Related papers: Weak neural variational inference for solving Baye…

Developing efficient solutions for inference problems in intelligent sensor networks is crucial for the next generation of location, tracking, and mapping services. This paper develops a scalable distributed probabilistic inference…

Discovering governing Partial Differential Equations (PDEs) from sparse and noisy data is a challenging issue in data-driven scientific computing. Conventional sparse regression methods often suffer from two major limitations: (i) the…

Traditional partial differential equations with constant coefficients often struggle to capture abrupt changes in real-world phenomena, leading to the development of variable coefficient PDEs and Markovian switching models. Recently,…

Recently, Neural Ordinary Differential Equations has emerged as a powerful framework for modeling physical simulations without explicitly defining the ODEs governing the system, but instead learning them via machine learning. However, the…

In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…

We present parameter learning in a Gaussian variational inference setting using only noisy measurements (i.e., no groundtruth). This is demonstrated in the context of vehicle trajectory estimation, although the method we propose is general.…

Posterior distributions arising in ill-posed Bayesian inverse problems are often both analytically intractable and highly sensitive to parameters of the chosen prior family. We aim to understand the sensitivity of intractable posterior…

Optimization problems constrained by high-dimensional, time-dependent partial differential equations require repeated forward and sensitivity solves, making high-fidelity optimization computationally prohibitive in many-query design and…

Recent progress in variational inference has paid much attention to the flexibility of variational posteriors. One promising direction is to use implicit distributions, i.e., distributions without tractable densities as the variational…

In this tutorial, we explore Variational Autoencoders (VAEs), an essential framework for unsupervised learning, particularly suited for high-dimensional datasets such as neuroimaging. By integrating deep learning with Bayesian inference,…

This paper considers a bearings-only tracking problem using noisy measurements of unknown noise statistics from a passive sensor. It is assumed that the process and measurement noise follows the Gaussian distribution where the measurement…

We investigate the use of neural networks (NNs) for the estimation of hidden model parameters and uncertainty quantification from noisy observational data for inverse parameter estimation problems. We formulate the parameter estimation as a…

This paper is concerned with a lesser-studied problem in the context of model-based, uncertainty quantification (UQ), that of optimization/design/control under uncertainty. The solution of such problems is hindered not only by the usual…

We consider a structured estimation problem where an observed matrix is assumed to be generated as an $s$-sparse linear combination of $N$ given $n\times n$ positive-semidefinite matrices. Recovering the unknown $N$-dimensional and…

Due to its non-invasive and non-radiating nature, along with its low cost, ultrasound (US) imaging is widely used in medical applications. Typical B-mode US images have limited resolution and contrast and weak physical interpretation.…

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that…

In this paper we focus on a type of inverse problem in which the data is expressed as an unknown function of the sought and unknown model function (or its discretised representation as a model parameter vector). In particular, we deal with…

The nonconforming virtual element method (NCVEM) for the approximation of the weak solution to a general linear second-order non-selfadjoint indefinite elliptic PDE in a polygonal domain is analyzed under reduced elliptic regularity. The…

We consider the problem of lossy image compression with deep latent variable models. State-of-the-art methods build on hierarchical variational autoencoders (VAEs) and learn inference networks to predict a compressible latent representation…

We introduce a scheme for probabilistic hypocenter inversion with Stein variational inference. Our approach uses a differentiable forward model in the form of a physics informed neural network, which we train to solve the Eikonal equation.…