Prediction Is Not Physics: Learning and Evaluating Conserved Quantities in Neural Simulators

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 motio

Related evidence

These records share source-supplied organisations, an exact publisher byline, automatic topics or regions. The reason is shown on every link; related does not mean supporting, agreeing with or verifying this record.

How to cite this record

ethics.ai (16 May 2026), “Prediction Is Not Physics: Learning and Evaluating Conserved Quantities in Neural Simulators,” evidence record 4232, https://ethics.ai/record/4232 (originally published by arXiv).

Use and limitations

This page is a stable index and citation surface for a source record. ethics.ai did not author the underlying report and has not independently verified every claim. Automatic topics may be imperfect. For consequential use, quote and cite the original publisher.