| Summary: | 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 under
conditions relevant for fusion and cosmic plasmas. A simple 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.
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