Molecular dynamics (MD) simulations provide computational chemists insight into the behavior of chemical systems at atomic-scale resolution over time. However, these simulations are slow, since they essentially integrate the differential equations of motion in time, to track the movement of typically a large number of atoms with precision. Computational chemists are always on the lookout for new ways to optimize simulations. One notable technique is multiple time-scale integration, which allows to compute slowly varying forces less frequently, in a stable and accurate manner.

In this preliminary work, we began constructing an optimization framework for MD simulations, in order to allow an automatic exploration of novel optimizations for molecular dynamics codes. We combine the power of two approaches: equality saturation and stochastic mutations.

First, we apply equality saturation in this new domain. To be effective, this requires domain-specific rewrite rules and flexible extraction and custom cost functions, that are necessary to optimize real-world programs for scientific computation.

We also explore a mutation-based optimization workflow aimed at discovering changes we cannot prove the axiomatic equivalence of. This may be because they make big changes to the control flow, or because the change leads to non-equivalent code, still accurate enough by chemical theory, but that returns slightly different results. A promising approach is iteratively applying e-graph transformations, e.g., operator splitting, to restructure the simulation code, then building variants via mutation‐based techniques.

Our aim is to build a mutate-verify loop that can reproduce known optimizations and potentially discover novel ones. Our early results and conceptual framework suggest a transformative methodology for optimizing simulation code, that promises both significant performance improvements and the automated discovery of new optimization constructs.