Related papers: Fast dynamical similarity analysis
Modeling dynamical systems plays a crucial role in capturing and understanding complex physical phenomena. When physical models are not sufficiently accurate or hardly describable by analytical formulas, one can use generic function…
The applications of traditional statistical feature selection methods to high-dimension, low sample-size data often struggle and encounter challenging problems, such as overfitting, curse of dimensionality, computational infeasibility, and…
We formulate a nonlinear synergistic theory of coevolutionary systems, disentangling and explaining dynamic complexity in terms of fundamental processes for optimised data analysis and dynamic model design: Dynamic Source Analysis (DSA).…
The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and…
Dynamic analysis of structures subjected to earthquake excitation is a time-consuming process, particularly in the case of extremely small time step required, or in the presence of high geometric and material nonlinearity. Performing…
Similarity analysis is one of the crucial steps in most fMRI studies. Representational Similarity Analysis (RSA) can measure similarities of neural signatures generated by different cognitive states. This paper develops Deep…
Digitising the 3D world into a clean, CAD model-based representation has important applications for augmented reality and robotics. Current state-of-the-art methods are computationally intensive as they individually encode each detected…
Sequence alignment algorithms are a basic and critical component of many bioinformatics fields. With rapid development of sequencing technology, the fast growing reference database volumes and longer length of query sequence become new…
We propose data-driven nonlinear smoother (DNS) to estimate a hidden state sequence of a complex dynamical process from a noisy, linear measurement sequence. The dynamical process is model-free, that is, we do not have any knowledge of the…
Complex systems often show macroscopic coherent behavior due to the interactions of microscopic agents like molecules, cells, or individuals in a population with their environment. However, simulating such systems poses several…
Linear dimensionality reduction methods are commonly used to extract low-dimensional structure from high-dimensional data. However, popular methods disregard temporal structure, rendering them prone to extracting noise rather than…
Deep neural networks (DNNs) have achieved great success in the area of computer vision. The disparity estimation problem tends to be addressed by DNNs which achieve much better prediction accuracy in stereo matching than traditional…
Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article develops and analyzes a data-dependent metric known as diffusion state distance (DSD), which compares points using a…
We present a fast method for nonlinear data-driven model reduction of dynamical systems onto their slowest nonresonant spectral submanifolds (SSMs). We use observed data to locate a low-dimensional, attracting slow SSM and compute a…
Nonlinear system design is often a multi-objective optimization problem involving search for a design that satisfies a number of predefined constraints. The design space is typically very large since it includes all possible system…
Subgraph matching has garnered increasing attention for its diverse real-world applications. Given the dynamic nature of real-world graphs, addressing evolving scenarios without incurring prohibitive overheads has been a focus of research.…
Applications of Discrete Fracture Network (DFN) modeling are becoming increasingly prevalent in engineering analyses involving fractured rock masses. For example, kinematic evaluations of slope or underground excavation stability and the…
Many time series data mining problems can be solved with repeated use of distance measure. Examples of such tasks include similarity search, clustering, classification, anomaly detection and segmentation. For over two decades it has been…
In this paper, a two-step strategy for parametric sensitivity analysis for such systems is proposed, exploiting advantages and synergies between two recently proposed sensitivity analysis methodologies for stochastic dynamics. The first…
Nonlinear dynamical systems are complex and typically only simple systems can be analytically studied. In applications, these systems are usually defined with a set of tunable parameters and as the parameters are varied the system response…