# Background

Many systems in engineering and science are modeled using variables that live on **continuous domains** (e.g., space-time), making them infinite-dimensional (i.e., variables are functions). Specific engineering applications include REE-CM supply chains, wildfire simulations, process systems, climate modeling, reaction surfaces, microbial communities, complex fluid flows, and molecular dynamics. My unifying abstraction (InfiniteOpt) enables simultaneous innovation across these areas. Here, incorporating \textbf{random phenomena} (e.g., wind, porosity, random particle trajectories) is vital in many applications, but this is rarely done in practice due to the difficulty in representing/solving such problems.

**Random field theory** provides a powerful mathematical abstraction for characterizing uncertainty over space-time. Random fields generalize of the stochastic processes and Gaussian processes that are at the forefront of current research in the fields of spatio-temporal modeling, machine learning, topological data analysis, and Bayesian optimization. Here, application areas have included functional brain imaging, computer-generated imagery, weather forecasting, structural topological design, and robotic modeling. However, random field theory has not been incorporated into optimization theory.

# Innovating Decision-Making

Using my unifying abstraction, I proposed a new optimization framework called **random field optimization** that incorporates random field uncertainty into mathematical decision-making problems. This enables us to better capture **real-world behavior** and tackle emergent applications. Building upon this foundation, we will develop tractable **high-fidelity solution** approaches by potentially adapting PDE-constrained optimization decomposition techniques.