Optimization of Stochastic Processes Using Automatic Differentiation

This research program focuses on the study and understanding of energy transfers, their efficiency, and the associated fluctuations in stochastic processes of mesoscale systems subject to significant thermal fluctuations. Typical examples include colloidal particle systems dissolved in a solvent that can be manipulated with optical tweezers, biomolecular motors, microelectric circuits, micro-mechanical oscillators, microbial biomass, and more. Due to their small size, these systems are highly susceptible to thermal fluctuations. The general goal is to establish theoretical foundations for the development of energy transfer mechanisms at the microscopic and mesoscale levels. To achieve this purpose, we propose designing control protocols for mesoscale systems that optimize the work performed and facilitate the system’s transition from a thermally equilibrated configuration to a new configuration, ensuring rapid thermal equilibration. This design will be carried out computationally, simulating the system and subsequently adjusting the control protocol to optimize it. This adjustment is feasible with the help of machine learning tools in artificial neural networks, particularly through automatic differentiation.