Efficient Multi-Objective History-Matching Using Gaussian Processes
Bibliographic record
Abstract
Summary In a multiobjective optimization approach, a trade-off is sought to balance between the optimality of different objectives. In this paper, we introduce a new efficient multiobjective optimization approach using sequential Gaussian Process (GP) modeling that can quickly find the Pareto solutions in a minimal number of model evaluations. This is the first time that we present this approach for history-matching. The difference with other optimization algorithms is elucidated for the cases where we can only afford to run a limited number of simulations. Unlike other surrogate-based methods, we do not aim for a greedy approach by minimizing the surface itself as there can be a large uncertainty in the surrogate approximations. Instead, statistical criteria are introduced to account for both proxy model uncertainty as well as its extrema. This multiobjective optimization approach has been successfully applied for the first time to history match the production data (i.e. pressure, water and hydrocarbon rates) from a multi-fractured horizontal well in a tight formation. A GP surface is constructed for each misfit, to provide the predictions and the associated uncertainty for any unknown location. Multiobjective criteria, i.e., the hypervolume-based Probability of Improvement (PoI) and Expected Improvement (EI), are developed to account for the uncertainty of the misfit surfaces. The maximization of these statistical criteria ensures to balance between exploration and exploitation, even in higher dimensions. As such, a new point is selected whose values in different objectives are predicted to hopefully extend or dominate the solutions in the current Pareto set.
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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 | 0.002 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.002 |
| 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".