Recent advances in satellite altimetry enable high-resolution sea surface height (SSH) observations (e.g. SWOT), offering new opportunities to study upper-ocean submesoscale dynamics, yet reconstructing submesoscale dynamics from SSH observations remains challenging. This study presents a physics-informed deep learning framework that infers ageostrophic submesoscale dynamics from SSH by embedding oceanic strain as a physical constraint, achieving about a 40% reduction in RMSE compared with classical surface quasi-geostrophic methods in certain region. The framework is applied to five representative ocean regions to assess spatial and seasonal variations in reconstruction performance. Results indicate that prediction skill strongly depends on the underlying dynamical regime, with high accuracy in submesoscale-dominated regions and degraded performance in the presence of strong internal gravity waves. This dependence is further supported by a global evaluation of prediction skill. When applied to 2-km-resolution SWOT Level-3 SSH data, the trained model successfully reveals upper-ocean submesoscale dynamics, demonstrating the potential of physics-informed deep learning for observation-based reconstruction of submesoscale dynamics.