Related papers: Higher order multi-dimension reduction methods via…
In this work, we investigate Riemannian geometry based dimensionality reduction methods that respect the underlying manifold structure of the data. In particular, we focus on Principal Geodesic Analysis (PGA) as a nonlinear generalization…
We consider the problem of reducing the dimensions of parameters and data in non-Gaussian Bayesian inference problems. Our goal is to identify an "informed" subspace of the parameters and an "informative" subspace of the data so that a…
Derivative expansion and large-$D$ expansion are two perturbation techniques, which are used to generate dynamical black-brane solutions to Einstein's equations in presence of negative cosmological constant. In this note we have compared…
In this thesis special emphasis is put on the quantization of the spherically reduced Einstein-massless-Klein-Gordon model using a first order approach for geometric quantities, because phenomenologically it is probably the most relevant of…
These notes are an overview of some classical linear methods in Multivariate Data Analysis. This is a good old domain, well established since the 60's, and refreshed timely as a key step in statistical learning. It can be presented as part…
We introduce a deep residual recurrent neural network (DR-RNN) as an efficient model reduction technique for nonlinear dynamical systems. The developed DR-RNN is inspired by the iterative steps of line search methods in finding the residual…
In the vast landscape of visualization research, Dimensionality Reduction (DR) and graph analysis are two popular subfields, often essential to most visual data analytics setups. DR aims to create representations to support neighborhood and…
It is well known that the Einstein-Hilbert action in two dimensions is topological and yields an identically vanishing Einstein tensor. Consequently one is faced with difficulties when formulating a non-trivial gravity model. We present a…
An analysis of high-dimensional data can offer a detailed description of a system but is often challenged by the curse of dimensionality. General dimensionality reduction techniques can alleviate such difficulty by extracting a few…
Spectral dimensionality reduction algorithms are widely used in numerous domains, including for recognition, segmentation, tracking and visualization. However, despite their popularity, these algorithms suffer from a major limitation known…
Complex design problems are common in the scientific and industrial fields. In practice, objective functions or constraints of these problems often do not have explicit formulas, and can be estimated only at a set of sampling points through…
Dimension reduction (DR) aims to learn low-dimensional representations of high-dimensional data with the preservation of essential information. In the context of manifold learning, we define that the representation after…
Many machine learning applications deal with high dimensional data. To make computations feasible and learning more efficient, it is often desirable to reduce the dimensionality of the input variables by finding linear combinations of the…
High dynamic range (HDR) imaging has recently drawn much attention in multimedia community. In this paper, we proposed a HDR image forensics method based on convolutional neural network (CNN).To our best knowledge, this is the first time to…
This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order…
Embedding high-dimensional data onto a low-dimensional manifold is of both theoretical and practical value. In this paper, we propose to combine deep neural networks (DNN) with mathematics-guided embedding rules for high-dimensional data…
This paper studies the $d$-dimensional extension of a fictitious domain penalization technique that we previously proposed for Neumann or Robin boundary conditions. We apply Droniou's approach for non-coercive linear elliptic problems to…
Constructing the landscape of vacua of higher-dimensional theories of gravity by directly solving the low-energy (semi-)classical equations of motion is notoriously difficult. In this work, we investigate the feasibility of Machine Learning…
We present novel model reduction methods for rapid solution of parametrized nonlinear partial differential equations (PDEs) in real-time or many-query contexts. Our approach combines reduced basis (RB) space for rapidly convergent…
Motivated by integrability of the sine-Gordon equation, we investigate a technique for constructing desired solutions to Einstein's equations by combining a dressing technique with a control-theory approach. After reviewing classical…