相关论文: Model sets: a survey

Weather forecasting has seen a shift in methods from numerical simulations to data-driven systems. While initial research in the area focused on deterministic forecasting, recent works have used diffusion models to produce skillful ensemble…

An introduction to applied mathematics written for students in engineering and science. Focus is on a rigorous presentation that also builds understanding by discussion, analogy, and examples. Discussion of concepts involved in modeling…

A graph is a data structure composed of dots (i.e. vertices) and lines (i.e. edges). The dots and lines of a graph can be organized into intricate arrangements. The ability for a graph to denote objects and their relationships to one…

Diffusion Models (DMs), also referred to as score-based diffusion models, utilize neural networks to specify score functions. Unlike most other probabilistic models, DMs directly model the score functions, which makes them more flexible to…

The inverse problem of diffraction theory in essence amounts to the reconstruction of the atomic positions of a solid from its diffraction image. From a mathematical perspective, this is a notoriously difficult problem, even in the…

There have been rapid developments in model-based clustering of graphs, also known as block modelling, over the last ten years or so. We review different approaches and extensions proposed for different aspects in this area, such as the…

This work presents a reduced order modelling technique built on a high fidelity embedded mesh finite element method. Such methods, and in particular the CutFEM method, are attractive in the generation of projection-based reduced order…

Driven by the visions of Internet of Things and 5G communications, the edge computing systems integrate computing, storage and network resources at the edge of the network to provide computing infrastructure, enabling developers to quickly…

Dynamical sampling refers to a class of problems in which space-time samples are taken from a signal evolving under an underlying dynamical system. The goal is to use these samples to recover relevant information about the system, such as…

This paper introduces a comprehensive unified framework for constructing multi-view diffusion geometries through intertwined multi-view diffusion trajectories (MDTs), a class of inhomogeneous diffusion processes that iteratively combine the…

Point processes model the distribution of random point sets in mathematical spaces, such as spatial and temporal domains, with applications in fields like seismology, neuroscience, and economics. Existing statistical and machine learning…

Starting from a variational formulation, we present a model for image segmentation that employs both region statistics and edge information. This combination allows for improved flexibility, making the proposed model suitable to process a…

We present a method of discrete modeling and analysis of multilevel dynamics of complex large-scale hierarchical dynamic systems subject to external dynamic control mechanism. Architectural model of information system supporting simulation…

Models for the microstructure evolution during hot rolling are reviewed. The basic macroscopic phenomena related to recrystallization are summarized. Constitutive models based on semi empirical equations are compared to more sophisticated…

In this short note, we discuss the basic approach to computational modeling of dynamical systems. If a dynamical system contains multiple time scales, ranging from very fast to slow, computational solution of the dynamical system can be…

Feature extraction is a critical technology to realize the automatic transmission of feature information throughout product life cycles. As CAD models primarily capture the 3D geometry of products, feature extraction heavily relies on…

The complex dynamics of physical systems can often be modeled with stochastic differential equations. However, computational constraints inhibit the estimation of dynamics from large time-series datasets. I present a method for estimating…

Diffusion models have become a new SOTA generative modeling method in various fields, for which there are multiple survey works that provide an overall survey. With the number of articles on diffusion models increasing exponentially in the…

The wide application of estimation techniques in system analysis enable us to best determine and understand the history of system states. This paper attempts to delineate the theory behind linear and non-linear estimation with a suitable…

Finite mixture models have been a very important tool for exploring complex data structures in many scientific areas, for example, economics, epidemiology, finance. In the past decade, semiparametric techniques have been popularly…