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 sequences. 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 integration. 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.