trajectensampling

Trajecten sampling, or trajectory sampling, is a set of computational methods for generating and analyzing time-ordered sequences of states—trajectories—drawn from a dynamical system or stochastic process. The aim is to characterize the distribution over paths, estimate path-dependent observables, and study dynamic behavior, with particular emphasis on rare events or transitions between metastable states.

Practically, trajectory sampling can proceed by direct simulation to produce an ensemble of sample paths. When efficiency is required, specialized techniques are employed to sample path ensembles rather than single states. These include transition path sampling, shooting and shifting moves in path space, umbrella sampling along a reaction coordinate, and forward flux sampling. Path-space Markov chain methods, or path-space MCMC, are used to sample trajectories with particular endpoints or constraints. Together, these approaches allow estimation of quantities such as transition rates, free-energy landscapes, and other path-dependent statistics.

Applications span multiple disciplines. In chemical physics and molecular dynamics, trajectory sampling is used to explore reaction mechanisms and conformational changes. In materials science and biophysics, it helps quantify kinetic pathways and metastable states. In finance, path-dependent options and risk measures rely on sampling over price trajectories. In robotics and control, trajectory sampling informs planning under uncertainty and data-driven model verification.

Key considerations include computational cost, choice of coordinate representations or reaction coordinates, and convergence diagnostics. Limitations involve potential bias from sampling schemes and the need for adequate exploration of path space. Related concepts encompass path sampling, path integral methods, and sequential Monte Carlo used for trajectory inference.