Related papers: Error-in-variables modelling for operator learning

Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often overlook the domain knowledge inherent in the underlying PDEs…

Physically Guided Neural Networks with Internal Variables are SciML tools that use only observable data for training and and have the capacity to unravel internal state relations. They incorporate physical knowledge both by prescribing the…

We propose a new neural network based method for solving inverse problems for partial differential equations (PDEs) by formulating the PDE inverse problem as a bilevel optimization problem. At the upper level, we minimize the data loss with…

Gravitational waves from core-collapse supernovae offer a unique probe of the equation of state (EOS) of dense nuclear matter. For rapidly rotating stars, previous machine-learning studies demonstrated promising EOS classification accuracy.…

Physics-informed Neural Networks (PINNs) have been shown as a promising approach for solving both forward and inverse problems of partial differential equations (PDEs). Meanwhile, the neural operator approach, including methods such as Deep…

Despite advances in deep probabilistic models, learning discrete latent representations remains challenging. This work introduces a novel method to improve inference in discrete Variational Autoencoders by reframing the inference problem…

Operator learning is a data-driven approximation of mappings between infinite-dimensional function spaces, such as the solution operators of partial differential equations. Kernel-based operator learning can offer accurate, theoretically…

When measurements from dynamical systems are noisy, it is useful to have estimation algorithms that have low sensitivity to measurement noises and outliers. In the first set of results described in this paper we obtain optimal estimators…

Variational autoencoder (VAE) neural networks can be trained to generate power system states that capture both marginal distribution and multivariate dependencies of historical data. The coordinates of the latent space codes of VAEs have…

This paper describes recursive algorithms for state estimation of linear dynamical systems when measurements are noisy with unknown bias and/or outliers. For situations with noisy and biased measurements, algorithms are proposed that…

Loewner rational interpolation provides a versatile tool to learn low-dimensional dynamical-system models from frequency-response measurements. This work investigates the robustness of the Loewner approach to noise. The key finding is that…

A new approach for blind channel equalization and decoding, variational inference, and variational autoencoders (VAEs) in particular, is introduced. We first consider the reconstruction of uncoded data symbols transmitted over a noisy…

Machine learning techniques have recently been of great interest for solving differential equations. Training these models is classically a data-fitting task, but knowledge of the expression of the differential equation can be used to…

Distributed learning and Edge AI necessitate efficient data processing, low-latency communication, decentralized model training, and stringent data privacy to facilitate real-time intelligence on edge devices while reducing dependency on…

Variational autoencoders (VAEs) are a standard framework for inducing latent variable models that have been shown effective in learning text representations as well as in text generation. The key challenge with using VAEs is the {\it…

Learning with noisy labels is an important topic for scalable training in many real-world scenarios. However, few previous research considers this problem in the online setting, where the arrival of data is streaming. In this paper, we…

Dynamical variational autoencoders (DVAEs) are a class of deep generative models with latent variables, dedicated to model time series of high-dimensional data. DVAEs can be considered as extensions of the variational autoencoder (VAE) that…

A multivariate errors-in-variables (EIV) model with an intercept term, and a polynomial EIV model are considered. Focus is made on a structural homoskedastic case, where vectors of covariates are i.i.d. and measurement errors are i.i.d. as…

Instrumental variable (IV) regression is a standard strategy for learning causal relationships between confounded treatment and outcome variables from observational data by utilizing an instrumental variable, which affects the outcome only…

Machine learning methods often need a large amount of labeled training data. Since the training data is assumed to be the ground truth, outliers can severely degrade learned representations and performance of trained models. Here we apply…