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We propose a new method in which a generative network (GN) integrate into areduced-order model (ROM) framework is used to solve inverse problems forpartial differential equations (PDE). The aim is to match availablemeasurements and estimate the corresponding uncertainties associated with thestates and parameters of a numerical physical simulation. The GN is trainedusing only unconditional simulations of the discretized PDE model. We comparethe proposed method with the golden standard Markov chain Monte Carlo. We applythe proposed approaches to a spatio-temporal compartmental model inepidemiology. The results show that the proposed GN-based ROM can efficientlyquantify uncertainty and accurately match the measurements and the goldenstandard, using only a few unconditional simulations of the full-ordernumerical PDE model.

Generative Network-Based Reduced-Order Model for Prediction, Data Assimilation and Uncertainty Quantification