Inverse problems play a crucial role in computational cardiology, where the challenge is to infer hidden pathological or functional features from non-invasive measurements. In this work, we address the inverse reconstruction of ischemic regions and the localization of externally applied stimuli from pseudo-electrocardiographic (pseudo-ECG) signals, using the cardiac monodomain model [1] as the underlying physiological framework. The forward problem maps spatial patterns of ischemia and initial stimulus configurations to body-surface pseudo-ECG signals. To accelerate this mapping, we employ Latent Dynamics Networks (LDNets) [2] as efficient neural surrogates, enabling fast and accurate simulations. Our analysis spans both 2D square domains and anatomically realistic 3D geometries, including an ellipsoidal mesh that emulates a human cardiac ventricle. This contribution highlights the growing synergy between deep learning and mechanistic models in tackling complex inverse problems in cardiac electrophysiology. Our work illustrates the promise of neural surrogates not only for accelerating simulations but also for enabling robust inverse reconstructions in potential clinically relevant scenarios. [1] P. Colli Franzone, L.F. Pavarino, S. Scacchi, S. (2014). Mathematical cardiac electrophysiology. Vol. 13. Springer, 2014. [2] F. Regazzoni, S. Pagani, M. Salvador, L. Dede', A. Quarteroni, Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks. Nature Communications (2024) 15, 1834