Related papers: Latent Mode Decomposition
This work proposes a new framework of model reduction for parametric complex systems. The framework employs a popular model reduction technique dynamic mode decomposition (DMD), which is capable of combining data-driven learning and physics…
The conventional modal analysis techniques face difficulties in handling nonstationary phenomena, such as transient, nonperiodic, or intermittent phenomena. This paper presents a variational mode decomposition--based nonstationary coherent…
Automatically determining the number of intrinsic mode functions (IMFs) and their center frequencies in Variational Mode Decomposition (VMD) remains an open mathematical challenge. Existing methods rely on heuristic settings,…
Turbulent flows are chaotic and multi-scale dynamical systems, which have large numbers of degrees of freedom. Turbulent flows, however, can be modelled with a smaller number of degrees of freedom when using the appropriate coordinate…
Low-rank decomposition (LRD) is a state-of-the-art method for visual data reconstruction and modelling. However, it is a very challenging problem when the image data contains significant occlusion, noise, illumination variation, and…
The interaction of multiple fluids through a heterogeneous pore space leads to complex pore-scale flow dynamics, such as intermittent pathway flow. The non-local nature of these dynamics, and the size of the 4D datasets acquired to capture…
Large vision-language models (LVLMs) have shown remarkable capabilities in visual-language understanding for downstream multi-modal tasks. Despite their success, LVLMs still suffer from generating hallucinations in complex generation tasks,…
Large Vision-Language Models (LVLMs) have shown strong performance across multimodal tasks. However, they often produce hallucinations -- text that is inconsistent with visual input, due to the limited ability to verify information in…
This note proposes a simple and general framework of dynamic mode decomposition (DMD) and a mode selection for large datasets. The proposed framework explicitly introduces a preconditioning step using an incremental proper orthogonal…
Dynamic mode decomposition (DMD) has emerged as a popular data-driven modeling approach to identifying spatio-temporal coherent structures in dynamical systems, owing to its strong relation with the Koopman operator. For dynamical systems…
We introduce a computationally efficient method for the automation of inverse design in science and engineering. Based on simple least-square regression, the underlying dynamic mode decomposition algorithm can be used to construct a…
The dynamic mode decomposition (DMD) is a broadly applicable dimensionality reduction algorithm that approximates a matrix containing time-series data by the outer product of a matrix of exponentials, representing Fourier-like time…
This research introduces a transformative framework for integrating Vision-Enhanced Large Language Models (LLMs) with advanced transformer-based architectures to tackle challenges in high-resolution image synthesis and multimodal data…
We propose a new technique for obtaining reduced order models for nonlinear dynamical systems. Specifically, we advocate the use of the recently developed Dynamic Mode Decomposition (DMD), an equation-free method, to approximate the…
Autoregressive vision-language models (VLMs) deliver strong multimodal capability, but their token-by-token decoding imposes a fundamental inference bottleneck. Diffusion VLMs offer a more parallel decoding paradigm, yet directly converting…
Modal decomposition techniques are important tools for the analysis of unsteady flows and, in order to provide meaningful insights with respect to coherent structures and their characteristic frequencies, the modes must possess a robust…
Low-rank decomposition has emerged as an important problem in Large Language Model (LLM) fine-tuning and inference. Through Singular Value Decomposition (SVD), the weight matrix can be factorized into low-rank spaces optimally. Previously,…
Question decomposition has emerged as an effective strategy for prompting Large Language Models (LLMs) to answer complex questions. However, while existing methods primarily focus on unimodal language models, the question decomposition…
The EMD algorithm, first proposed in [11], made more robust as well as more versatile in [12], is a technique that aims to decompose into their building blocks functions that are the superposition of a (reasonably) small number of…
We introduce the method of compressed dynamic mode decomposition (cDMD) for background modeling. The dynamic mode decomposition (DMD) is a regression technique that integrates two of the leading data analysis methods in use today: Fourier…