  We present a machine learning based approach to address the study of
transport processes, ubiquitous in continuous mechanics, with particular
attention to those phenomena ruled by complex micro-physics, impractical to
theoretical investigation, yet exhibiting emergent behavior describable by a
closed mathematical expression. Our machine learning model, built using simple
components and following a few well established practices, is capable of
learning latent representations of the transport process substantially closer
to the ground truth than expected from the nominal error characterising the
data, leading to sound generalisation properties. This is demonstrated through
an idealized study of the long standing problem of heat flux suppression
relevant to fusion and cosmic plasmas. Our analysis shows that the result
applies beyond those case specific assumptions and that, in particular, the
accuracy of the learned representation is controllable through knowledge of the
data quality (error properties) and a suitable choice of the dataset size.
While the learned representation can be used as a plug-in for numerical
modeling purposes, it can also be leveraged with the above error analysis to
obtain reliable mathematical expressions describing the transport mechanism and
of great theoretical value.
