Generative model-based framework for parameter estimation and uncertainty quantification applied to a compartmental model in epidemiology
File(s)
Published version
Author(s)
Silva, Vinicius LS
Heaney, Claire E
Nenov, Nenko
Pain, Christopher C
Type
Journal Article
Abstract
We propose a new method in which a generative network (GN) set within a reduced-order model (ROM) framework is used to solve inverse problems for partial differential equations (PDE). The aim is to match available measurements and estimate the corresponding uncertainties associated with the states and parameters of a numerical physical simulation. We train the GN using only unconditional simulations of the discretized PDE model. A GN is used here to exploit the ability of these methods to generate realistic outputs from complex probability distributions, such as the ones that represent the possible states and parameters of a physical problem. We compare the proposed method with the gold standard Markov chain Monte Carlo (MCMC). Additionally, we suggest the use of a novel type of time-stepping regularization to improve the representativeness of the physical solution, and we present a new way of evaluating the GN training, taking advantage of the real/generated sample structure. We apply the proposed approaches to a spatio-temporal compartmental model in epidemiology. The results show that the proposed GN-based ROM can efficiently quantify uncertainty and accurately match the measurements and the gold standard. This is achieved using only a limited number of unconditional simulations from the full-order numerical PDE model (40 simulations). The GN-based ROM operates 60 times faster than the gold standard (MCMC), while producing uncertainties that closely match those generated by the MCMC approach. The proposed method is a general framework for quantifying uncertainties in numerical physical simulations and is not restricted to the specific physics of this application.
Date Issued
2024-12
Date Acceptance
2024-09-24
Citation
Journal of Computational Science, 2024, 83
ISSN
1877-7503
Publisher
Elsevier
Journal / Book Title
Journal of Computational Science
Volume
83
Copyright Statement
© 2024 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
License URL
Identifier
https://www.sciencedirect.com/science/article/pii/S1877750324002448?via%3Dihub
Subjects
Compartmental model
Computer Science
Computer Science, Interdisciplinary Applications
Computer Science, Theory & Methods
Data assimilation
Epidemiology
FLUID-DYNAMICS
Generative adversarial network
Generative model
MONTE-CARLO METHODS
NEURAL-NETWORKS
Reduced-order model
Science & Technology
SYSTEMS
Technology
Uncertainty Quantification
Publication Status
Published
Article Number
102451
Date Publish Online
2024-10-15