Utilization of an Adaptive Monte Carlo Framework for Benchmarking of Data-Driven Tools and Physics-Based Models
Loading...
Date
2024-05
Authors
Ostavitz, Andrew
Journal Title
Journal ISSN
Volume Title
Publisher
The Ohio State University
Abstract
There is a concurrent need for physics-based models of complex systems and data-driven tools for the design, analysis, and uncertainty quantification of such systems in a variety of fields. As the fidelity of these models increase, computational cost grows in hand. A benchmarking scheme utilizing the Adaptive Monte Carlo (AMC) framework developed at The Ohio State University will allow for more effective cross model comparison. With AMC serving as a reference, the precision and accuracy of different implementations and the associated computational cost can be contrasted to inform decisions on which model will best address the needs of the target case.
A case study involving a Direct Moment Closure (DMC) implementation for the propagation of Van der Pol Oscillator moment dynamics was examined. The DMC implementation directly integrated the moment dynamics derived from the Van der Pol equations of motion using the ode45 solver function in MATLAB. AMC is a user-defined process in which accuracy is guaranteed for the selected quantities of interest. This is achieved through particle addition to the distribution to maintain results within the user-specified error bounds and is what makes AMC a capable benchmark for model comparison. With AMC the particles were propagated according to the Van der Pol dynamics and the moments of the data set were computed in post processing.
Examination of the first order moments showed divergent behavior from zero in the DMC implementation. This is due to the truncation of the stable higher order terms which must occur in the direct integration. The AMC model remained a zero mean process due to its accuracy being guaranteed. Results indicated that AMC did a better job of capturing the zero-mean process of the first order moment dynamics over time. However, the AMC simulation took far more computational power than the DMC model.
Future work involving models that are currently being used in industry can further develop this framework. This benchmarking scheme could serve as to inform industry professionals about the performance and computational cost of various models and methods when trying to predict, design, or analyze real-world applications.
Description
Keywords
Model Benchmarking, Uncertainty Forecasting, Adaptive Monte Carlo