Empirical Study of RoA Penalty Functions in NeuralLyapunov.jl

Problem

Learned Lyapunov functions certify stability for nonlinear systems, but the penalty formulation used during training changes both optimisation stability and the region of attraction recovered. The trade-offs were not systematically characterised.

Approach

• 01Implemented an experimental framework on NeuralLyapunov.jl, NeuralPDE.jl, and Lux to learn Lyapunov functions for nonlinear dynamical systems.
• 02Designed controlled experiments across region-of-attraction penalty formulations and gating functions, evaluated on the Van der Pol oscillator.
• 03Automated pipelines for training diagnostics, RoA contour estimation, and experiment reporting covering loss dynamics and Lyapunov derivative validation.
• 04Investigated how smooth against hard gating functions affect optimisation stability and RoA boundary learning.