Data-Driven and Algorithmic Acceleration of Excited-State Dynamics: from Attosecond Electronic Excitations to Picosecond Phonon Thermalization

Understanding excited-state dynamics of electrons and phonons is key to advancing electronic devices, ultrafast spectroscopies, and materials science. In recent years, the development of real-time first-principles methods has advanced the description of nonequilibrium dynamics. These methods consist of explicit propagation in time of an equation that characterizes the state of a system. Different schemes are successful in different regimes. RT-TDDFT effectively models pure electron dynamics on the attosecond timescale, while the rt-BTE addresses coupled electron-phonon dynamics on femto- and picosecond timescales. Both of these ab initio methods require significant computational resources due to large basis sets and high temporal resolution.



In this talk, I will discuss our recent advancements in data-driven techniques and time solvers for modeling nonequilibrium electron dynamics in solids and molecules. I will first present a data-driven method based on dynamic mode decomposition (DMD). With a few snapshots obtained from an explicit time solution, DMD identifies the dominant modes governing the dynamics, allowing for the prediction of system evolution with minimal cost. I will demonstrate the application of the DMD approach to two case studies: (1) high-field electron-phonon dynamics within the rt-BTE framework and (2) optical spectra predictions using RT-TDDFT. In both cases, DMD achieves an order-of-magnitude computational speed-up while retaining the full accuracy of first-principles calculations.



I will conclude with a discussion on phonon-phonon interactions incorporated within the rt-BTE, where electron-phonon and phonon-phonon interactions evolve on different time scales. Here, we leverage adaptive and multirate time integration methods enabling efficient computation of ultrafast lattice dynamics and thermal diffuse scattering. I will also show how algorithmic and data-driven techniques reveal microscopic insights into the underlying processes.