HamiFormer：具有仿射辛映射的双专家扩散场
HamiFormer: Dual-Expert Diffusion Fields with Affine Symplectic Maps
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中文总结 AI 辅助
HamiFormer提出双专家扩散场，结合全窗口去噪与残差校正哈密顿传播，通过仿射辛映射实现高效并行精化，在动力学预测中显著降低误差。
中文摘要 AI 辅助
预测平滑动力学和碰撞需要建模连续演化与突变状态变化。我们提出HamiFormer，一种双专家扩散场，结合了全窗口去噪与残差校正的哈密顿传播。其混合状态反馈削弱了继承自回归误差的直接贡献：每个混合状态在联合精化的窗口内引导后续传播。并行局部仿射扫描（PLAS）在整流流步骤间分摊迭代精化，并在物理时间上并行计算导数。在我们的评估中，PLAS的仿射辛映射相比顺序显式欧拉方法实现了更低的求解器误差和运行时间。一种机制模型树专门处理残差和路由，以平衡典型状态精度与大的尾部误差。我们的分析给出了物理一致精化和热启动跟踪的条件，以及扩散反馈下的有限窗口误差界。在192步评估中，HamiFormer在HamiBalls-1上相比PhysiFormer将归一化相空间均方误差降低了26.3%，在HamiBalls-2上相比DiT降低了21.4%，且模型容量相当。不相交区间比较显示，在两个数据集上，HamiFormer在晚期水平位置和动量误差方面均优于基线。项目页面：此https URL。
英文摘要
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/.
