Related papers: Weak neural variational inference for solving Baye…

Neural Operators offer a powerful, data-driven tool for solving parametric PDEs as they can represent maps between infinite-dimensional function spaces. In this work, we employ physics-informed Neural Operators in the context of…

Deep Learning based methods have emerged as the indisputable leaders for virtually all image restoration tasks. Especially in the domain of microscopy images, various content-aware image restoration (CARE) approaches are now used to improve…

Well-established methods for the solution of stochastic partial differential equations (SPDEs) typically struggle in problems with high-dimensional inputs/outputs. Such difficulties are only amplified in large-scale applications where even…

Variational Bayes (VB) has become a widely-used tool for Bayesian inference in statistics and machine learning. Nonetheless, the development of the existing VB algorithms is so far generally restricted to the case where the variational…

Bayesian neural networks (BNNs) promise improved generalization under covariate shift by providing principled probabilistic representations of epistemic uncertainty. However, weight-based BNNs often struggle with high computational…

Variational inference is computationally challenging in models that contain both conjugate and non-conjugate terms. Methods specifically designed for conjugate models, even though computationally efficient, find it difficult to deal with…

Current variational inference methods for hierarchical Bayesian nonparametric models can neither characterize the correlation structure among latent variables due to the mean-field setting, nor infer the true posterior dimension because of…

In this paper we propose a wavelet-based methodology for estimation and variable selection in partially linear models. The inference is conducted in the wavelet domain, which provides a sparse and localized decomposition appropriate for…

This paper is concerned with the approximation of probability distributions known up to normalization constants, with a focus on Bayesian inference for large-scale inverse problems in scientific computing. In this context, key challenges…

In Bayesian inverse problems sampling the posterior distribution is often a challenging task when the underlying models are computationally intensive. To this end, surrogates or reduced models are often used to accelerate the computation.…

Seismic full-waveform inversion (FWI), which uses iterative methods to estimate high-resolution subsurface models from seismograms, is a powerful imaging technique in exploration geophysics. In recent years, the computational cost of FWI…

The recognition network in deep latent variable models such as variational autoencoders (VAEs) relies on amortized inference for efficient posterior approximation that can scale up to large datasets. However, this technique has also been…

Full Waveform Inversion (FWI) is a promising technique for achieving high-resolution imaging in medical ultrasound. However, conventional FWI methods suffer from issues related to computational efficiency, dependence on initial models, and…

The present paper proposes a novel Bayesian, computational strategy in the context of model-based inverse problems in elastostatics. On one hand we attempt to provide probabilistic estimates of the material properties and their spatial…

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…

Modern neural network architectures have achieved remarkable accuracies but remain highly dependent on their training data, often lacking interpretability in their learned mappings. While effective on large datasets, they tend to overfit on…

There have been growing interests in leveraging experimental measurements to discover the underlying partial differential equations (PDEs) that govern complex physical phenomena. Although past research attempts have achieved great success…

This paper presents an online algorithm for identification of partial differential equations (PDEs) based on the weak-form sparse identification of nonlinear dynamics algorithm (WSINDy). The algorithm is online in a sense that if performs…

Programmatic Weak Supervision (PWS) enables supervised model training without direct access to ground truth labels, utilizing weak labels from heuristics, crowdsourcing, or pre-trained models. However, the absence of ground truth…

In recent years, deep learning has proven to be a viable methodology for surrogate modeling and uncertainty quantification for a vast number of physical systems. However, in their traditional form, such models can require a large amount of…