TOOL LyZNet: A Lightweight Python Tool for Learning and Verifying Neural Lyapunov Functions and Regions of Attraction
Bibliographic record
Abstract
In this paper, we describe a lightweight Python framework that provides integrated learning and verification of neural Lyapunov functions for stability analysis. The proposed tool, named LyZNet, learns neural Lyapunov functions using physics-informed neural networks (PINNs) to solve Zubov’s equation and verifies them using satisfiability modulo theories (SMT) solvers. What distinguishes this tool from others in the literature is its ability to provide verified regions of attraction close to the domain of attraction. This is achieved by encoding Zubov’s partial differential equation (PDE) into the PINN approach. By embracing the non-convex nature of the underlying optimization problems, we demonstrate that in cases where convex optimization, such as semidefinite programming, fails to capture the domain of attraction, our neural network framework proves more successful. The tool also offers automatic decomposition of coupled nonlinear systems into a network of low-dimensional subsystems for compositional verification. We illustrate the tool’s usage and effectiveness with several numerical examples, including both non-trivial low-dimensional nonlinear systems and high-dimensional systems.
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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 | 0.011 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.034 | 0.007 |
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".