Master’s Thesis

Abstract

The control and calibration of complex physical systems with nonlinear dynamics, partial observability, and uncertain parameters remain a central challenge in modern engineering. This thesis investigates active inference as a principled probabilistic control paradigm for such systems, with a specific focus on the calibration of an industrial nanoliter Drop-on-Demand dispensing process.

Active inference, grounded in Bayesian mechanics and the free energy principle, unifies perception, learning, and control through the minimization of variational free energy. In this work, these theoretical concepts are operationalized for an engineering application through the development of a physics-informed probabilistic generative model of droplet dispensing dynamics. The model leverages computer-vision-based measurements of droplet volume, shape, and position and is embedded within an active inference controller. The controller is implemented via variational message passing on factor graphs. This enables online learning and control through the joint inference of model parameters and control actions that minimize variational free energy.

The proposed controller is evaluated in a realistic closed-loop simulation environment based on experimental data from a piezoelectric Drop-on-Demand dispensing system. A systematic investigation analyzes the influence of model priors, learning mechanisms, and action-selection strategies on convergence behavior, robustness, and calibration performance. The active inference controller is benchmarked against a conventional Proportional–Integral–Derivative (PID) controller and a Bayesian-optimization-based controller representing the state-of-the- art in sample-efficient process optimization. Compared to the baseline methods, the proposed controller exhibits superior calibration performance, reducing the required number of droplets for calibration on average by 92% and 85%, respectively. The results demonstrate that active inference enables robust and sample-efficient calibration by effectively balancing exploration and exploitation.

Beyond the specific application to nanoliter droplet dispensing, this thesis contributes a structured and engineering-oriented exposition of Bayesian mechanics and active inference, bridging theoretical foundations and practical implementation. The presented methodology establishes active inference as a viable and scalable control framework for complex, vision- based physical systems and provides design guidelines to support its adoption in future in- dustrial and autonomous experimentation settings.