Related papers: MODULO: A software for Multiscale Proper Orthogona…
In the present work, we introduce a data-driven approach to enhance the accuracy of non-intrusive Reduced Order Models (ROMs). In particular, we focus on ROMs built using Proper Orthogonal Decomposition (POD) in an under-resolved and…
In this paper, we propose novel proper orthogonal decomposition (POD)--based model reduction methods that effectively address the issue of inverse crime in solving parabolic inverse problems. Both the inverse initial value problems and…
We introduce a new adaptive decomposition tool, which we refer to as Nonlinear Mode Decomposition (NMD). It decomposes a given signal into a set of physically meaningful oscillations for any waveform, simultaneously removing the noise. NMD…
The dynamic mode decomposition (DMD) has become a leading tool for data-driven modeling of dynamical systems, providing a regression framework for fitting linear dynamical models to time-series measurement data. We present a simple…
The dynamic mode decomposition (DMD) is a simple and powerful data-driven modeling technique that is capable of revealing coherent spatiotemporal patterns from data. The method's linear algebra-based formulation additionally allows for a…
Multiobjective Evolutionary Algorithms based on Decomposition (MOEA/D) represent a widely used class of population-based metaheuristics for the solution of multicriteria optimization problems. We introduce the MOEADr package, which offers…
The freud Python package is a powerful library for analyzing simulation data. Written with modern simulation and data analysis workflows in mind, freud provides a Python interface to fast, parallelized C++ routines that run efficiently on…
In autonomous driving, data augmentation is commonly used for improving 3D object detection. The most basic methods include insertion of copied objects and rotation and scaling of the entire training frame. Numerous variants have been…
Dynamic Mode Decomposition (DMD) is a data-driven decomposition technique extracting spatio-temporal patterns of time-dependent phenomena. In this paper, we perform a comprehensive theoretical analysis of various variants of DMD. We provide…
At the forefront of state-of-the-art human alignment methods are preference optimization methods (*PO). Prior research has often concentrated on identifying the best-performing method, typically involving a grid search over hyperparameters,…
We propose Orthogonal Monte Carlo Dropout, a mechanism that enforces strict orthogonality when combining sparse semantic vectors without extra time complexity. Low-Rank Adaptation (LoRA), a popular fine-tuning method for large models,…
The multicomponent oxide solid solution is a versatile platform to tune the delicate balance between competing spin, charge, orbital, and lattice degrees of freedom for materials design and discovery. The development of compositionally…
There is a broad need in the neuroscience community to understand and visualize large-scale recordings of neural activity, big data acquired by tens or hundreds of electrodes simultaneously recording dynamic brain activity over minutes to…
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…
In this paper, we present a Localized Orthogonal Decomposition (LOD) in Petrov-Galerkin formulation for a two-scale Helmholtz-type problem. The two-scale problem is, for instance, motivated from the homogenization of the Helmholtz equation…
The use of multitaper estimates for spectral proper orthogonal decomposition (SPOD) is explored. Multitaper and multitaper-Welch estimators that use discrete prolate spheroidal sequences (DPSS) as orthogonal data windows are compared to 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…
The error analysis of a proper orthogonal decomposition (POD) data assimilation (DA) scheme for the Navier-Stokes equations is carried out. A grad-div stabilization term is added to the formulation of the POD method. Error bounds with…
In this paper, we consider the model reduction problem of large-scale systems, such as systems obtained through the discretization of partial differential equations. We propose a computationally optimal randomized proper orthogonal…
Aligning large language models (LLMs) to desirable human values requires balancing multiple, potentially conflicting objectives such as helpfulness, truthfulness, and harmlessness, which presents a multi-objective optimisation challenge.…