung Q. Ngo , XuanLong Nguyen , Dan Olteanu , Maximilian Schleich

We consider the {\em Shaped Partition Problem} of partitioning $n$ given vectors in real $k$-space into $p$ parts so as to maximize an arbitrary objective function which is convex on the sum of vectors in each part, subject to arbitrary…

Combinatorics · Mathematics 2016-09-07 Frank K. Hwang , Shmuel Onn , Uriel G. Rothblum

In this article, we address a class of non convex, integer, non linear mathematical programs using dynamic programming. The mathematical program considered, whose properties are studied in this article, may be used to model the optimal…

Discrete Mathematics · Computer Science 2021-12-28 David Nizard , Nicolas Dupin , Dominique Quadri

Although many real-world stochastic planning problems are more naturally formulated by hybrid models with both discrete and continuous variables, current state-of-the-art methods cannot adequately address these problems. We present the…

Artificial Intelligence · Computer Science 2012-07-19 Carlos E. Guestrin , Milos Hauskrecht , Branislav Kveton

We consider the numerical solution of large scale time-harmonic Maxwell equations. To this day, this problem remains difficult, in particular because the equations are neither Hermitian nor semi-definite. Our approach is to compare…

Numerical Analysis · Mathematics 2025-07-18 Elise Fressart , Sébastien Dubois , Loïc Gouarin , Marc Massot , Michel Nowak , Nicole Spillane

Analog computing using non-volatile memristors has emerged as a promising solution for energy-efficient deep learning. New materials, like perovskites-based memristors are recently attractive due to their cost-effectiveness, energy…

This paper investigates two related optimal input selection problems for fixed (non-switched) and switched structured systems. More precisely, we consider selecting the minimum cost of inputs from a prior set of inputs, and selecting the…

Systems and Control · Electrical Eng. & Systems 2022-10-20 Yuan Zhang , Yuanqing Xia , Shenyu Liu , Zhongqi Sun

This paper focuses on distributed learning-based control of decentralized multi-agent systems where the agents' dynamics are modeled by Gaussian Processes (GPs). Two fundamental problems are considered: the optimal design of experiment for…

Systems and Control · Electrical Eng. & Systems 2021-04-06 Viet-Anh Le , Truong X. Nghiem

Neural schedulers based on deep reinforcement learning (DRL) have shown considerable potential for solving real-world resource allocation problems, as they have demonstrated significant performance gain in the domain of cluster computing.…

Machine Learning · Computer Science 2024-10-28 Tegg Taekyong Sung , Bo Ryu