Related papers: Deep Adaptive Dimension Reduction for Bayesian Inf…

Incorporating a deep generative model as the prior distribution in inverse problems has established substantial success in reconstructing images from corrupted observations. Notwithstanding, the existing optimization approaches use gradient…

We introduce a novel adaptive Gaussian Process Regression (GPR) methodology for efficient construction of surrogate models for Bayesian inverse problems with expensive forward model evaluations. An adaptive design strategy focuses on…

Deep Gaussian processes (DGPs), a hierarchical composition of GP models, have successfully boosted the expressive power of their single-layer counterpart. However, it is impossible to perform exact inference in DGPs, which has motivated the…

We consider nonparametric Bayesian estimation inference using a rescaled smooth Gaussian field as a prior for a multidimensional function. The rescaling is achieved using a Gamma variable and the procedure can be viewed as choosing an…

Variational autoencoders employ an amortized inference model to approximate the posterior of latent variables. However, such amortized variational inference faces two challenges: (1) the limited posterior expressiveness of fully-factorized…

Super-resolution is widely used in medical imaging to enhance low-quality data, reducing scan time and improving abnormality detection. Conventional super-resolution approaches typically rely on paired datasets of downsampled and original…

Semi-supervised learning is sought for leveraging the unlabelled data when labelled data is difficult or expensive to acquire. Deep generative models (e.g., Variational Autoencoder (VAE)) and semisupervised Generative Adversarial Networks…

The Bayesian update step poses significant computational challenges in high-dimensional nonlinear estimation. While log-homotopy particle flow filters offer an alternative to stochastic sampling, existing formulations usually yield stiff…

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…

Solving high-dimensional Fokker-Planck (FP) equations is a challenge in computational physics and stochastic dynamics, due to the curse of dimensionality (CoD) and unbounded domains. Existing deep learning approaches, such as…

Many scientific investigations require that the values of a set of model parameters are estimated using recorded data. In Bayesian inference, information from both observed data and prior knowledge is combined to update model parameters…

Matrix completion and robust principal component analysis have been widely used for the recovery of data suffering from missing entries or outliers. In many real-world applications however, the data is also time-varying, and the naive…

Variational autoencoders (VAEs) rely on amortized variational inference to enable efficient posterior approximation, but this efficiency comes at the cost of a shared parametrization, giving rise to the amortization gap. We propose the…

We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems. Starting from a model trained on low-fidelity or observational data, we apply a…

This work presents a non-intrusive surrogate modeling scheme based on machine learning technology for predictive modeling of complex systems, described by parametrized time-dependent PDEs. For these problems, typical finite element…

In order to predict future performance of subsurface fluid reservoirs under possible operating scenarios, a dynamic, porous-medium flow simulation model must be tuned to include representative properties of the reservoir. Estimating…

Variational inference (VI) has emerged as a popular method for approximate inference for high-dimensional Bayesian models. In this paper, we propose a novel VI method that extends the naive mean field via entropic regularization, referred…

We consider optimal experimental design (OED) for Bayesian nonlinear inverse problems governed by partial differential equations (PDEs) under model uncertainty. Specifically, we consider inverse problems in which, in addition to the…

In this work we propose and analyze a Hessian-based adaptive sparse quadrature to compute infinite-dimensional integrals with respect to the posterior distribution in the context of Bayesian inverse problems with Gaussian prior. Due to the…

Inferring the number of distinct components contributing to an observation, while simultaneously estimating their parameters, remains a long-standing challenge across signal processing, astrophysics, and neuroscience. Classical…