Figure 2
From: Enhancing high-fidelity nonlinear solver with reduced order model
Example 1—results: (a,b) are samples of test case results. We have an heterogeneous conductivity as a parameter \(\varvec{\mu }\). The FOM and ROM results shown here are pressure head. Both conductivity field and pressure head shown here are dimensionless (see Supplementary sec. 1). (c) relative error results of validation set as a function of training steps—we note that each step refers to each time we perform back-propagation, including updating both generator and discriminator’s parameters. The blue text represents a mean value. (d) Number of nonlinear iterations: using FOM default initialization, zero-vector initialization, (black square) and using cGAN-ROM-assisted (green cross) and (e) relative error of test dataset (red dot). The relative error (see Eq. 3) is calculated between FOM with default initialization (black square) and cGAN-ROM (green cross).
