Neural Networks Struggle to Learn Conserved Quantities from Physical Trajectories
A recent study posted on arXiv indicates that diffusion models relying on Hamiltonian pathways can achieve a rollout mean squared error (MSE) approaching 10^-3. However, they struggle significantly with energy conservation, showing inaccuracies that range from 7,500 to 36,000 times higher than anticipated. Researchers explored three Hamiltonian systems: spring-mass, pendulum, and projectile motion, utilizing multiple approaches. Among them, a structured energy model demonstrated an impressive R² of 0.9999 with clean data, while a black-box Conservation Discovery Network attained an R² of 0.996 when adequately trained, revealing a notable disparity between predictive accuracy and physical realism.
Key facts
- Diffusion model achieves rollout MSE near 10^-3
- Energy standard deviation is 7500–36000 times larger than ground truth
- Study investigates three Hamiltonian systems: projectile motion, pendulum, spring-mass
- Structured T(v)+V(q) energy model achieves R^2 ≥ 0.9999 on clean data
- Black-box CDN reaches R^2 ≥ 0.996 with temporal consistency and alignment loss
- Alignment loss parameter λ_align = 0.2
- Paper published on arXiv with ID 2605.18883
- Central question: can neural networks learn globally conserved quantities?
Entities
Institutions
- arXiv