Accelerating Electronic Stopping Power Predictions by 10 Million Times with a Combination of Time-Dependent Density Functional Theory and Machine Learning

Knowing the rate at which particle radiation releases energy in a material, the stopping power, is key to designing nuclear reactors, medical treatments, semiconductor and quantum materials, and many other technologies. While the nuclear contribution to stopping power, i.e., elastic scattering between atoms, is well understood in the literature, the route for gathering data on the electronic contribution has for decades remained costly and reliant on many simplifying assumptions, including that materials are isotropic. We establish a method that combines time-dependent density functional theory (TDDFT) and machine learning to reduce the time to assess new materials to mere hours on a supercomputer and provides valuable data on how atomic details influence electronic stopping. Our approach uses TDDFT to compute the electronic stopping contributions to stopping power from first principles in several directions and then machine learning to interpolate to other directions at a cost of 10 million times fewer core-hours. We demonstrate the combined approach in a study of proton irradiation in aluminum and employ it to predict how the depth of maximum energy deposition, the "Bragg Peak," varies depending on incident angle -- a quantity otherwise inaccessible to modelers. The lack of any experimental information requirement makes our method applicable to most materials, and its speed makes it a prime candidate for enabling quantum-to-continuum models of radiation damage. The prospect of reusing valuable TDDFT data for training the model make our approach appealing for applications in the age of materials data science.