Deterministic particle flows for constraining stochastic nonlinear systems

Dimitra Maoutsa, Manfred Opper

Abstract:

Devising optimal interventions for constraining stochastic systems is a challenging endeavor that has to confront the interplay between randomness and dynamical nonlinearity. Existing intervention methods that employ stochastic path sampling scale poorly with increasing system dimension and are slow to converge. Here we propose a generally applicable and practically feasible methodology that computes the optimal interventions in a noniterative scheme. We formulate the optimal dynamical adjustments in terms of deterministically sampled probability flows approximated by an interacting particle system. Applied to several biologically inspired models, we demonstrate that our method provides the necessary optimal controls in settings with terminal, transient, or generalized collective state constraints and arbitrary system dynamics.

Keywords: stochastic control, stochastic dynamics, score functions, probability flow ODEs, particle filters, synchronisation control, stochastic Kuramoto oscillators