On the Scalability of Adaptive Monte Carlo for Trustworthy Uncertainty Forecasting

Abstract:
The overall objective of this dissertation is to provide timely, trustworthy, and actionable intelligence to decision making entities through accurate uncertainty quantification. Specifically, this dissertation will study the problem of uncertainty quantification for complex dynamical systems in the framework of particle methods and address the effectiveness of the solution methodology known as adaptive Monte Carlo (AMC). Forecasting results obtained through the AMC platform will also be leveraged alongside sensor data and adaptation routines towards the goal of improving model trustworthiness. Traditional Monte Carlo (MC) methods involve the discretization of the initial probability density function followed by forward propagation of individual particles through the system dynamics to obtain an approximate particle representation of the evolved state uncertainty. While simple to implement, traditional MC faces questions of transient statistical consistency and rate of convergence criticisms. On the other hand, AMC which is adopted here, addresses these issues on-the-fly using defined bounds on estimation accuracy as well as ensemble enrichment routines. Still, the computational efficiency of numerous routines within the AMC framework have yet to be addressed, leading to the first pillar of this dissertation. Sampling routines, quantities of interest, propagation techniques, and ensemble enrichment routines all contribute to the timeliness of AMC. Efficient algorithms lead to an effective forecasting platform, which can also be leveraged for systematic model adaptation. This leads to the dissertation's second pillar and further contributes to trustworthy forecasting rooted in AMC. That is, because AMC is capable of bounding errors in uncertainty quantification with respect to a quantity of interest, it can be utilized in a closed-loop architecture to guide the model improvement process. Numerical results will be given with respect to both pillars and will be in the context of computational efficiency as well as forecasting trustworthiness.

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Committee Members
Dr. Mrinal Kumar
Dr. Manoj Srinivasan
Dr. Stephanie Stockar
Dr. Abhishek Gupta