Related papers: Generalized and Multiscale Modal Analysis
Time-delay embedding is an increasingly popular starting point for data-driven reduced-order modeling efforts. In particular, the singular value decomposition (SVD) of a block Hankel matrix formed from successive delay embeddings of the…
The classical persistence algorithm computes the unique decomposition of a persistence module implicitly given by an input simplicial filtration. Based on matrix reduction, this algorithm is a cornerstone of the emergent area of topological…
Modal identification is crucial for structural health monitoring and structural control, providing critical insights into structural dynamics and performance. This study presents a novel deep learning framework that integrates graph neural…
We propose a new algorithm to compute a shifted proper orthogonal decomposition (sPOD) for systems dominated by multiple transport velocities. The sPOD is a recently proposed mode decomposition technique which overcomes the poor performance…
In this work we combine the framework of the Reduced Basis method (RB) with the framework of the Localized Orthogonal Decomposition (LOD) in order to solve parametrized elliptic multiscale problems. The idea of the LOD is to split a high…
We provide a generalization of the normal mode decomposition for non-symmetric or locality constrained situations. This allows for instance to locally decouple a bipartitioned collection of arbitrarily correlated oscillators up to…
We present a new methodology for the real-time reduced-order modeling of stochastic partial differential equations called the dynamically/bi-orthonormal (DBO) decomposition. In this method, the stochastic fields are approximated by a…
This work presents the application of the Complex Orthogonal Decomposition (C.O.D.) to a simple spatio-temporal signal. C.O.D. has been introduced rst in the article of B. Feeny, entitled "A Complex Orthogonal Decomposition for Wave Motion…
Multimodal learning leverages the integration of diverse data modalities to enhance performance in complex tasks. Yet, it frequently encounters incomplete or redundant modality data in real-world scenarios. This paper presents a…
We consider model order reduction by proper orthogonal decomposition (POD) for parametrized partial differential equations, where the underlying snapshots are computed with adaptive finite elements. We address computational and theoretical…
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…
We study partial fraction decompositions (PFDs) in several variables using tools from commutative algebra. We give criteria for when a rational function with poles on a hyperplane arrangement has a desirable PFD. Our criteria are obtained…
Deep learning-based reduced order models (DL-ROMs) have been recently proposed to overcome common limitations shared by conventional reduced order models (ROMs) - built, e.g., through proper orthogonal decomposition (POD) - when applied to…
The correlation and extraction of coherent structures from a turbulent flow is a principle objective of data-driven modal decomposition techniques. The Conditional space-time Proper Orthogonal Decomposition (CPOD) offers insight into…
We present the G-MAPLE (Generalised Modal Analysis from the Poles of the Laplace Expansion) software that allows decomposing data depending on a single parameter (such as time series data) into a set of exponential functions having complex…
The different orthogonal relationships that exists in the Lowdin orthogonalizations is presented. Other orthogonalization techniques such as polar decomposition (PD), principal component analysis (PCA) and reduced singular value…
In many mechanical, electrical, and general physical systems evolving over time or space, spectral analysis methods as Fast Fourier Transform (FFT), Short Term Fourier Transform (STFT), Power Spectrum Density (PSD) plays a very important…
This study investigates the generalization capabilities and robustness of purely deep learning (DL) models and hybrid models based on physical principles in fluid dynamics applications, specifically focusing on iteratively forecasting the…
In this study, an efficient reanalysis strategy for dynamic topology optimization is proposed. Compared with other related studies, an online successive dynamic reanalysis method and POD-based approximate dynamic displacement strategy are…
In a recent paper, we have shown that warped time-frequency representations provide a rich framework for the construction and study of smoothness spaces matched to very general phase space geometries obtained by diffeomorphic deformations…