Explore advanced Gaussian process function approximation and uncertainty quantification techniques for autonomous experimentation in this 52-minute lecture by Marcus Noack from Lawrence Berkeley Laboratory. Delve into the power of Gaussian processes and related stochastic processes for function approximation, uncertainty quantification, and autonomous control of data acquisition. Address common criticisms regarding poor approximation performance and scalability in real-life applications by examining the importance of flexibility and domain awareness in underlying prior probability distributions. Discover recent examples of GP applications in various approximation and decision-making problems, identifying challenges, intricacies, and complexities of the methodology. Learn how to improve performance by addressing these issues, gaining valuable insights for implementing Gaussian processes in complex scientific workflows at extreme computational scales.