Related papers: Learning low-dimensional representations of ensemb…

Multidimensional scaling of gene sequence data has long played a vital role in analysing gene sequence data to identify clusters and patterns. However the computation complexities and memory requirements of state-of-the-art dimensional…

A common pipeline in functional data analysis is to first convert the discretely observed data to smooth functions, and then represent the functions by a finite-dimensional vector of coefficients summarizing the information. Existing…

Nowadays, massive datasets are typically dispersed across multiple locations, encountering dual challenges of high dimensionality and huge sample size. Therefore, it is necessary to explore sufficient dimension reduction (SDR) methods for…

One of the fundamental problems in machine learning is the estimation of a probability distribution from data. Many techniques have been proposed to study the structure of data, most often building around the assumption that observations…

Reducing dimensionality is a key preprocessing step in many data analysis applications to address the negative effects of the curse of dimensionality and collinearity on model performance and computational complexity, to denoise the data or…

The emergence of low-cost sensor architectures for diverse modalities has made it possible to deploy sensor arrays that capture a single event from a large number of vantage points and using multiple modalities. In many scenarios, these…

Physics-constrained data-driven computing is an emerging computational paradigm that allows simulation of complex materials directly based on material database and bypass the classical constitutive model construction. However, it remains…

Multidimensional scaling (MDS) is a popular dimensionality reduction techniques that has been widely used for network visualization and cooperative localization. However, the traditional stress minimization formulation of MDS necessitates…

Variational autoencoders employ an encoding neural network to generate a probabilistic representation of a data set within a low-dimensional space of latent variables followed by a decoding stage that maps the latent variables back to the…

We present a systematic investigation of convolutional autoencoders for the reduced-order representation of three-dimensional interfacial multiphase flows. Focusing on the reconstruction of phase indicators, we examine how the choice of…

Weather forecasting presents several challenges, including the chaotic nature of the atmosphere and the high computational demands of numerical weather prediction models. To achieve the most accurate predictions, the ideal scenario involves…

Airfoil shape optimization plays a critical role in the design of high-performance aircraft. However, the high-dimensional nature of airfoil representation causes the challenging problem known as the "curse of dimensionality". To overcome…

Well-established methods for the solution of stochastic partial differential equations (SPDEs) typically struggle in problems with high-dimensional inputs/outputs. Such difficulties are only amplified in large-scale applications where even…

Building on recent advances in representation learning for wireless channels, this work investigates the cost-benefit trade-offs of high-dimensional channel embeddings in practical systems. We benchmark multiple wireless representations:…

Ensemble forecasting is a technique devised to palliate sensitivity to initial conditions in nonlinear dynamical systems. The basic idea to avoid this sensitivity is to run the model many times under several slightly-different initial…

The rapid advancement of artificial intelligence (AI) in weather research has been driven by the ability to learn from large, high-dimensional datasets. However, this progress also poses significant challenges, particularly regarding the…

This paper proposes a theoretical framework on the mechanism of autoencoders. To the encoder part, under the main use of dimensionality reduction, we investigate its two fundamental properties: bijective maps and data disentangling. The…

The use of deep learning methods for modeling fluid flow has drawn a lot of attention in the past few years. In situations where conventional numerical approaches can be computationally expensive, these techniques have shown promise in…

Global climate projections rely on computationally demanding Earth System Models (ESMs), which are typically limited to coarse spatial resolutions due to their high cost. To obtain high-resolution projections for regions of interest, it is…

Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…