“…Reduced-order models have been developed in many areas of engineering, such as circuits (e.g., [1][2][3][4]), power systems (e.g., [5][6][7]), electromagnetics (e.g., [8][9][10]), fluid mechanics (e.g., [11][12][13]), nonlinear structural mechanics and earthquake engineering (e.g., [14]), nonlinear hydraulic fracturing problems (e.g., [15]), etc., to cite a few. Deep-learning artificial neural networks have been introduced to build on more traditional model-order reduction methods, such as the Proper Orthogonal Decomposition (POD), 1 to increase computational efficiency [16][17][18][19][20][21].…”