The efficient learning of spatio-temporal dynamics is a fundamental challenge in scientific computing and an enabling methodology for digital twins and personalized medicine. This talk presents recent developments in Latent Dynamics Networks (LDNets), a scientific machine learning framework for constructing lightweight, accurate, and scalable reduced-order models of complex dynamical systems with spatio-temporal features. By bridging physics-based and data-driven approaches, LDNets enable real-time simulations while preserving predictive accuracy and computational efficiency.

A key application of this methodology is the construction of cardiac digital twins, where LDNets enable real-time whole-heart electromechanical simulations. By learning compact latent representations of high-fidelity cardiac models, these approaches dramatically reduce computational costs while retaining excellent accuracy. This enables efficient global sensitivity analysis, parameter estimation, and uncertainty quantification on standard computational hardware, making personalized cardiac modeling computationally feasible.

Building upon this framework, recent developments on 2nd-order LDNets further improve the representation of temporal dependencies by introducing second-order latent operators that capture acceleration-like effects in the evolution of the hidden state. These higher-order latent dynamics substantially enhance long-term predictive stability and accuracy, particularly for fast propagating spatio-temporal phenomena such as cardiac electrophysiology. The resulting methodology provides a robust and scalable framework for learning nonlinear dynamical systems and further strengthens the potential of cardiac digital twins to support personalized diagnosis, risk assessment, and therapy optimization.