Machine Learning Approach to Improve Accuracy of Warpage Simulations
Bibliographic record
Abstract
Warpage control of electronic packages has become a critical challenge given the requirement of thinner packaging solutions for the future. While modeling warpage using finite element models is a good way to predict stresses and warpage, the analysis results are only as good as the assumed model inputs such as material properties. This is especially true with warpage simulations and the anisotropic and temperature-dependent material properties of the electronic substrate. With the varying metal line patterns and densities across the substrate, the substrate material properties can be spatially varying in ultra-thin packages resulting in complex warpage profiles. To aid in better design for reliability of future ultra-thin packages, we propose here the use of the Markov Chain Monte Carlo (MCMC) approach (Bayesian inference) combined with finite element simulations to identify the sensitive material parameters that most affect warpage and learn the localized material properties based on warpage contours that have been measured using digital image correlation (DIC). The proposed technique can enable us to design better packages with locally tailored material properties (by tuning metal layer densities, for example) to enable us to stay within an acceptable warpage threshold.
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How this classification was reachedexpand
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".