Bayesian synergistic metamodeling (BSM), a novel technique for physical information infused data-driven metamodeling, is proposed. A core challenge for modeling is to construct an explainable and reliable model that represents the input-output relationship of concern. To tackle this challenge, the proposed BSM fuses the information of the physical mechanism and the implicit features extracted from the captured data to develop the most suitable representation. The model discrepancy of physical information infused modeling is compensated via data-driven modeling. The resultant representation achieves the optimal balance between data fitting and model complexity. In addition, the uncertainties of all estimates are quantified to reflect the quality of the estimation and prediction. To demonstrate the efficacy and applicability of the proposed BSM, we present two simulated examples under various modeling conditions and a case study for seismic attenuation modeling utilizing the in-situ seismic records of a strong earthquake.