Multilevel Monte Carlo Coupled With the Parabolic Wave Equation Method for Uncertainty Analysis of Radio Wave Propagation in Tunnels
Bibliographic record
Abstract
Radio wave propagation modeling in tunnels is crucial to design reliable wireless communication systems. Among the techniques available, the parabolic wave equation (PWE) methods have been widely utilized, due to their balance of accuracy and efficiency. However, the accuracy of the PWE methods depends on precise knowledge of tunnel environments, which are subject to uncertainties. While Monte Carlo (MC) methods are reliable for uncertainty analysis, they are computationally intensive. Polynomial chaos expansion (PCE) methods, though efficient, struggle with high-dimensional inputs. This paper applies the multilevel Monte Carlo (MLMC) method to the PWE method in a non-intrusive way. MLMC is employed to address uncertainties arising from various sources. Such MLMC-PWE method provides efficient estimations of the mean and variance of quantities of interest (QoI) by utilizing a multiscale hierarchy of spatial discretization. Numerical examples across different tunnel geometries demonstrate that the MLMC-PWE method achieves lower computational costs and improved efficiency relative to the MC-PWE method and the PCE-PWE method.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".