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Semi-supervised learning (SSL) has long been proved to be an effective technique to construct powerful models with limited labels. In the existing literature, consistency regularization-based methods, which force the perturbed samples to…
A high-order combined interpolation/finite element technique is developed for solving the coupled groundwater-surface water system that governs flows in karst aquifers. In the proposed high-order scheme we approximate the time derivative…
We propose a general dual ascent framework for Lagrangean decomposition of combinatorial problems. Although methods of this type have shown their efficiency for a number of problems, so far there was no general algorithm applicable to…
A recently developed upscaling technique, the multicontinuum homogenization method, has gained significant attention for its effectiveness in modeling complex multiscale systems. This method defines multiple continua based on distinct…
When approximating a function that depends on a parameter, one encounters many practical examples where linear interpolation or linear approximation with respect to the parameters prove ineffective. This is particularly true for responses…
In recent years, spectral clustering has become a standard method for data analysis used in a broad range of applications. In this paper we propose a new class of algorithms for multiway spectral clustering based on optimization of a…
Algebraic multigrid (AMG) is one of the most widely used solution techniques for linear systems of equations arising from discretized partial differential equations. The popularity of AMG stems from its potential to solve linear systems in…
In this paper we accomplish the development of the fast rank-adaptive solver for tensor-structured symmetric positive definite linear systems in higher dimensions. In [arXiv:1301.6068] this problem is approached by alternating minimization…
In non-private stochastic convex optimization, stochastic gradient methods converge much faster on interpolation problems -- problems where there exists a solution that simultaneously minimizes all of the sample losses -- than on…
For large-scale eigenvalue problems requiring many mutually orthogonal eigenvectors, traditional numerical methods suffer substantial computational and communication costs with limited parallel scalability, primarily due to explicit…
Convex optimizers have known many applications as differentiable layers within deep neural architectures. One application of these convex layers is to project points into a convex set. However, both forward and backward passes of these…
We discuss the interpolation of the electric and magnetic fields within a charge-conserving Particle-In-Cell scheme. The choice of the interpolation procedure for the fields acting on a particle can be constrained by analyzing conservation…
Efficient solutions of large-scale, ill-conditioned and indefinite algebraic equations are ubiquitously needed in numerous computational fields, including multiphysics simulations, machine learning, and data science. Because of their…
Distance-based anomaly detection methods rely on compact in-distribution (ID) embeddings that are well separated from anomalies. However, conventional contrastive learning strategies often struggle to achieve this balance, either promoting…
This paper investigates smart home energy management in consideration of tradeoffs between residential privacy and energy costs. A multiobjective approach that minimizes energy costs and maximizes privacy protection is proposed. The…
This paper proposes a higher-order multiscale computational method for nonlinear thermo-electric coupling problems of composite structures, which possess temperature-dependent material properties and nonlinear Joule heating. The innovative…
Motivated by various benefits of multi-energy integration, this paper establishes a bi-level framework based on transactive control to realize energy optimization among multiple interconnected energy hubs (EHs). A storage-energy-equivalent…
We propose a fast greedy algorithm to compute sparse representations of signals from continuous dictionaries that are factorizable, i.e., with atoms that can be separated as a product of sub-atoms. Existing algorithms strongly reduce the…
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…
Reduced-order modeling is an efficient approach for solving parameterized discrete partial differential equations when the solution is needed at many parameter values. An offline step approximates the solution space and an online step…