  Context. Determining properties of dust formed in and around supernovae from
observations remains challenging. This may be due to either incomplete coverage
of data in wavelength or time but also due to often inconspicuous signatures of
dust in the observed data. Aims. Here we address this challenge using modern
machine learning methods to determine the amount, composition and temperature
of dust from a large set of simulated data. We aim to determine whether such
methods are suitable to infer these properties from future observations of
supernovae. Methods. We calculate spectral energy distributions (SEDs) of dusty
shells around supernovae. We develop a neural network consisting of eight fully
connected layers and an output layer with specified activation functions that
allow us to predict the dust mass, temperature and composition and their
respective uncertainties from each SED. We conduct a feature importance
analysis via SHapley Additive exPlanations (SHAP) to find the minimum set of
JWST filters required to accurately predict these properties. Results. We find
that our neural network predicts dust masses and temperatures with a
root-mean-square error (RMSE) of $\sim$ 0.12 dex and $\sim$ 38 K, respectively.
Moreover, our neural network can well distinguish between the different dust
species included in our work, reaching a classification accuracy of up to 95\%
for carbon and 99\% for silicate dust. Conclusions. Our analysis shows that the
JWST filters NIRCam F070W, F140M, F356W, F480M and MIRI F560W, F770W, F1000W,
F1130W, F1500W, F1800W are likely the most important needed to determine the
properties of dust formed in and around supernovae from future observations. We
tested this on selected optical to infrared data of SN 1987A at 615 days past
explosion and find good agreement with dust masses and temperatures inferred
with standard fitting methods in the literature.
