We propose to expand and broaden the user base of a Cyberinfrastructure on stochastic simulation optimization called SimOpt. With this infrastructure, we ensure to orient the research agenda in stochastic simulation optimization towards 1) the development of solvers that deliver strong finite-time performance over a breadth of practical problems, especially by exploiting problem structure; 2) comprehensive and rigorous comparisons of solvers on a suite of test problems that showcase the relative strengths and weaknesses of the solvers; 3) capitalizing on developments in adjacent fields such as optimization in machine learning to advance the state of the art in simulation optimization, and vice versa; and 4) increasing the adoption of SimOpt as a framework for computational research in stochastic simulation and machine learning.

Many engineering systems with naval capabilities are too complex to be analyzed mathematically. Instead, computer simulations are built and validated to replicate the behavior of these systems. One primary purpose of using simulations is decision-making. Still, the challenge for such problems is that the underlying problem being optimized is in the form of a black box, and extracting direct derivative information from it to facilitate the optimization is either impossible or costly. Derivative-free stochastic optimization is a field that attempts to support decision-making in such a setting, particularly in continuous search spaces. Such optimization settings are relevant to situational awareness, EMW technology calibrations, and unmanned vehicle mobility problems. The current derivative-free optimization tools are slow in higher dimensions because of the additional effort they expend to draw information about the regional behavior of the system, which is, of course, stochastic. This proposal offers innovative tools stemming from applied probability and statistics, geometry, and quantum information science to evolve the computational ability of derivative-free stochastic optimization tools for high dimensional search. The success of this project provides new scientific knowledge for computing and large-scale data management that leads to enhanced real-time capabilities beneficial to the acquisition community.

This project will develop a simulation modeling tool to evaluate the effectiveness of and quantify risks associated with lagoon-sprayfield recycling of manure liquid and nutrients under different management and climate conditions. This goal will be accomplished through the following tasks: [1] data collection to develop and refine quantitative estimates of manure and wastewater generation, nutrient transformation, plant growth and nutrient uptake, [2] simulation modeling tool development to integrate these modules, [3] tool testing and validation using real farm datasets, [4] scenario assessment to incorporate uncertainty and different priorities and interventions, and [5] dissemination to and feedback collection from various stakeholder groups. This project will leverage primary results and a prototype model developed by the project team, through NCSU seed funding, as a basis to develop described modeling tools. The team expertise spans climate science, irrigation and drainage, waste management, modeling, optimization and uncertainty quantification for robust decision-making.

The incorporation of adaptive sampling with machine learning has many benefits owing to its proven efficiency. We introduce solving a calibration problem as a stochastic optimization problem where noisy realizations of the deviation between the computer model and the real system are minimized over the choice of model parameters. A variant of Derivative-Free Adaptive Sampling Trust-Region Optimization (ASTRO-DF) combined with bootstrapping and importance sampling ensures, when estimating the objective function, that small sample sizes are chosen away from a critical point and large sample sizes are chosen near a critical point. Finite-time performance and work-complexity of this algorithm are investigated with the calibration of wake effect in wind turbines. Wake represents the energy loss in downstream turbines and characterizing it is essential in designing wind farm layout and controlling turbines for maximum power generation. With large data, calibrating the wake parameters is a derivative-free optimization that can be computationally expensive. But with the proposed algorithm we are able to handle the large data and reach robust solutions by harnessing the uncertainty at two levels: the sample size and the sample choices. We do the former by generating a varying number of bootstraps and the latter by importance sampling.

Severe weather-based power outages are among the most widespread issues facing electric power utilities. In North Carolina, short-duration power outages from severe weather, such as winter ice storms and summer thunderstorms, regularly lead to tens of thousands of outages annually. A significant challenge in mitigating the impact of severe weather outages is the unpredictability of severe weather and the associated grid impacts. The inability to forecast storm damages leads to slow reaction times and an inability to preposition repair crews and supplies, collectively leading to more prolonged restoration times for customers. We aim to develop a predictive analytics tool to forecast storm-based outages in advance of weather phenomena to aid in pre-positioning supplies and support crews. To do this, we will train and validate statistical models that integrate land cover data, historical storm and weather data, and detailed records of previous weather outages. The goal is to provide estimates of likely future severe weather outages with sufficient lead time to make staffing and crew dispatching decisions. We have partnered with the North Carolina Electric Membership Corporation (NCEMC), an organization supporting North Carolina���s 26 electric cooperatives, which has identified winter ice storms and summer thunderstorms as among their most difficult-to-staff challenges.

The concentration of this project is the theory of optimization for problems whose responses can only be observed inexactly from a stochastic simulation model, and their decision variables are in continuous space. We broadly call this class of problems nonconvex stochastic optimization. There is accumulating evidence that stochastic trust-region (TR) methods effectively solve first-order nonconvex stochastic optimization problems due to TR������������������s natural ability to self-tune step sizes and facility for curvature estimation. This paper provides almost sure sample complexity results for general stochastic TR methods that estimate function and gradient values adaptively, using sample sizes that are stopping times concerning the sigma-algebra of the generated observations. Adaptive sampling is a powerful formalism that allows algorithm-trajectory-dependent sampling within frameworks such as TR. We respond to an efficiency trade-off question: How much sampling effort to spend on constructing a local model that approximates the stochastic objective function? Too much effort is undesirable from the standpoint of computational efficiency but suitable for obtaining a more accurate local model, which is more likely to lead to a better candidate solution. To the best of our knowledge, this paper is the first to prove the sampling efficiency of the stochastic TR algorithms with the advantage of adaptive sampling. This research paper has lingered in the pipeline for several years due to the little time after first and second-year junior faculty engagements, especially during COVID-19 - teaching, advising, writing proposals, and service. The paper is more than 60% complete, but some results are still in progress or need further validation.

Climate change is expected to impact agriculture in North Carolina profoundly. The impacts of climate shifts on crop and animal systems are not entirely understood, leading to significant challenges to planning efforts. For example, NC will likely experience an increase in rainfall, impacting poultry and swine lagoon systems by manure spillovers, which can also decrease water quality. In the proposed work, we will build (i) a domain-informed simulation that mechanistically approximates the lagoon systems dynamics and (ii) a data-driven domain-agnostic prediction model using publicly available data. The data after necessary processing provides information about conditions in NC lagoon systems and climate variables, providing current and future rainfall probabilities and volumes. Upon validation of these models, we will predict future chances of lagoon levels exceeding maximum storage capacity. We will focus on robust results by incorporating plausible probability distributions that model noise in the observations due to unknown effects or uncontrollable randomness in the system. Our ultimate goal is to use these preliminary results in a larger scale external proposal that pursues mitigation strategies for adverse climate impacts in the animal agriculture systems, which remain robust to shifts in the projected future climate.

Monte Carlo methodology has made advances in the recent decades due to its versatility, particularly in the presence of uncertainty in high-dimensional systems. However, Monte Carlo methods are slow in theory and in finite-time implementations, limiting their applications in today������������������s quickly evolving world with continuous mass production of data. Quantum computing has exhibited promise for the enhancement of computational and numerical algorithms. This proposal aims at exploiting quantum computing to dramatically enhance computational efficiency and statistical reliability of Monte Carlo methods with data and simulation. The outcome of a year-long study will provide context and proof of concept for an NSF CAREER proposal in 2022.