Phonons and magnons are low energy quasiparticles that determine many of key properties of nano-structured materials, such as heat transport in CPUs or operation of spintronic devices among others. Latest generation of monochromators introduced to scanning transmission electron microscopy in 2014 has granted microscopists an access to new domains of physics of excitation processes. Vibrational spectroscopy is a rapidly developing field, today reaching atomic scale spatial resolutions. At the level of theory, excitations of phonons were previously considered as "quasi-elastic" processes, since they could not be distinguished separately from the elastic scattering. Existing alternative descriptions based on quantum mechanical transition matrix elements are computationally expensive and hard to apply to systems with defects, interfaces, surfaces. We will employ novel simulation techniques developed in our group, namely the frequency-resolved frozen phonon multislice simulations (FRFPMS) and time auto-correlation of auxiliary wave-functions (TACAW). These approaches allow circumventing explicit calculations of transition matrix elements, offering thus a versatile and extremely efficient path to simulation of vibrational spectra in transmission electron microscopes with full access to arbitrary beam, detector and sample geometries. Phonon simulations utilize molecular dynamics (MD) simulations, while magnons rely on atomistic spin dynamics (ASD) calculations. We will explore coupled spin-lattice dynamics simulations that allow to simultaneously treat phonons and magnons on equal footing. A new aspect in our research is a use neural network foundational models for interatomic potentials in MD, which efficiently run on GPUs. Initial testing of the potentials offers very promising outlook. Such universal interatomic potentials will enormously extend the reach of our computational schemes, allowing to treat materials with non-trivial nano-structures. Theories developed in this project also permit simulations of time and temperature dependent processes. Possibility to measure atomic resolution phonon spectroscopies at low temperatures is a very recent extension in the microscopy instrumentation, allowing to reach sub-10K temperatures. At these low temperatures the nuclear quantum effects become important, which are neglected in classical MD simulations. For that purpose we will explore new computational approaches employing thermostatted ring polymer molecular dynamics simulations (TRPMD).