Shortcuts to Parameter Sweeps

Abstract

Efficient evaluation of stationary parametric sensitivities over broad parameter ranges is important for identifying influential training data, fitting force fields, and predicting material responses, but standard pointwise approaches require repeated relaxation and sampling. Here we introduce Shortcuts to Parameter Sweeps (STPS), an engineered control strategy that uses an auxiliary control to transport the probability density along a prescribed family of instantaneous stationary states during a finite-time parameter sweep. This enables the continuous response curve over the full parameter interval to be estimated from a single controlled sweep using covariance-based response relations. STPS applies to both equilibrium and nonequilibrium steady-state systems, including those with unknown stationary distributions, and can be implemented directly using stationary samples in high-dimensional settings. Numerical tests on single-particle and interacting many-body systems show that STPS yields response curves in close agreement with reference results. These findings establish STPS as an efficient, sample-based framework for continuous sensitivity analysis in stochastic simulations.