Bayesian neural network priors for edge-preserving inversion
We consider Bayesian inverse problems wherein the unknown state is assumed to be a function with discontinuous structure a priori. A class of prior distributions based on the output of neural networks with heavy-tailed weights is introduced, motivated by existing results concerning the infinite-width limit of such networks. We show theoretically that samples from such priors have desirable discontinuous-like properties even when the network width is finite, making them appropriate for edge-preserving inversion. Numerically we consider deconvolution problems defined on one- and two-dimensional spatial domains to illustrate the effectiveness of these priors; MAP estimation, dimension-robust MCMC sampling and ensemble-based approximations are utilized to probe the posterior distribution. The accuracy of point estimates is shown to exceed those obtained from non-heavy tailed priors, and uncertainty estimates are shown to provide more useful qualitative information.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Functional-prior-based approaches to Bayesian PDE-constrained inversion using physics-informed neural networks
Physics-informed neural networks (PINNs) provide a mesh-free framework for solving PDE-constrained inverse problems, but their extension to Bayesian inversion still faces a fundamental difficulty: prior distributions are…
Bayesian InferenceGeometric Autoencoder Priors for Bayesian Inversion: Learn First Observe Later
Uncertainty Quantification (UQ) is paramount for inference in engineering. A common inference task is to recover full-field information of physical systems from a small number of noisy observations, a usually highly ill-…
Bayesian Inversion for Nonlinear Imaging Models using Deep Generative Priors
Most modern imaging systems incorporate a computational pipeline to infer the image of interest from acquired measurements. The Bayesian approach to solve such ill-posed inverse problems involves the characterization of …
RetrievalGaussian processes for Bayesian inverse problems associated with linear partial differential equations
This work is concerned with the use of Gaussian surrogate models for Bayesian inverse problems associated with linear partial differential equations. A particular focus is on the regime where only a small amount of train…
Gaussian ProcessesNovel and flexible parameter estimation methods for data-consistent inversion in mechanistic modeling
Predictions for physical systems often rely upon knowledge acquired from ensembles of entities, e.g., ensembles of cells in biological sciences. For qualitative and quantitative analysis, these ensembles are simulated wi…
Bayesian Inferenceparameter estimation