Synthetic magnetic resonance imaging (MRI) offers a scanning paradigm where a fast multi-contrast sequence can be used to estimate underlying quantitative tissue parameter maps, which are then used to synthesize any desirable clinical contrast by retrospectively changing scan parameters in silico. Two benefits of this approach are the reduced exam time and the ability to generate arbitrary contrasts offline. However, synthetically generated contrasts are known to deviate from the contrast of experimental scans. The reason for contrast mismatch is the necessary exclusion of some unmodeled physical effects such as partial voluming, diffusion, flow, susceptibility, magnetization transfer, and more. The inclusion of these effects in signal encoding would improve the synthetic images, but would make the quantitative imaging protocol impractical due to long scan times. Therefore, in this work, we propose a novel deep learning approach that generates a multiplicative correction term to capture unmodeled effects and correct the synthetic contrast images to better match experimental contrasts for arbitrary scan parameters. The physics inspired deep learning model implicitly accounts for some unmodeled physical effects occurring during the scan. As a proof of principle, we validate our approach on synthesizing arbitrary inversion recovery fast spin-echo scans using a commercially available 2D multi-contrast sequence. We observe that the proposed correction visually and numerically reduces the mismatch with experimentally collected contrasts compared to conventional synthetic MRI. Finally, we show results of a preliminary reader study and find that the proposed method statistically significantly improves in contrast and SNR as compared to synthetic MR images.