  Multiscale phenomena exhibit complex structure-function relationships, and
predicting their macroscopic behavior requires deducing differential equations
at different scales. The complexity of these equations and the number of
essential parameters make developing effective, predictive models challenging.
To overcome this, researchers explore leveraging advanced numerical techniques
from artificial intelligence and machine learning. Here, we focus on a
fundamental aspect in multiscale phenomena, i.e the recognition of the
hierarchical role of variables. By adopting a Pareto front interpretation, we
aim to deduce simple and accurate relations for material modeling, starting
from experimental multiscale analyses. From a physical point of view, the aim
is to deduce information at higher scales from lower scales data, possibly
respecting their hierarchical order. A crucial aspect of the proposed approach
is the deduction of causality relations among the different variables to be
compared with the available theoretical notions and possibly new
interpretations resulting by the data modelling. This result in a stepwise
approximation going from data modelling to theoretical equations and back to
data modelling. To demonstrate the key advantages of our multiscale numerical
approach, compared to classical, non-physically based data modelling
techniques, we consider the explicit example of spider silk, known for its
exceptional properties and bioinspiration potential. Indeed, it presents a
complex behavior resulting from mesostructures formed by the aggregation of
amino acids at the molecular scale. We argue that, due to the generality of our
results, our approach may represent a proof of concept in many fields where
multiscale, hierarchical differential equations regulate the observed
phenomenon.
