HamiFormer improves long-term smooth dynamics prediction accuracy
HamiFormer: Dual-Expert Diffusion Fields with Affine Symplectic Maps
Machine Learning
Summary
Predicting how things move smoothly but also suddenly bump is hard for computers. The authors designed HamiFormer, which combines two ways of guessing motion and corrections to improve predictions over whole time windows. It uses a new scanning method to speed up calculations while keeping accuracy high. Tests show it predicts movement more accurately than previous methods over long periods.
What this means in practice
- •For robotics engineers: Improve robot motion prediction over long time horizons by modeling smooth movement and sudden changes more accurately.
- •For computer graphics developers: Generate more realistic simulations of physical systems with smoother dynamics and better handling of collisions in virtual environments.
Authors
Haoxiang Huang, Xiang Liu, Shuwei Wang, Jingheng Ma, Sen Cui
Abstract
Predicting smooth dynamics and collisions requires modeling continuous evolution and abrupt state changes. We introduce HamiFormer, a dual-expert diffusion field combining whole-window denoising with residual-corrected Hamiltonian propagation. Their mixed-state feedback attenuates the direct contribution of inherited autoregressive error: each mixed state guides subsequent propagation within the jointly refined window. Parallel Local Affine Scan (PLAS) amortizes iterative refinement across rectified-flow steps and evaluates derivatives in parallel across physical time. PLAS's affine symplectic maps achieve lower solver error and runtime than sequential explicit Euler in our evaluation. A Regime Model Tree specializes residuals and routing to balance typical-state accuracy against large tail errors. Our analysis gives conditions for physically consistent refinement and warm-start tracking, and finite-window error bounds under diffusion feedback. In 192-step evaluations, HamiFormer reduces normalized phase-space MSE by 26.3% against PhysiFormer on HamiBalls-1 and 21.4% against DiT on HamiBalls-2, with comparable model capacities. Disjoint-interval comparisons show the lowest late-horizon position and momentum errors among baselines on both datasets. Project page: https://hamiformer.github.io/.