  Simulation of reasonable timescales for any long physical process using
molecular dynamics (MD) is a major challenge in computational physics. In this
study, we have implemented an approach based on multi-fidelity physics informed
neural network (MPINN) to achieve long-range MD simulation results over a large
sample space with significantly less computational cost. The fidelity of our
present multi-fidelity study is based on the integration timestep size of MD
simulations. While MD simulations with larger timestep produce results with
lower level of accuracy, it can provide enough computationally cheap training
data for MPINN to learn an accurate relationship between these low-fidelity
results and high-fidelity MD results obtained using smaller simulation
timestep. We have performed two benchmark studies, involving one and two
component LJ systems, to determine the optimum percentage of high-fidelity
training data required to achieve accurate results with high computational
saving. The results show that important system properties such as system energy
per atom, system pressure and diffusion coefficients can be determined with
high accuracy while saving 68% computational costs. Finally, as a demonstration
of the applicability of our present methodology in practical MD studies, we
have studied the viscosity of argon-copper nanofluid and its variation with
temperature and volume fraction by MD simulation using MPINN. Then we have
compared them with numerous previous studies and theoretical models. Our
results indicate that MPINN can predict accurate nanofluid viscosity at a wide
range of sample space with significantly small number of MD simulations. Our
present methodology is the first implementation of MPINN in conjunction with MD
simulation for predicting nanoscale properties. This can pave pathways to
investigate more complex engineering problems that demand long-range MD
simulations.
