Purpose: Visualization of subcortical gray matter is essential in neuroscience and clinical practice, particularly for disease understanding and surgical planning.While multi-inversion time (multi-TI) T$_1$-weighted (T$_1$-w) magnetic resonance (MR) imaging improves visualization, it is rarely acquired in clinical settings. Approach: We present SyMTIC (Synthetic Multi-TI Contrasts), a deep learning method that generates synthetic multi-TI images using routinely acquired T$_1$-w, T$_2$-weighted (T$_2$-w), and FLAIR images. Our approach combines image translation via deep neural networks with imaging physics to estimate longitudinal relaxation time (T$_1$) and proton density (PD) maps. These maps are then used to compute multi-TI images with arbitrary inversion times. Results: SyMTIC was trained using paired MPRAGE and FGATIR images along with T$_2$-w and FLAIR images. It accurately synthesized multi-TI images from standard clinical inputs, achieving image quality comparable to that from explicitly acquired multi-TI data.The synthetic images, especially for TI values between 400-800 ms, enhanced visualization of subcortical structures and improved segmentation of thalamic nuclei. Conclusion: SyMTIC enables robust generation of high-quality multi-TI images from routine MR contrasts. It generalizes well to varied clinical datasets, including those with missing FLAIR images or unknown parameters, offering a practical solution for improving brain MR image visualization and analysis.