Recent progress in machine learning has highlighted the potential for developing tools that are both effective and interpretable, which is particularly valuable in fields like the astrophysics of compact stars. In our  work, we propose an approach to incorporate physical constraints within a neural network, aiming to improve its ability to capture physical behavior accurately. Specifically, we focus on an autoencoder architecture tailored to connect the neutron star equation of state with observables such as mass, radius, and tidal deformability, creating a directly interpretable latent space.  By introducing a few simple relationships in the loss function, we demonstrate an improvement in both performance and precision. This approach provides a proof-of-concept tool for analyzing data and potentially directly extracting equations of state information from future inspiral event waveforms. Additionally, this flexible architecture can be extended to different physical systems that require linking theoretical parameters to measurable quantities.
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Francesco Di Clemente
INFN Ferrara

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