Related papers: A Unified Multiscale Framework for Discrete Energy…
We present an ordinary differential equations approach to the analysis of algorithms for constructing $l_1$ minimizing solutions to underdetermined linear systems of full rank. It involves a relaxed minimization problem whose minimum is…
Robust optimization is becoming increasingly important in machine learning applications. In this paper, we study a unified framework of robust submodular optimization. We study this problem both from a minimization and maximization…
In this work, we study physics-informed neural networks (PINNs) constrained by partial differential equations (PDEs) and their application in approximating PDEs with two characteristic scales. From a continuous perspective, our formulation…
Solving large-scale nonlinear minimization problems is computationally demanding. Nonlinear multilevel minimization (NMM) methods explore the structure of the underlying minimization problem to solve such problems in a computationally…
We propose a general and versatile framework that significantly speeds-up graphical model optimization while maintaining an excellent solution accuracy. The proposed approach relies on a multi-scale pruning scheme that is able to…
We introduce a multi-scale framework for low-level vision, where the goal is estimating physical scene values from image data---such as depth from stereo image pairs. The framework uses a dense, overlapping set of image regions at multiple…
The fully connected conditional random field (CRF) with Gaussian pairwise potentials has proven popular and effective for multi-class semantic segmentation. While the energy of a dense CRF can be minimized accurately using a linear…
A numerical framework is developed to solve various types of PDEs on complicated domains, including steady and time-dependent, non-linear and non-local PDEs, with different boundary conditions that can also include non-linear and non-local…
Designing nanophotonic structures traditionally grapples with the complexities of discrete parameters, such as real materials, often resorting to costly global optimization methods. This paper introduces an approach that leverages…
Addressing complex meteorological processes at a fine spatial resolution requires substantial computational resources. To accelerate meteorological simulations, researchers have utilized neural networks to downscale meteorological variables…
We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…
We review basic design principles underpinning the construction of mimetic finite difference and a few finite volume and finite element schemes for mixed formulations of elliptic problems. For a class of low-order mixed-hybrid schemes, we…
We present a fully iterative adaptive algorithm for the numerical minimization of strongly convex energy functionals in Hilbert spaces. The proposed approach, which we first present in abstract form, generates a hierarchical sequence of…
Neural Architecture Search (NAS) for automatically finding the optimal network architecture has shown some success with competitive performances in various computer vision tasks. However, NAS in general requires a tremendous amount of…
Recent multi-view subspace clustering achieves impressive results utilizing deep networks, where the self-expressive correlation is typically modeled by a fully connected (FC) layer. However, they still suffer from two limitations. i) The…
The goal of Feature Selection - comprising filter, wrapper, and embedded approaches - is to find the optimal feature subset for designated downstream tasks. Nevertheless, current feature selection methods are limited by: 1) the selection…
We present a new multilevel minimization framework for the training of deep residual networks (ResNets), which has the potential to significantly reduce training time and effort. Our framework is based on the dynamical system's viewpoint,…
Modern buildings encompass complex dynamics of multiple electrical, mechanical, and control systems. One of the biggest hurdles in applying conventional model-based optimization and control methods to building energy management is the huge…
Today's intelligent applications can achieve high performance accuracy using machine learning (ML) techniques, such as deep neural networks (DNNs). Traditionally, in a remote DNN inference problem, an edge device transmits raw data to a…
The problem of minimizing a polynomial over a set of polynomial inequalities is an NP-hard non-convex problem. Thanks to powerful results from real algebraic geometry, one can convert this problem into a nested sequence of…