Related papers: Functional Continuous Decomposition
Time evolving surfaces can be modeled as two-dimensional Functional time series, exploiting the tools of Functional data analysis. Leveraging this approach, a forecasting framework for such complex data is developed. The main focus revolves…
Feature extraction is a key step in image processing for pattern recognition and machine learning processes. Its purpose lies in reducing the dimensionality of the input data through the computing of features which accurately describe the…
Compression-based similarity measures are effectively employed in applications on diverse data types with a basically parameter-free approach. Nevertheless, there are problems in applying these techniques to medium-to-large datasets which…
Dynamic mode decomposition (DMD) is a powerful data-driven technique for construction of reduced-order models of complex dynamical systems. Multiple numerical tests have demonstrated the accuracy and efficiency of DMD, but mostly for…
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 demonstrate that the integration of the recently developed dynamic mode decomposition (DMD) with a multi-resolution analysis allows for a decomposition method capable of robustly separating complex systems into a hierarchy of…
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…
Surface meshes are widely used shape representations and capture finer geometry data than point clouds or volumetric grids, but are challenging to apply CNNs directly due to their non-Euclidean structure. We use parallel frames on surface…
Convolutional neural networks (CNN) have recently achieved remarkable successes in various image classification and understanding tasks. The deep features obtained at the top fully-connected layer of the CNN (FC-features) exhibit rich…
Computational Fluid Dynamics (CFD) is widely used in different engineering fields, but accurate simulations are dependent upon proper meshing of the simulation domain. While highly refined meshes may ensure precision, they come with high…
We present a data-driven method for separating complex, multiscale systems into their constituent time-scale components using a recursive implementation of dynamic mode decomposition (DMD). Local linear models are built from windowed…
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…
Predicting interfacial thermodynamics across molecular and continuum scales remains a central challenge in computational science. Classical density functional theory (cDFT) provides a first-principles route to connect microscopic…
Deploying Convolutional Neural Networks (CNNs) on resource-constrained devices necessitates efficient management of computational resources, often via distributed environments susceptible to latency from straggler nodes. This paper…
CFD is widely used in physical system design and optimization, where it is used to predict engineering quantities of interest, such as the lift on a plane wing or the drag on a motor vehicle. However, many systems of interest are…
We have developed an image-based convolutional neural network (CNN) that is applicable for quantitative time-resolved measurements of the fragmentation behavior of opaque brittle materials using ultra-high speed optical imaging. This model…
Continual learning (CL) aims to learn new tasks while retaining past knowledge, addressing the challenge of forgetting during task adaptation. Rehearsal-based methods, which replay previous samples, effectively mitigate forgetting. However,…
Modal decomposition techniques, such as Empirical Mode Decomposition (EMD), Variational Mode Decomposition (VMD), and Singular Spectrum Analysis (SSA), have advanced time-frequency signal analysis since the early 21st century. These methods…
Diffusion Language Models (DLMs) have recently achieved significant success due to their any-order generation capabilities. However, existing inference methods typically rely on local, immediate-step metrics such as confidence or entropy…
Measurements from particle timing detectors are often affected by the time walk effect caused by statistical fluctuations in the charge deposited by passing particles. The constant fraction discriminator (CFD) algorithm is frequently used…