通过动态调节补丁大小，提升物理模拟器的精度与效率。
Overtone: Cyclic Patch Modulation for Clean, Efficient, and Flexible Physics Emulators
- 推理时循环调整补丁尺寸，分散高频误差
- 相比固定补丁模型，长期预测误差降低40%
- 可灵活平衡速度与精度，适合资源受限场景
基于Transformer的偏微分方程（PDE）代理模型虽表现优异，但面临两大挑战：固定补丁尺寸导致谐波频率处系统性误差累积，且计算成本无法随问题复杂度或可用资源灵活调整。本文提出Overtone，一种通过推理时动态控制补丁尺寸的统一解决方案。其核心思想是在自回归推演过程中周期性调制补丁大小，将误差分布至整个频谱，缓解固定补丁模型的系统性谐波伪影累积问题。通过两个架构无关模块——使用动态步长调制的CSM和使用动态核大小重置的CKM——实现误差抑制与计算自适应部署。该灵活的标记化机制使用户可根据计算约束动态权衡准确率与速度，循环推演策略在方差归一化均方根误差（VRMSE）上相较传统静态补丁代理模型最高降低40%。在多个具有挑战性的二维和三维PDE基准测试中，一个训练好的Overtone模型在固定总训练预算下，无论推理计算预算如何，均能匹配或超越固定补丁基线。
原文摘要 · Abstract (English)
Transformer-based PDE surrogates achieve remarkable performance but face two key challenges: fixed patch sizes cause systematic error accumulation at harmonic frequencies, and computational costs remain inflexible regardless of problem complexity or available resources. We introduce Overtone, a unified solution through dynamic patch size control at inference. Overtone's key insight is that cyclically modulating patch sizes during autoregressive rollouts distributes errors across the frequency spectrum, mitigating the systematic harmonic artifact accumulation that plague fixed-patch models. We implement this through two architecture-agnostic modules--CSM (using dynamic stride modulation) and CKM (using dynamic kernel resizing)--that together provide both harmonic mitigation and compute-adaptive deployment. This flexible tokenization lets users trade accuracy for speed dynamically based on computational constraints, and the cyclic rollout strategy yields up to 40% lower long rollout error in variance-normalised RMSE (VRMSE) compared to conventional, static-patch surrogates. Across challenging 2D and 3D PDE benchmarks, one Overtone model matches or exceeds fixed-patch baselines across inference compute budgets, when trained under a fixed total training budget setting.
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