Reproduce “Learning piecewise-smooth dynamical systems” on OpenResearch

About this paper

Davide Murari, Erik Jansson, Chris Budd OBE, Carola-Bibiane Schönlieb

The authors present a pipeline that estimates switching planes from trajectory velocity changes using RANSAC and TLS, then fits dynamics with a neural architecture that confines discontinuities to those planes. On PP04, at zero observation noise, the learned-geometry model achieves rollout RMSE 2.66 × 10⁻³, versus 3.28 × 10⁻² for a smooth Neural ODE. The comparison is limited to low-dimensional synthetic benchmarks.

Key insights

• The geometry-preserving neural network architecture ensures that learned discontinuities are strictly confined to predefined switching hyperplanes, preventing spurious jumps and enhancing model interpretability.
• Robust recovery of switching geometries from noisy trajectory data is achievable by focusing on large derivative jumps and employing robust fitting techniques like RANSAC-TLS.
• Incorporating domain-specific prior knowledge, such as second-order mechanical structure or known forcing frequencies, consistently improves model accuracy and generalization for piecewise-smooth systems.

Summary by alphaXiv.