Related papers: Localized Dynamic Mode Decomposition with Temporal…

Elastic topological states have been receiving increased intention in numerous scientific and engineering fields due to their defect-immune nature, resulting in applications of vibration control and information processing. Here, we present…

Numerical approximation methods for the Koopman operator have advanced considerably in the last few years. In particular, data-driven approaches such as dynamic mode decomposition (DMD) and its generalization, the extended-DMD (EDMD), are…

One of the most common methods to train machine learning algorithms today is the stochastic gradient descent (SGD). In a distributed setting, SGD-based algorithms have been shown to converge theoretically under specific circumstances. A…

We introduce the Mori-Zwanzig Mode Decomposition (MZMD), a novel data-driven technique for efficient modal analysis of and reduced-order modeling of large-scale spatio-temporal dynamical systems. MZMD represents an extension of Dynamic Mode…

We develop innovative algorithms for solving the strong-constraint formulation of four-dimensional variational data assimilation in large-scale applications. We present a space-time decomposition approach that employs domain decomposition…

Long-term time series forecasting is a vital task and has a wide range of real applications. Recent methods focus on capturing the underlying patterns from one single domain (e.g. the time domain or the frequency domain), and have not taken…

Extended Dynamic Mode Decomposition (EDMD) is a popular data-driven method to approximate the action of the Koopman operator on a linear function space spanned by a dictionary of functions. The accuracy of EDMD model critically depends on…

Predicting multivariate time series is crucial, demanding precise modeling of intricate patterns, including inter-series dependencies and intra-series variations. Distinctive trend characteristics in each time series pose challenges, and…

Delay-coordinates dynamic mode decomposition (DC-DMD) is widely used to extract coherent spatiotemporal modes from high-dimensional time series. A central challenge is distinguishing dynamically meaningful modes from spurious modes induced…

This dissertation explores block decomposable methods for large-scale optimization problems. It focuses on alternating direction method of multipliers (ADMM) schemes and block coordinate descent (BCD) methods. Specifically, it introduces a…

Designing faster optimization algorithms is of ever-growing interest. In recent years, learning to learn methods that learn how to optimize demonstrated very encouraging results. Current approaches usually do not effectively include the…

Automated optimization modeling via Large Language Models (LLMs) has emerged as a promising approach to assist complex human decision-making. While post-training has become a pivotal technique to enhance LLMs' capabilities in this domain,…

Distributed machine learning has been widely studied in the literature to scale up machine learning model training in the presence of an ever-increasing amount of data. We study distributed machine learning from another perspective, where…

Stochastic video prediction enables the consideration of uncertainty in future motion, thereby providing a better reflection of the dynamic nature of the environment. Stochastic video prediction methods based on image auto-regressive…

Early and reliable detection of gear faults in complex drivetrain systems is critical for aviation safety and operational availability. We present the Local Damage Mode Extractor (LDME), a structured, physics-informed signal processing…

Recent medical image reconstruction techniques focus on generating high-quality medical images suitable for clinical use at the lowest possible cost and with the fewest possible adverse effects on patients. Recent works have shown…

We study the convergence of a variant of distributed gradient descent (DGD) on a distributed low-rank matrix approximation problem wherein some optimization variables are used for consensus (as in classical DGD) and some optimization…

Manifold learning (ML) aims to seek low-dimensional embedding from high-dimensional data. The problem is challenging on real-world datasets, especially with under-sampling data, and we find that previous methods perform poorly in this case.…

This work proposes convolutional-sparse-coded dynamic mode decomposition (CSC-DMD) by unifying extended dynamic mode decomposition (EDMD) and convolutional sparse coding. EDMD is a data driven analysis method for describing a nonlinear…

We present a data-driven learning approach for unknown nonautonomous dynamical systems with time-dependent inputs based on dynamic mode decomposition (DMD). To circumvent the difficulty of approximating the time-dependent Koopman operators…