We establish an information complexity lower bound of randomized algorithms for simulating underdamped Langevin dynamics. More specifically, we prove that the worst $L^2$ strong error is order $\Omega(\sqrt{d}\, N^{-3/2})$, solving a family $d$-dimensional dynamics, by any algorithm with only $N$ queries to $\nabla U$, driving Brownian motion and its weighted integration, respectively. The matc...

The description of the dynamics of a complex, high-dimensional system in terms of a low-dimensional set of collective variables Y can be fruitful if the low-dimensional representation satisfies a Langevin equation with drift and diffusion coefficients that depend only on Y. We present a computational scheme to evaluate whether a given collective variable provides a faithful low-dimensional repr...

We develop a numerical method to simulate mechanical objects in a viscous medium at a scale where inertia is negligible. Fibers, spheres and other voluminous objects are represented with points. Different types of connections are used to link the points together and in this way create composite mechanical structures. The motion of such structures in a Brownian environment is described by a firs...