Machine Learning Adaptive Basis Sets for Efficient Large Scale Density Functional Theory Simulation

It is chemically
intuitive that an optimal atom centered basis
set must adapt to its atomic environment, for example by polarizing
toward nearby atoms. Adaptive basis sets of small size can be significantly
more accurate than traditional atom centered basis sets of the same
size. The small size and well conditioned nature of these basis sets
leads to large saving in computational cost, in particular in a linear
scaling framework. Here, it is shown that machine learning can be
used to predict such adaptive basis sets using local geometrical information
only. As a result, various properties of standard DFT calculations
can be easily obtained at much lower costs, including nuclear gradients.
In our approach, a rotationally invariant parametrization of the basis
is obtained by employing a potential anchored on neighboring atoms
to ultimately construct a rotation matrix that turns a traditional
atom centered basis set into a suitable adaptive basis set. The method
is demonstrated using MD simulations of liquid water, where it is
shown that minimal basis sets yield structural properties in fair
agreement with basis set converged results, while reducing the computational
cost in the best case by a factor of 200 and the required flops by
4 orders of magnitude. Already a very small training set yields satisfactory
results as the variational nature of the method provides robustness.