After obtaining the initial list of samples to test, experimentation or simulation is conducted to obtain their respective evaluations. These are then used to build a surrogate model. In PWAS, we use PARC to fit piecewise affine surrogates. The general procedures of PARC are illustrated in Fig. . PARC is a block descent algorithm, where it first groups samples in K init clusters. Clusters containing fewer samples than a predefined minimum threshold are discarded, resulting in K updated remaining clusters. We then fit piecewise affine (PWA) separation functions among these clusters to form K updated partitions of the design space. Within each partition, a PWA surrogate function is fitted to make predictions. We conducted a comparative study to evaluate the effectiveness of the PWA surrogate function on a set of benchmark functions. The results indicate that PWA can provide better fitting to the underlying functions compared to GP with RBF, Matérn, and linear kernels, particularly when the number of training samples is limited or when the problem involves discontinuous or sharp transitions caused by categorical variables. Full details and analysis can be found in the supplementary materials, Section 2.