Registration-based nonlinear model reduction of parametrized aerodynamics problems with applications to transonic Euler and RANS flows
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Bibliographic record
Abstract
We develop a registration-based nonlinear model-order reduction (MOR) method for partial differential equations (PDEs) with applications to transonic Euler and Reynolds-averaged Navier–Stokes (RANS) equations in aerodynamics. These PDEs exhibit discontinuous features, namely shocks, whose location depends on problem configuration parameters, and the associated parametric solution manifold exhibits a slowly decaying Kolmogorov N -width. As a result, conventional linear MOR methods, which use linear reduced approximation spaces, do not yield accurate low-dimensional approximations. We present a registration-based nonlinear MOR method to overcome this challenge. Our formulation builds on the following key ingredients: (i) a geometrically transformable parametrized PDE discretization; (ii) localized spline-based parametrized transformations which warp the domain to align discontinuities; (iii) an efficient dilation-based shock sensor and metric to compute optimal transformation parameters; (iv) hyperreduction and online-efficient output-based error estimates; and (v) simultaneous transformation and adaptive finite element training. Compared to existing methods in the literature, our formulation is efficiently scalable to larger problems and is equipped with error estimates and hyperreduction. We demonstrate the effectiveness of the method on two-dimensional inviscid and turbulent flows modeled by the Euler and RANS equations, respectively.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it