Related papers: Variational Autoencoding Neural Operators
Variational Autoencoders (VAEs) have become a popular approach for dimensionality reduction. However, despite their ability to identify latent low-dimensional structures embedded within high-dimensional data, these latent representations…
Scientific machine learning has enabled the extraction of physical insights and data-driven modeling of high-dimensional spatiotemporal data, yet achieving physically interpretable latent representations and computationally efficient…
While unsupervised variational autoencoders (VAE) have become a powerful tool in neuroimage analysis, their application to supervised learning is under-explored. We aim to close this gap by proposing a unified probabilistic model for…
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…
Supervised learning in function spaces is an emerging area of machine learning research with applications to the prediction of complex physical systems such as fluid flows, solid mechanics, and climate modeling. By directly learning maps…
Understanding the structure of complex, nonstationary, high-dimensional time-evolving signals is a central challenge in scientific data analysis. In many domains, such as speech and biomedical signal processing, the ability to learn…
Solving partial differential equations (PDEs) is a required step in the simulation of natural and engineering systems. The associated computational costs significantly increase when exploring various scenarios, such as changes in initial or…
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…
A variational autoencoder (VAE) is a probabilistic machine learning framework for posterior inference that projects an input set of high-dimensional data to a lower-dimensional, latent space. The latent space learned with a VAE offers…
Quantum machine learning -- and specifically Variational Quantum Algorithms (VQAs) -- offers a powerful, flexible paradigm for programming near-term quantum computers, with applications in chemistry, metrology, materials science, data…
Autoencoders have found widespread application in both their original deterministic form and in their variational formulation (VAEs). In scientific applications and in image processing it is often of interest to consider data that are…
Variational autoencoders (VAEs) are a popular class of deep generative models with many variants and a wide range of applications. Improvements upon the standard VAE mostly focus on the modelling of the posterior distribution over the…
Existing architectures for operator learning require that the number and locations of sensors (where the input functions are evaluated) remain the same across all training and test samples, significantly restricting the range of their…
With massive advancements in sensor technologies and Internet-of-things, we now have access to terabytes of historical data; however, there is a lack of clarity in how to best exploit the data to predict future events. One possible…
The key idea of variational auto-encoders (VAEs) resembles that of traditional auto-encoder models in which spatial information is supposed to be explicitly encoded in the latent space. However, the latent variables in VAEs are vectors,…
Learning a generative model from partial data (data with missingness) is a challenging area of machine learning research. We study a specific implementation of the Auto-Encoding Variational Bayes (AEVB) algorithm, named in this paper as a…
In end-to-end optimized learned image compression, it is standard practice to use a convolutional variational autoencoder with generalized divisive normalization (GDN) to transform images into a latent space. Recently, Operational Neural…
Fourier neural operators (FNOs) can learn highly nonlinear mappings between function spaces, and have recently become a popular tool for learning responses of complex physical systems. However, to achieve good accuracy and efficiency, FNOs…
Learned image reconstruction techniques using deep neural networks have recently gained popularity, and have delivered promising empirical results. However, most approaches focus on one single recovery for each observation, and thus neglect…
Real-world scientific applications frequently encounter incomplete observational data due to sensor limitations, geographic constraints, or measurement costs. Although neural operators significantly advanced PDE solving in terms of…