Related papers: Learning latent representations in high-dimensiona…
We introduce an unsupervised machine-learning framework that discovers optimally compressed representations of quantum many-body ground states. Using an autoencoder neural network architecture on data from $L$-site Fermi-Hubbard models, we…
A common belief in high-dimensional data analysis is that data are concentrated on a low-dimensional manifold. This motivates simultaneous dimension reduction and regression on manifolds. We provide an algorithm for learning gradients on…
Datasets such as images, text, or movies are embedded in high-dimensional spaces. However, in important cases such as images of objects, the statistical structure in the data constrains samples to a manifold of dramatically lower…
Manifold learning is a hot research topic in the field of computer science and has many applications in the real world. A main drawback of manifold learning methods is, however, that there is no explicit mappings from the input data…
Autonomous robots require high degrees of cognitive and motoric intelligence to come into our everyday life. In non-structured environments and in the presence of uncertainties, such degrees of intelligence are not easy to obtain.…
In this paper we present a fully Bayesian latent variable model which exploits conditional nonlinear(in)-dependence structures to learn an efficient latent representation. The latent space is factorized to represent shared and private…
We consider the problem of learning low-dimensional representations for large-scale Markov chains. We formulate the task of representation learning as that of mapping the state space of the model to a low-dimensional state space, called the…
This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…
Representation learning is typically applied to only one mode of a data matrix, either its rows or columns. Yet in many applications, there is an underlying geometry to both the rows and the columns. We propose utilizing this coupled…
Dimensionality reduction techniques map data represented on higher dimensions onto lower dimensions with varying degrees of information loss. Graph dimensionality reduction techniques adopt the same principle of providing latent…
Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…
Manifold learning flows are a class of generative modelling techniques that assume a low-dimensional manifold description of the data. The embedding of such a manifold into the high-dimensional space of the data is achieved via learnable…
For functional data lying on an unknown nonlinear low-dimensional space, we study manifold learning and introduce the notions of manifold mean, manifold modes of functional variation and of functional manifold components. These constitute…
Data living on manifolds commonly appear in many applications. Often this results from an inherently latent low-dimensional system being observed through higher dimensional measurements. We show that under certain conditions, it is possible…
We develop data-driven methods for incorporating physical information for priors to learn parsimonious representations of nonlinear systems arising from parameterized PDEs and mechanics. Our approach is based on Variational Autoencoders…
This work proposes an algorithm for explicitly constructing a pair of neural networks that linearize and reconstruct an embedded submanifold, from finite samples of this manifold. Our such-generated neural networks, called Flattening…
Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…
Sparse autoencoders have become a standard tool for uncovering interpretable latent representations in neural networks. Yet salient concepts often span manifolds that current linear methods cannot capture without post hoc analysis. This…
This work proposes an approach for latent-dynamics learning that exactly enforces physical conservation laws. The method comprises two steps. First, the method computes a low-dimensional embedding of the high-dimensional dynamical-system…
Recently developed reduced-order modeling techniques aim to approximate nonlinear dynamical systems on low-dimensional manifolds learned from data. This is an effective approach for modeling dynamics in a post-transient regime where the…