Deep Learning Based Priors in Quantifying Uncertainty
Abstract
Motivation Bayesian inference is a well-established technique for quantifying uncertainty in inverse problems that are constrained by physical principles. It has found applications in diverse fields including geophysics, astrophysics, advanced manufacturing, materials modeling and detection and diagnosis of disease. Bayesian inference involves selecting a prior distribution for the field of interest and updating it using the measurement of a related field and the knowledge of the physics that links the measurement to the field of interest. The updated distribution, which is called the posterior distribution, is then sampled to quantify the uncertainty in the recovered field. Despite its numerous applications and successes in solving inverse problems, Bayesian inference faces two significant challenges. These are, defining a prior distribution when the prior knowledge about the recovered field is difficult to characterize mathematically, and efficiently sampling from the posterior distribution when the dimension of the recovered field is large. Key ideas In the proposed research program we develop algorithms to address the challenges described above by employing generative adversarial networks (GANs) as priors in the Bayesian inference problem. GANs are a class of generative deep neural networks based on a two-player min-max game that comprise of a generator and a discriminator. The generator component of a GAN can be trained to produce samples whose distribution is close to the true complex distribution of a given field. Thus it is ideally suited to represent priors for fields whose distributions are difficult to quantify mathematically. Further, since the generator produces these samples of the field of interest by mapping a stochastic latent vector of much smaller dimension, the generator of a GAN provides a means to efficiently sample the posterior distribution. Objectives The main goal of the proposed research is to establish the use of GANs in representing complex prior distributions for the inferred field in a Bayesian update, and in efficiently quantifying and sampling the posterior distribution for the inferred field by generating GAN-based reduced order models. This goal will be achieved through a series of specific aims developed for Bayesian inference problems in which the prior is represented by a GAN. These aims will include 1. Developing efficient algorithms for computing the maximum a-posteriori estimate (MAP). 2. Developing efficient algorithms for approximating the posterior distribution about the MAP as a Gaussian. 3. Developing efficient techniques for sampling the posterior using MCMC techniques. 4. Analyzing the proposed technique with regard to approximation error, and its performance when compared to other methods. 5. Developing reduced-order physics-aware GANs. 6. Verifying the proposed algorithms by applying them to canonical inverse problems. 7. Applying the proposed algorithms to challenging inverse problems of interest to the US Army.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jul 09, 2020
- Source ID
- W911NF2010050
Entities
People
- Assad A Oberai
Organizations
- Army Contracting Command
- United States Army
- University of Southern California