Overtone: Cyclic Patch Modulation for Cleaner, Faster Physics Emulators

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, preventing the systematic harmonic artifacts that plague fixed-patch models. We implement this through two architecture-agnostic modules—CSM (Cyclic Stride Modulator, using dynamic stride modulation) and CKM (Cyclic Kernel Modulator, using dynamic kernel resizing)—that together provide both harmonic mitigation and compute-adaptive deployment. The harmonic mitigation alone yields up to 40% error reduction in long rollouts, while the flexible tokenization allows users to trade accuracy for speed dynamically based on computational constraints. Applied to challenging 2D and 3D PDE benchmarks, a single Overtone model matches or exceeds multiple fixed-patch baselines across all compute budgets.