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Uncertainty analysis in the outcomes of model predictions is a key element in decision-based material design to establish confidence in the models and evaluate the fidelity of models. Uncertainty Propagation (UP) is a technique to determine model output uncertainties based on the uncertainty in its input variables. The most common and simplest approach to propagate the uncertainty from a model inputs to its outputs is by feeding a large number of samples to the model, known as Monte Carlo (MC) simulation which requires exhaustive sampling from the input variable distributions. However, MC simulations are impractical when models are computationally expensive. In this work, we investigate the hypothesis that while all samples are useful on average, some samples must be more useful than others. Thus, reordering MC samples and propagating more useful samples can lead to enhanced convergence in statistics of interest earlier and thus, reducing the computational burden of UP process. Here, we introduce a methodology to adaptively reorder MC samples and show how it results in reduction of computational expense of UP processes.
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Accelerating the estimation of collisionless energetic particle confinement statistics in stellarators using multifidelity Monte Carlo
Abstract In the design of stellarators, energetic particle confinement is a critical point of concern which remains challenging to study from a numerical point of view. Standard Monte Carlo (MC) analyses are highly expensive because a large number of particle trajectories need to be integrated over long time scales, and small time steps must be taken to accurately capture the features of the wide variety of trajectories. Even when they are based on guiding center trajectories, as opposed to full-orbit trajectories, these standard MC studies are too expensive to be included in most stellarator optimization codes. We present the first multifidelity Monte Carlo (MFMC) scheme for accelerating the estimation of energetic particle confinement in stellarators. Our approach relies on a two-level hierarchy, in which a guiding center model serves as the high-fidelity model, and a data-driven linear interpolant is leveraged as the low-fidelity surrogate model. We apply MFMC to the study of energetic particle confinement in a four-period quasi-helically symmetric stellarator, assessing various metrics of confinement. Stemming from the very high computational efficiency of our surrogate model as well as its sufficient correlation to the high-fidelity model, we obtain speedups of up to 10 with MFMC compared to standard MC.
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- PAR ID:
- 10343277
- Date Published:
- Journal Name:
- Nuclear Fusion
- Volume:
- 62
- Issue:
- 7
- ISSN:
- 0029-5515
- Page Range / eLocation ID:
- 076019
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1088/1741-4326/ac4777
