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Efficient computation of min-max problems is a central question in optimization, learning, games, and controls. Arguably the most natural algorithm is gradient-descent-ascent (GDA). However, since the 1970s, conventional wisdom has argued…

Many engineering problems involve learning hidden dynamics from indirect observations, where the physical processes are described by systems of partial differential equations (PDE). Gradient-based optimization methods are considered…

Stochastic gradient descent (SGD) holds as a classical method to build large scale machine learning models over big data. A stochastic gradient is typically calculated from a limited number of samples (known as mini-batch), so it…

Anomaly detection on dynamic graphs refers to detecting entities whose behaviors obviously deviate from the norms observed within graphs and their temporal information. This field has drawn increasing attention due to its application in…

In 2D image processing, some attempts decompose images into high and low frequency components for describing edge and smooth parts respectively. Similarly, the contour and flat area of 3D objects, such as the boundary and seat area of a…

In point cloud analysis tasks, the existing local feature aggregation descriptors (LFAD) are unable to fully utilize information in the neighborhood of central points. Previous methods rely solely on Euclidean distance to constrain the…

The high-index saddle dynamics (HiSD) method provides a powerful framework for finding saddle points and constructing solution landscapes. While originally derived for nondegenerate critical points, HiSD has demonstrated empirical success…

Many problems encountered in science and engineering can be formulated as estimating a low-rank object (e.g., matrices and tensors) from incomplete, and possibly corrupted, linear measurements. Through the lens of matrix and tensor…

Anomaly detection (AD) has been recently employed in the context of edge cloud computing, e.g., for intrusion detection and identification of performance issues. However, state-of-the-art anomaly detection procedures do not systematically…

Robust correlation estimation is essential in high-dimensional settings, particularly when data are contaminated by outliers or exhibit heavy-tailed behavior. Many robust loss functions of practical interest-such as those involving…

Approximating wind flows using computational fluid dynamics (CFD) methods can be time-consuming. Creating a tool for interactively designing prototypes while observing the wind flow change requires simpler models to simulate faster. Instead…

In this paper, we propose a simple yet effective method to represent point clouds as sets of samples drawn from a cloud-specific probability distribution. This interpretation matches intrinsic characteristics of point clouds: the number of…

Recent focus on robustness to adversarial attacks for deep neural networks produced a large variety of algorithms for training robust models. Most of the effective algorithms involve solving the min-max optimization problem for training…

Adaptive Moment Estimation (Adam), which combines Adaptive Learning Rate and Momentum, would be the most popular stochastic optimizer for accelerating the training of deep neural networks. However, it is empirically known that Adam often…

A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent)…

We propose AEGD, a new algorithm for first-order gradient-based optimization of non-convex objective functions, based on a dynamically updated energy variable. The method is shown to be unconditionally energy stable, irrespective of the…

We present a class of simple algorithms that allows to find the reaction path in systems with a complex potential energy landscape. The approach does not need any knowledge on the product state and does not require the calculation of any…

This paper investigates gradient-based adaptive prediction and control for nonlinear stochastic dynamical systems under a weak convexity condition on the prediction-based loss. This condition accommodates a broad range of nonlinear models…

The aim of decentralized gradient descent (DGD) is to minimize a sum of $n$ functions held by interconnected agents. We study the stability of DGD in open contexts where agents can join or leave the system, resulting each time in the…

A fundamental objective of materials modeling is identifying atomic structures that align with experimental observables. Conventional approaches for disordered materials involve sampling from thermodynamic ensembles and hoping for an…