Manifold-Guided Stabilization of Nonlinear Dynamical Systems with Diffusion Models
Bibliographic record
Abstract
This paper introduces Manifold-Guided Stabilizing Control (MGSC), a novel approach to synthesizing stabilizing controllers for nonlinear dynamical systems using diffusion models. Our method formulates control synthesis as a search for the closest asymptotically stable vector field within a learned manifold of stable dynamics. We train a diffusion model on a dataset of asymptotically stable vector fields and employ Tweedie’s estimate to iteratively adjust control parameters, ensuring convergence to a stabilizing controller. This formulation enables zero-shot stabilization for previously unseen systems with significantly reduced computational cost. Our numerical experiments demonstrate that MGSC achieves stabilization in just 16 seconds, compared to 2 minutes in prior work, while generalizing effectively across different nonlinear control problems. These results highlight the potential of diffusion models as a powerful tool for fast, data-driven control synthesis.
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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".