Using the Buckingham π Theorem for Multi-System Transfer Learning: A Case-Study with 3 Vehicles Sharing a Database
Bibliographic record
Abstract
Many advanced driver assistance schemes or autonomous vehicle controllers are based on a motion model of the vehicle behavior, i.e., a function predicting how the vehicle will react to a given control input. Data-driven models, based on experimental or simulated data, are very useful, especially for vehicles difficult to model analytically, for instance, ground vehicles for which the ground-tire interaction is hard to model from first principles. However, learning schemes are limited by the difficulty of collecting large amounts of experimental data or having to rely on high-fidelity simulations. This paper explores the potential of an approach that uses dimensionless numbers based on Buckingham’s π theorem to improve the efficiency of data for learning models, with the goal of facilitating knowledge sharing between similar systems. A case study using car-like vehicles compares traditional and dimensionless models on simulated and experimental data to validate the benefits of the new dimensionless learning approach. Preliminary results from the case study presented show that this new dimensionless approach could accelerate the learning rate and improve the accuracy of the model prediction when transferring the learned model between various similar vehicles. Prediction accuracy improvements with the dimensionless scheme when using a shared database, that is, predicting the motion of a vehicle based on data from various different vehicles was found to be 480% more accurate for predicting a simple no-slip maneuver based on simulated data and 11% more accurate to predict a highly dynamic braking maneuver based on experimental data. A modified physics-informed learning scheme with hand-crafted dimensionless features was also shown to increase the improvement to precision gains of 917% and 28% respectively. A comparative study also shows that using Buckingham’s π theorem is a much more effective preprocessing step for this task than principal component analysis (PCA) or simply normalizing the data. These results show that the use of dimensionless variables is a promising tool to help in the task of learning a more generalizable motion model for vehicles, and hence potentially taking advantage of the data generated by fleets of vehicles on the road even though they are not identical.
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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 | 0.001 |
| 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".