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We consider a two-stage stochastic optimization problem, in which a long-term optimization variable is coupled with a set of short-term optimization variables in both objective and constraint functions. Despite that two-stage stochastic…

Data compression and decompression have become vital components of big-data applications to manage the exponential growth in the amount of data collected and stored. Furthermore, big-data applications have increasingly adopted GPUs due to…

Prompt engineering is crucial for fully leveraging large language models (LLMs), yet most existing optimization methods follow a single trajectory, resulting in limited adaptability, gradient conflicts, and high computational overhead. We…

In this paper, we propose an augmented subspace based adaptive proper orthogonal decomposition (POD) method for solving the time dependent partial differential equations. By augmenting the POD subspace with some auxiliary modes, we obtain…

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…

This paper studies the underlying combinatorial structure of a class of object rearrangement problems, which appear frequently in applications. The problems involve multiple, similar-geometry objects placed on a flat, horizontal surface,…

By taking the idea of divide-and-conquer, cooperative coevolution (CC) provides a powerful architecture for large scale global optimization (LSGO) problems, but its efficiency relies highly on the decomposition strategy. It has been shown…

Uncertainty estimation is crucial for machine learning models to detect out-of-distribution (OOD) inputs. However, the conventional discriminative deep learning classifiers produce uncalibrated closed-set predictions for OOD data. A more…

\emph{Over-fitting} and \emph{over-smoothing} are two main obstacles of developing deep Graph Convolutional Networks (GCNs) for node classification. In particular, over-fitting weakens the generalization ability on small dataset, while…

Existing results on decomposition methods and algorithms for nonconvex problems are minimal. Parallel decomposition algorithms do not exist for nonconvex problems with coupling nonlinear equality constraints. Besides, decomposition…

Since the seminal paper of Hendrycks et al. arXiv:1610.02136, Post-hoc deep Out-of-Distribution (OOD) detection has expanded rapidly. As a result, practitioners working on safety-critical applications and seeking to improve the robustness…

While deep learning demonstrates its strong ability to handle independent and identically distributed (IID) data, it often suffers from out-of-distribution (OoD) generalization, where the test data come from another distribution (w.r.t. the…

Opioid Use Disorder (OUD) has emerged as a significant global public health issue, with complex multifaceted conditions. Due to the lack of effective treatment options for various conditions, there is a pressing need for the discovery of…

The linear primal-dual hybrid gradient (PDHG) method is a first-order method that splits convex optimization problems with saddle-point structure into smaller subproblems. Unlike those obtained in most splitting methods, these subproblems…

Stochastic gradient descent (SGD) is a simple and popular method to solve stochastic optimization problems which arise in machine learning. For strongly convex problems, its convergence rate was known to be O(\log(T)/T), by running SGD for…

In this paper, we develop a nonlinear reduction framework based on our recently introduced extended group finite element method. By interpolating nonlinearities onto approximation spaces defined with the help of finite elements, the…

In this paper, we introduce a higher-order multiscale method for time-dependent problems with highly oscillatory coefficients. Building on the localized orthogonal decomposition (LOD) framework, we construct enriched correction operators to…

A wide range of modern science and engineering applications are formulated as optimization problems with a system of partial differential equations (PDEs) as constraints. These PDE-constrained optimization problems are typically solved in a…

Out-of-distribution (OOD) detection is essential for ensuring the reliability and safety of machine learning systems. In recent years, it has received increasing attention, particularly through post-hoc detection and training-based methods.…

Likelihood-based deep generative models (DGMs) have gained significant attention for their ability to approximate the distributions of high-dimensional data. However, these models lack a performance guarantee in assigning higher likelihood…