Improved imaging of the spatio-temporal growth of fault slip is crucial for understanding driving mechanisms of earthquakes and faulting. This is especially critical to properly evaluate the evolution of seismic swarms and earthquake precursory phenomena. Fault slip inversion is an ill-posed problem and hence regularization is required to obtain stable and interpretable solutions. An analysis of compiled finite fault slip models shows that slip distributions can be approximated with a generic elliptical shape, particularly well for M≤7.5 events. Therefore, we introduce a new physically-informed regularization to constrain the spatial pattern of fault slip distribution. Our approach adapts a crack model derived from mechanical laboratory experiments and extends it to allow for complex slipping patterns by stacking multiple cracks. The new inversion method successfully recovered different simulated time-dependent patterns of slip propagation, i.e., crack-like and pulse-like ruptures, directly using wrapped InSAR phase observations. We find that the new method reduces model parameter space, and favors simpler interpretable spatio-temporal fault slip distributions. We apply the proposed method to the 2011 March-September normal-faulting seismic swarm at Hawthorne (Nevada, USA), by computing ENVISAT and RADARSAT-2 interferograms to estimate the spatio-temporal evolution of fault slip distribution. The results show that (1) aseismic slip might play a significant role during the initial stage, and (2) this shallow seismic swarm had slip rates consistent with those of slow earthquake processes. The newly proposed method will be useful in retrieving time-dependent fault slip evolution, and is expected to be widely applicable to study fault mechanics, particularly in slow earthquakes.