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We develop a strategy that integrates machine learning and first-principles calculations to achieve technical accurate predictions of infrared spectra. Specifically, the methodology allows to predict infrared spectra for complex systems at finite temperatures. The method's effectiveness is demonstrated in challenging scenarios, such as the analysis of water and the organic-inorganic halide perovskite MAPbI$_{3}$, where our results consistently align with experimental data. A distinctive feature of the methodology is the incorporation of derivative learning, which proves indispensable for obtaining accurate polarization data in bulk materials and facilitates the training of a machine learning surrogate model of the polarization adapted to rotational and translational symmetries. We achieve polarisation prediction accuracies of about 1 % by training only on the predicted Born effective charges., Comment: 9 pages, 4 figures

In this paper we investigate the performance of different machine learning potentials (MLPs) in predicting key thermodynamic properties of water using RPBE+D3. Specifically, we scrutinize kernel-based regression and high-dimensional neural networks trained on a highly accurate dataset consisting of about 1,500 structures, as well as a smaller data set, about half the size, obtained using only on-the-fly learning. The study reveals that despite minor differences between the MLPs, their agreement on observables such as the diffusion constant and pair-correlation functions is excellent, especially for the large training dataset. Variations in the predicted density isobars, albeit somewhat larger, are also acceptable, particularly given the errors inherent to approximate density functional theory. Overall, the study emphasizes the relevance of the database over the fitting method. Finally, the study underscores the limitations of root mean square errors and the need for comprehensive testing, advocating the use of multiple MLPs for enhanced certainty, particularly when simulating complex thermodynamic properties that may not be fully captured by simpler tests.