We investigate whether Hamiltonian Neural Networks (HNNs) can recover energy- conserving dynamics from real, noisy data rather than synthetic simulations. To accomplish this, we reinterpret MNIST digits as 2D trajectories by using stroke se- quences. We set momentum equal to velocity (p := q̇ ), estimate accelerations with finite differences, align starting points, restrict to single-stroke examples, and fix initial momenta to match typical writing directions. We compare two sampled feed-forward architectures trained without backpropagation: a sampled HNN, and a sampled ODE- Net. For the rollouts, we use forward or symplectic Euler integration. Across digits 2, 3, and 6, both models tend to infer a single ”idealized” pen path. HNNs are able to preserve an energy-like quantity and show greater stability under symplectic inte- gration. However, conventional relative L2 errors remain high, reflecting the mismatch with many distinct ground-truth traces. We propose more comprehensive data curation and alternative methods for determining p as promising next steps.     «

We investigate whether Hamiltonian Neural Networks (HNNs) can recover energy- conserving dynamics from real, noisy data rather than synthetic simulations. To accomplish this, we reinterpret MNIST digits as 2D trajectories by using stroke se- quences. We set momentum equal to velocity (p := q̇ ), estimate accelerations with finite differences, align starting points, restrict to single-stroke examples, and fix initial momenta to match typical writing directions. We compare two sampled feed-fo...     »