Related papers: Variational Autoencoders for Learning Nonlinear Dy…

We develop data-driven methods incorporating geometric and topological information to learn parsimonious representations of nonlinear dynamics from observations. The approaches learn nonlinear state-space models of the dynamics for general…

The manifold hypothesis states that high-dimensional data can be modeled as lying on or near a low-dimensional, nonlinear manifold. Variational Autoencoders (VAEs) approximate this manifold by learning mappings from low-dimensional latent…

The recently developed variational autoencoders (VAEs) have proved to be an effective confluence of the rich representational power of neural networks with Bayesian methods. However, most work on VAEs use a rather simple prior over the…

Variational Autoencoders (VAEs) are well-established as a principled approach to probabilistic unsupervised learning with neural networks. Typically, an encoder network defines the parameters of a Gaussian distributed latent space from…

Variational autoencoders (VAEs) have been used extensively to discover low-dimensional latent factors governing neural activity and animal behavior. However, without careful model selection, the uncovered latent factors may reflect noise in…

Integrating physics models within machine learning models holds considerable promise toward learning robust models with improved interpretability and abilities to extrapolate. In this work, we focus on the integration of incomplete physics…

The combination of machine learning models with physical models is a recent research path to learn robust data representations. In this paper, we introduce p$^3$VAE, a variational autoencoder that integrates prior physical knowledge about…

Representation learning seeks to expose certain aspects of observed data in a learned representation that's amenable to downstream tasks like classification. For instance, a good representation for 2D images might be one that describes only…

The paper presents the application of Variational Autoencoders (VAE) for data dimensionality reduction and explorative analysis of mass spectrometry imaging data (MSI). The results confirm that VAEs are capable of detecting the patterns…

Given the notably increasing complexity of mathematical models to study realistic systems and their coupling to their environment that constrains their dynamics, both analytical approaches and numerical methods that build on these models,…

We develop Riemannian approaches to variational autoencoders (VAEs) for PDE-type ambient data with regularizing geometric latent dynamics, which we refer to as VAE-DLM, or VAEs with dynamical latent manifolds. We redevelop the VAE framework…

In just three years, Variational Autoencoders (VAEs) have emerged as one of the most popular approaches to unsupervised learning of complicated distributions. VAEs are appealing because they are built on top of standard function…

Recent advances in electron, scanning probe, optical, and chemical imaging and spectroscopy yield bespoke data sets containing the information of structure and functionality of complex systems. In many cases, the resulting data sets are…

Electron, optical, and scanning probe microscopy methods are generating ever increasing volume of image data containing information on atomic and mesoscale structures and functionalities. This necessitates the development of the machine…

System identification of complex and nonlinear systems is a central problem for model predictive control and model-based reinforcement learning. Despite their complexity, such systems can often be approximated well by a set of linear…

Variational autoencoders (VAEs) are widely used deep generative models capable of learning unsupervised latent representations of data. Such representations are often difficult to interpret or control. We consider the problem of…

Autoencoders exhibit impressive abilities to embed the data manifold into a low-dimensional latent space, making them a staple of representation learning methods. However, without explicit supervision, which is often unavailable, the…

Recently there has been an increased interest in unsupervised learning of disentangled representations using the Variational Autoencoder (VAE) framework. Most of the existing work has focused largely on modifying the variational cost…

Motion planning with constraints is an important part of many real-world robotic systems. In this work, we study manifold learning methods to learn such constraints from data. We explore two methods for learning implicit constraint…

The variational auto-encoder (VAE) is a popular method for learning a generative model and embeddings of the data. Many real datasets are hierarchically structured. However, traditional VAEs map data in a Euclidean latent space which cannot…