Raising Compute Density of Molecular Dynamics Simulation Through Approximate Memoization

Molecular dynamics (MD) simulation involves simulating the interactions of particles. MD has many applications in basic biological sciences, drug discovery, materials science, and other fields. Simulating
$1\mu \mathrm{s}$
of a 100K-atom system can take hours or days
^1
1
https://www.bdr.riken.jp/en/research/labs/taiji-mlmdgrape4.html, where the compute-heavy aspect of MD is calculating the long-range forces between pairs of particles. In this paper, we explore the application of approximate computing in MD as a means to improve compute density. Specifically, we employ approximate memoization, where previously computed forces (and more) are stored in a table, and are retrieved in subsequent force calculations, provided the inputs to the force calculation are the same or similar. If the prior-computed table values can be used, significant computational work is avoided. In an experimental study, we apply software simulation to understand the degree to which approximation is feasible. We then propose a hardware implementation of memoization to be used within an ASIC MD simulator, MDGRAPE-4A [18]. We show that compute density, measured as
$\text{pair-interactions}/(s\cdot\mu m^{2})$
is improved substantially, between 40 % and 70 % for the studied cases. This is contingent on the particular system being simulated, the table size, and permitted level of approximation.