Constructing low-dimensional control forces for variational path sampling

Determine effective procedures to construct control forces parameterized by low-dimensional collective coordinates for variational path sampling, including principled choices of collective variables and parameterizations that maintain accuracy while reducing statistical uncertainty.

Background

In complex systems, optimal control forces are formally high-dimensional. VPS often relies on low-rank parameterizations over collective coordinates to render learning tractable, but systematic guidance on how to choose and parameterize these coordinates is lacking.

Clarifying best practices for low-dimensional constructions would improve VPS accuracy and efficiency, especially for processes where spatial locality is limited (e.g., nucleation) and statistical estimators become noisy.