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Manifold learning has been proven to be an effective method for capturing the implicitly intrinsic structure of non-Euclidean data, in which one of the primary challenges is how to maintain the distortion-free (isometry) of the data…

The encoder network of an autoencoder is an approximation of the nearest point projection onto the manifold spanned by the decoder. A concern with this approximation is that, while the output of the encoder is always unique, the projection…

Guided wave-based structural health monitoring (SHM) remains a powerful strategy for identifying early-stage defects and safeguarding vital aerospace structures. Yet, its practical use is often hindered by the enormous, high-dimensional…

Variational autoencoders (VAEs) learn representations of data by jointly training a probabilistic encoder and decoder network. Typically these models encode all features of the data into a single variable. Here we are interested in learning…

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…

In this paper we propose Structuring AutoEncoders (SAE). SAEs are neural networks which learn a low dimensional representation of data which are additionally enriched with a desired structure in this low dimensional space. While traditional…

Autoencoders have emerged as powerful models for visualization and dimensionality reduction based on the fundamental assumption that high-dimensional data is generated from a low-dimensional manifold. A critical challenge in autoencoder…

Transformer models have consistently achieved remarkable results in various domains such as natural language processing and computer vision. However, despite ongoing research efforts to better understand these models, the field still lacks…

A convolutional autoencoder is trained using a database of airfoil aerodynamic simulations and assessed in terms of overall accuracy and interpretability. The goal is to predict the stall and to investigate the ability of the autoencoder to…

This paper demonstrates that spatial information can be used to learn interpretable representations in medical images using Self-Supervised Learning (SSL). Our proposed method, ISImed, is based on the observation that medical images exhibit…

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…

Molecular dynamics simulations produce data with complex nonlinear dynamics. If the timestep behavior of such a dynamic system can be represented by a linear operator, future states can be inferred directly without expensive simulations.…

Four-dimensional scanning transmission electron microscopy (4D-STEM) of local atomic diffraction patterns is emerging as a powerful technique for probing intricate details of atomic structure and atomic electric fields. However, efficient…

We present an algorithm to learn the relevant latent variables of a large-scale discretized physical system and predict its time evolution using thermodynamically-consistent deep neural networks. Our method relies on sparse autoencoders,…

The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of the success of convolutional neural networks (ConvNets) in image data analysis and other tasks. Inspired by recent interest…

Graph transformers typically embed every node in a single Euclidean space, blurring heterogeneous topologies. We prepend a lightweight Riemannian mixture-of-experts layer that routes each node to various kinds of manifold, mixture of…

Learning a latent embedding to understand the underlying nature of data distribution is often formulated in Euclidean spaces with zero curvature. However, the success of the geometry constraints, posed in the embedding space, indicates that…

One of the key challenges in learning joint embeddings of multiple modalities, e.g. of images and text, is to ensure coherent cross-modal semantics that generalize across datasets. We propose to address this through joint Gaussian…

The variational autoencoder (VAE) can learn the manifold of natural images on certain datasets, as evidenced by meaningful interpolating or extrapolating in the continuous latent space. However, on discrete data such as text, it is unclear…

Network embedding aims to learn a latent, low-dimensional vector representations of network nodes, effective in supporting various network analytic tasks. While prior arts on network embedding focus primarily on preserving network topology…