Adaptive Surrogate Modelling for the Uncertainty Quantification of Large-Scale Nonlinear PDE-based Problems
Bibliographic record
Abstract
The quantification and control of uncertainty is paramount for the simulation-based characterization of engineering systems. However, the high costs of uncertainty quantification (UQ) often preclude engineers from developing a comprehensive understanding of the uncertainty inherent in large-scale simulations. This thesis presents work towards scaling UQ to large-scale, engineering-relevant problems via three distinct contributions. First, we develop a goal-oriented, adaptive method for the forward UQ of systems modeled by stochastically parametrized nonlinear conservation laws. The method exploits localized structure in the spatio-parameter approximation spaces to enable efficient and reliable UQ of quantities of interest. The formulation comprises (i) a discontinuous Galerkin method; (ii) element-wise polynomial chaos expansions; (iii) spatio-stochastic dual-weighted residual error estimates; and (iv) a projection-based spatio-parameter anisotropic error indicator and the associated adaptation mechanics. We demonstrate the effectiveness of the formulation for transonic turbulent flows with uncertainties in flow conditions and turbulence model parameters. Second, we develop an efficient multi-fidelity data assimilation method for large-scale nonlinear dynamical systems. The formulation comprises (i) an ensemble Kalman filter (EnKF) to tractably handle high-dimensional, nonlinear dynamical models; (ii) projection-based reduced order models (ROMs), which accelerate the evaluation of ensemble forecast by several orders of magnitude and are constructed on the fly using the ensemble of full-order model (FOM) trajectories; and (iii) multi-fidelity statistical estimates that optimally combine the FOM and ROM forecasts. We demonstrate the effectiveness of the formulation using unsteady aerodynamic flow past an airfoil. Lastly, we develop a data assimilation method for large-scale dynamical systems that exhibit strong nonlinearities, which can render the standard EnKF less effective. The formulation comprises (i) ensemble transport filter (EnTF), which generalizes the EnKF to stronger nonlinarities using the transport map, (ii) ROMs, which reduce the state dimension and accelerate the ensemble forecast to overcome the scaling challenges associated with transport maps, and (iii) a method to mitigate stability issues that arise when constructing transport maps for ROMs. We demonstrate the efficacy of the EnTF relative to EnKF using unsteady aerodynamics flow past an airfoil.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.001 | 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".