https://www.chenk.top/en/tags/structure-preserving-learning/Recent content in Structure-Preserving Learning on Chen Kai BlogHugoenMon, 28 Jul 2025 09:00:00 +0000https://www.chenk.top/en/standalone/symplectic-geometry-and-structure-preserving-neural-networks/Mon, 28 Jul 2025 09:00:00 +0000https://www.chenk.top/en/standalone/symplectic-geometry-and-structure-preserving-neural-networks/<p>Train a vanilla feedforward network to predict a one-dimensional harmonic oscillator. Validate it on the next ten time steps — the error is fine. Now roll it out for a thousand steps. The orbit no longer closes, the energy creeps upward, and what should be periodic motion turns into a slow spiral. The network learned to fit data points but never learned the <em>physics</em>. Structure-preserving networks fix this by incorporating geometric invariants — energy conservation, the symplectic 2-form, and the Euler-Lagrange equations — directly into the architecture, ensuring the learned model cannot violate them no matter how long you integrate.</p>