Trajectory-Based DEIM TDEIM Model Reduction Applied to Reservoir Simulation
Bibliographic record
Abstract
Abstract Two well-known model reduction methods, namely the trajectory piecewise linearization (TPWL) approximation and the discrete empirical interpolation method (DEIM) are combined to utilize their benefits and avoid their shortcomings to generate reduced order models for reservoir simulation. To this end, we use the trajectory-based DEIM (TDEIM) to approximate the nonlinear terms in the simulation. Specifically, the nonlinear terms in the test simulation can be expressed as the sum of the nonlinear terms evaluated at the closest available training point from the high-fidelity training trajectory and a perturbed term defined as the difference between the the test and the training terms. We only interpolate this perturbed term in the reduced space of DEIM instead of the original nonlinear term, resulting in computational savings and improvement in accuracy. TDEIM is further combined with the proper orthogonal decomposition (POD) method to provide an efficient POD-TDEIM framework. We test our new methodology on two examples, involving two-phase (water-oil) heterogeneous reservoir models. First, the performance of POD-TDEIM is compared with POD-TPWL and POD-DEIM on a 2D reservoir model. For the same set of high-fidelity training runs, POD-TDEIM outperforms the other two methods. We further propose an extended TDEIM in which the nonlinear term is expanded along the training trajectory to include one more derivative term. An example with a 3D reservoir model is then presented to show the capability of the extended TDEIM to further improve the accuracy of the reduced model.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 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".