Related papers: Fast dynamical similarity analysis
Fitting nonlinear dynamical models to sparse and noisy observations is fundamentally challenging. Identifying dynamics requires data assimilation (DA) to estimate system states, but DA requires an accurate dynamical model. To break this…
Multivariate functional data from a complex system are naturally high-dimensional and have complex cross-correlation structure. The complexity of data structure can be observed as that (1) some functions are strongly correlated with similar…
In the context of model-based control of industrial processes, it is a common practice to develop a data-driven linear dynamical model around a specified operating point. However, in applications involving wider operating conditions,…
Scientific research and engineering practice often require the modeling and decomposition of nonlinear systems. The Dynamic Mode Decomposition (DMD) is a novel Koopman-based technique that effectively dissects high-dimensional nonlinear…
The dynamic emulation of non-linear deterministic computer codes where the output is a time series, possibly multivariate, is examined. Such computer models simulate the evolution of some real-world phenomenon over time, for example models…
Ordinary differential equations (ODE) have been widely used for modeling dynamical complex systems. For high-dimensional ODE models where the number of differential equations is large, it remains challenging to estimate the ODE parameters…
In this draft, fault diagnosis in nonlinear dynamic systems is addressed. The objective of this work is to establish a framework, in which not only model-based but also data-driven and machine learning based fault diagnosis strategies can…
Modern power systems with high penetration of inverter-based resources exhibit complex dynamic behaviors that challenge the scalability and generalizability of traditional stability assessment methods. This paper presents a dynamic…
System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along…
Motivation: The multiple sequence alignment (MSA) problem has been extensively studied, with numerous approaches developed over recent years. With the rapid growth of sequence data, there is an increasing need for fast and accurate MSA…
This work develops a fast, memory-efficient, and general algorithm for accelerated/undersampled dynamic MRI by assuming an approximate LR model on the matrix formed by the vectorized images of the sequence. By general, we mean that our…
Originally introduced in the fluid mechanics community, dynamic mode decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of nonlinear systems. However, existing DMD theory deals primarily with sequential time…
We present a real-time method for robust estimation of multiple instances of geometric models from noisy data. Geometric models such as vanishing points, planar homographies or fundamental matrices are essential for 3D scene analysis.…
Our work tackles the fundamental challenge of image segmentation in computer vision, which is crucial for diverse applications. While supervised methods demonstrate proficiency, their reliance on extensive pixel-level annotations limits…
Homogenisation empowers the efficient macroscale system level prediction of physical scenarios with intricate microscale structures. Here we develop an innovative powerful, rigorous and flexible framework for asymptotic homogenisation of…
We introduce a nonlinear stochastic model reduction technique for high-dimensional stochastic dynamical systems that have a low-dimensional invariant effective manifold with slow dynamics, and high-dimensional, large fast modes. Given only…
Recent advances in Dynamic Sparse Training (DST) have pushed the frontier of sparse neural network training in structured and unstructured contexts, matching dense-model performance while drastically reducing parameter counts to facilitate…
To obtain explicit understanding of the behavior of dynamical systems, geometrical methods and slow-fast analysis have proved to be highly useful. Such methods are standard for smooth dynamical systems, and increasingly used for continuous,…
Dynamic mode decomposition (DMD) gives a practical means of extracting dynamic information from data, in the form of spatial modes and their associated frequencies and growth/decay rates. DMD can be considered as a numerical approximation…
Previous deep image registration methods that employ single homography, multi-grid homography, or thin-plate spline often struggle with real scenes containing depth disparities due to their inherent limitations. To address this, we propose…