Generative Network-Based Reduced-Order Model for Prediction, Data Assimilation and Uncertainty Quantification
This provides a computationally efficient approach for uncertainty quantification in PDE-based inverse problems, such as epidemiological modeling, though it appears incremental as it combines existing techniques (generative networks and reduced-order models).
The authors tackled the problem of solving inverse problems for partial differential equations (PDEs) by integrating a generative network into a reduced-order model framework, resulting in a method that efficiently quantifies uncertainty and accurately matches measurements and the golden standard Markov chain Monte Carlo using only a few unconditional simulations.
We propose a new method in which a generative network (GN) integrate into 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. The GN is trained using only unconditional simulations of the discretized PDE model. We compare the proposed method with the golden standard Markov chain Monte Carlo. 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 golden standard, using only a few unconditional simulations of the full-order numerical PDE model.