In recent years, control of small, fluctuating systems coupled to an environment has emerged as a central topic across disciplines, from statistical physics to applications in nanotechnology and biological physics. The stochastic systems of interest often operate far from thermal equilibrium and pose fundamental challenges regarding transport, stabilization of certain states, and efficiency. Current research in the area of control just starts to develop from single-particle model systems, like a Brownian particle in a harmonic trap, to more complex matter involving many degrees of freedom and/or complex potential landscapes. For these problems, methods from machine learning (ML), particularly automatic differentiation, is emerging as a promising tool. The present project aims at using automatic differentiation, or alternative strategies if necessary, to advance optimal control protocols for several types of stochastic multi-variable systems in and out of equilibrium. The overall control goal is a speed-up of relaxation into equilibrium or nonequilibrium steady states (plus additional constraints, where desired).
Specifically, the project focuses on three, partially interconnected, topics: (i) underdamped systems and the role of inertia and nonlinearity, (ii) effect of pair interactions, particularly long-range and (non-)reciprocal linear couplings, and (iii) control strategies for active systems from individual active (Ornstein-Uhlenbeck) particles in nonlinear potentials to (repulsively) interacting active matter. By this choice of problems, we aim at advancing the field of control of stochastic systems towards previously unexplored regimes, with relevance to both fundamental science and future experimental applications. The envisioned ML-based control framework will be implemented via numerical simulations and benchmarked using analytical results whenever possible.
The project is planned to combine and advance the comprehensive expertise of the two applicants in the areas of nonequilibrium systems and control (S. Klapp, TU Berlin) and applications of ML for stochastic systems (G. Téllez, Universidad de los Andes), where an algorithm for automatic differentiation to optimize fast thermal equilibration in overdamped single-particle systems has already been developed.
