AI RESEARCH
Prediction Is Not Physics: Learning and Evaluating Conserved Quantities in Neural Simulators
arXiv CS.AI
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ArXi:2605.18883v1 Announce Type: cross A diffusion model trained on Hamiltonian trajectories can achieve rollout MSE near $10^{-3}$, but the standard deviation of its energy over time is between 7500 and 36000 times larger than the ground-truth energy standard deviation, indicating a failure to preserve conservation laws. This gap motivates our central question of whether neural networks can learn or select globally conserved quantities from physical trajectories. We investigate this across three Hamiltonian systems: projectile motion, pendulum, and spring-mass.