-calculations from ML inferences and hence a well-trained ML model is capable of quickly characterizing planetary interiors. [Baumeister et al. (2020)](https://iopscience.iop.org/article/10.3847/1538-4357/ab5d32) applied MDN-based ML to infer the distribution of possible thicknesses of each planetary layer for exoplanets up to 25 Earth masses, where MDN inference for one planet takes only few miliseconds compared with the inversion computing time of potentially several hours. In [Zhao & Ni (2021)](https://www.aanda.org/articles/aa/abs/2021/06/aa40375-21/aa40375-21.html) and [Zhao & Ni (2022)](https://www.aanda.org/articles/aa/abs/2022/02/aa42874-21/aa42874-21.html), the MDN was used to simultaneously predict the layer thicknesses and core properties of exoplanets including Earth-like planets and gas giants.
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