  We present a machine learning based model that can predict the electronic
structure of quasi-one-dimensional materials while they are subjected to
deformation modes such as torsion and extension/compression. The technique
described here applies to important classes of materials such as nanotubes,
nanoribbons, nanowires, miscellaneous chiral structures and nano-assemblies,
for all of which, tuning the interplay of mechanical deformations and
electronic fields is an active area of investigation in the literature. Our
model incorporates global structural symmetries and atomic relaxation effects,
benefits from the use of helical coordinates to specify the electronic fields,
and makes use of a specialized data generation process that solves the
symmetry-adapted equations of Kohn-Sham Density Functional Theory in these
coordinates. Using armchair single wall carbon nanotubes as a prototypical
example, we demonstrate the use of the model to predict the fields associated
with the ground state electron density and the nuclear pseudocharges, when
three parameters - namely, the radius of the nanotube, its axial stretch, and
the twist per unit length - are specified as inputs. Other electronic
properties of interest, including the ground state electronic free energy, can
then be evaluated with low-overhead post-processing, typically to chemical
accuracy. We also show how the nuclear coordinates can be reliably determined
from the pseudocharge field using a clustering based technique. Remarkably,
only about 120 data points are found to be enough to predict the three
dimensional electronic fields accurately, which we ascribe to the symmetry in
the problem setup, the use of low-discrepancy sequences for sampling, and
presence of intrinsic low-dimensional features in the electronic fields. We
comment on the interpretability of our machine learning model and discuss its
possible future applications.
