Hard-Constrained Invariant-Preserving Neural Networks for Conservative Dynamical Systems: A Statistically Validated Approach
Abstract
This version (v2.0) introduces hard structural constraints via multiplicative manifold projection, achieving 72.2% improvement in invariant preservation (p < 1e-11, Cohen's d = 5.03) compared to baseline, and 66.9% improvement over soft penalty methods. Includes three-way statistical comparison: Baseline PINN vs. Soft IP-PINN vs. Hard IP-PINN.
Fields of Study & Subjects
Model Reduction and Neural Networks
Neural Networks and Applications
Numerical methods for differential equations
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 4 February 2026
- Language
- EN