Controllable Patching for Compute-Adaptive Surrogate Modeling of Partial Differential Equations

Abstract: Patch-based transformer surrogates have become increasingly effective for modeling spatiotemporal dynamics, but the fixed patch size is a major limitation for budget-conscience deployment in production. We introduce two lightweight, architecture-agnostic modules-the Convolutional Kernel Modulator (CKM) and Convolutional Stride Modulator (CSM)-that enable dynamic patch size control at inference in patch based models, without retraining or accuracy loss. Combined with a cyclic patch-size rollout, our method mitigates patch artifacts and improves long-term stability for video-like prediction tasks. Applied to a range of challenging 2D and 3D PDE benchmarks, our approach improves rollout fidelity and runtime efficiency. To our knowledge, this is the first framework to enable inference-time patch-size tunability in patch-based PDE surrogates. Its plug-and-play design makes it broadly applicable across architectures-establishing a general foundation for compute-adaptive modeling in PDE surrogate tasks.