Information-Optimal Sensing and Control in High-Intensity Laser Experiments

High-intensity laser systems present unique measurement and optimization challenges due to their high complexity, low repetition rates, and shot-to-shot variations. We discuss recent developments towards a unified framework based on information theory and Bayesian inference that addresses these challenges. Starting from fundamental constraints on the physical field structure, we recently demonstrated how to capture complete spatio-temporal information about individual petawatt laser pulses. Building on this foundation, we demonstrate how Bayesian frameworks can leverage temporal correlations between consecutive pulses to improve measurement precision. We then extend these concepts to active sensing strategies that adaptively select measurements to maximize information gain, exemplified through Bayesian autocorrelation spectroscopy. Finally, we show how these information-optimal measurement principles naturally extend to Bayesian optimization. This progression represents a paradigm shift where measurement devices transition from passive data collectors to active participants in complex experiments.