[2507.09264] Overtone: Cyclic Patch Modulation for Clean, Efficient, and Flexible Physics Emulators

Computer Science > Machine Learning arXiv:2507.09264 (cs) [Submitted on 12 Jul 2025 (v1), last revised 5 Mar 2026 (this version, v2)] Title:Overtone: Cyclic Patch Modulation for Clean, Efficient, and Flexible Physics Emulators Authors:Payel Mukhopadhyay, Michael McCabe, Ruben Ohana, Miles Cranmer View a PDF of the paper titled Overtone: Cyclic Patch Modulation for Clean, Efficient, and Flexible Physics Emulators, by Payel Mukhopadhyay and 3 other authors View PDF HTML (experimental) Abstract: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 erro...