Hamiltonian-based neural networks for systems under nonholonomic constraints
Bibliographic record
Abstract
There has been increasing interest in methodologies that incorporate physics priors into neural network architectures to enhance their modeling capabilities. A family of these methodologies that has gained traction are Hamiltonian neural networks (HNN) and their variations. These architectures explicitly encode Hamiltonian mechanics both in their structure and loss function. Although Hamiltonian systems under nonholonomic constraints are in general not Hamiltonian, it is possible to formulate them in pseudo-Hamiltonian form, equipped with a Lie bracket which is almost Poisson. This opens the possibility of using some principles of HNNs in systems under nonholonomic constraints. The goal of the present work is to develop a modified Hamiltonian neural network architecture capable of modeling Hamiltonian systems under holonomic and nonholonomic constraints. A three-network parallel architecture is proposed to simultaneously learn the Hamiltonian of the system, the constraints, and their associated multipliers. A rolling disk and a ball on a spinning table are considered as canonical examples to assess the performance of the proposed Hamiltonian architecture. The experiments are then repeated with a noisy training set to study modeling performance under more realistic conditions.
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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 | 0.002 |
| 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 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".