  High-performance computing, together with a neural network model trained from
data generated with first-principles methods, has greatly boosted applications
of \textit{ab initio} molecular dynamics in terms of spatial and temporal
scales on modern supercomputers. Previous state-of-the-art can achieve $1-2$
nanoseconds molecular dynamics simulation per day for 100-million atoms on the
entire Summit supercomputer. In this paper, we have significantly reduced the
memory footprint and computational time by a comprehensive approach with both
algorithmic and system innovations. The neural network model is compressed by
model tabulation, kernel fusion, and redundancy removal. Then optimizations
such as acceleration of customized kernel, tabulation of activation function,
MPI+OpenMP parallelization are implemented on GPU and ARM architectures.
Testing results of the copper system show that the optimized code can scale up
to the entire machine of both Fugaku and Summit, and the corresponding system
size can be extended by a factor of $134$ to an unprecedented $17$ billion
atoms. The strong scaling of a $13.5$-million atom copper system shows that the
time-to-solution can be 7 times faster, reaching $11.2$ nanoseconds per day.
This work opens the door for unprecedentedly large-scale molecular dynamics
simulations based on {\it ab initio} accuracy and can be potentially utilized
in studying more realistic applications such as mechanical properties of
metals, semiconductor devices, batteries, etc. The optimization techniques
detailed in this paper also provide insight for relevant high-performance
computing applications.
