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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 thenuclear contribution to stopping power, i.e., elastic scattering between atoms,is well understood in the literature, the route for gathering data on theelectronic contribution has for decades remained costly and reliant on manysimplifying assumptions, including that materials are isotropic. We establish amethod that combines time-dependent density functional theory (TDDFT) andmachine learning to reduce the time to assess new materials to mere hours on asupercomputer and provides valuable data on how atomic details influenceelectronic stopping. Our approach uses TDDFT to compute the electronic stoppingcontributions to stopping power from first principles in several directions andthen machine learning to interpolate to other directions at rates 10 milliontimes higher. We demonstrate the combined approach in a study of protonirradiation in aluminum and employ it to predict how the depth of maximumenergy deposition, the "Bragg Peak," varies depending on incident angle -- aquantity otherwise inaccessible to modelers. The lack of any experimentalinformation requirement makes our method applicable to most materials, and itsspeed makes it a prime candidate for enabling quantum-to-continuum models ofradiation damage. The prospect of reusing valuable TDDFT data for training themodel make our approach appealing for applications in the age of materials datascience.

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