Machine learning for modeling the electronic stopping power of ions*

The International Atomic Energy Agency (IAEA) stopping power database is a highly valued public resource compiling most experimental measurements published in the last century. The database –accessible to the global scientific community– is continuously updated and has been extensively employed in theoretical and experimental research for over thirty years. In this work, we employ machine learning algorithms on the 2021 IAEA database to construct a model that can accurately predict the electronic stopping power cross sections for any ion and target combination in a wide range of incident energies. The raw values in the database originate from several publications; they were measured using different techniques across several decades. Hence, measurements for the same ion–target collision may show significant discrepancies (much larger than the error of the individual set of experimental data). Cleaning the database is crucial but manually impracticable. The immense difficulties of scrutinizing such an extensive dataset are resolved by implementing a straightforward ML-based method. A clustering-based algorithm was developed to automatically discard suspicious or erroneous data. The method implements a density-based clustering non-parametric algorithm along with three criteria on the data. The filtered values were divided into two sets: the training and test sets. The former dataset was used to train a deep neural network, while the latter was set aside. The converged model can reproduce the input data accurately within a one-digit mean absolute percentage error (MAPE). Considering the spread in some collisional systems and energy ranges, the model's performance is excellent. The neural network results were also compared with the test set (data not used in the training stage), which also showed an outstanding agreement. Exhaustive comparison with other semi-empirical and machine-learning-based methods proved our model to be the most accurate. The first version of the electronic stopping power neural network (ESPNN) code is available to users. The open-access ESPNN code with the forward propagation model runs with Python and has been published in pypi and a public repository.