Molecular dynamics (MD) is a powerful tool for exploring the behavior of atomistic systems, but its reliance on sequential numerical integration limits simulation efficiency. We present a novel neural network architecture, MDtrajNet, and a pre-trained foundational model, MDtrajNet-1, that directly generates MD trajectories across chemical space, bypassing force calculations and integration. This approach accelerates simulations by up to two orders of magnitude compared to traditional MD, even those enhanced by machine-learning interatomic potentials. MDtrajNet combines equivariant neural networks with a transformer-based architecture to achieve strong accuracy and transferability in predicting long-time trajectories. Remarkably, the errors of the trajectories generated by MDtrajNet-1 for various known and unseen molecular systems are close to those of the conventional ab initio MD. The architecture's flexible design supports diverse application scenarios, including different statistical ensembles, boundary conditions, and interaction types. By overcoming the intrinsic speed barrier of conventional MD, MDtrajNet opens new frontiers in efficient and scalable atomistic simulations.

Nonadiabatic couplings (NACs) play a crucial role in modeling photochemical and photophysical processes with methods such as the widely used fewest-switches surface hopping (FSSH). There is therefore a strong incentive to machine learn NACs for accelerating simulations. However, this is challenging due to NACs' vectorial, double-valued character and the singularity near a conical intersection seam. For the first time, we design NAC-specific descriptors based on our domain expertise and show that they allow learning NACs with never-before-reported accuracy of $R^2$ exceeding 0.99. The key to success is also our new ML phase-correction procedure. We demonstrate the efficiency and robustness of our approach on a prototypical example of fully ML-driven FSSH simulations of fulvene targeting the SA-2-CASSCF(6,6) electronic structure level. This ML-FSSH dynamics leads to an accurate description of $S_1$ decay while reducing error bars by allowing the execution of a large ensemble of trajectories. Our implementations are available in open-source MLatom.