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

• URL: http://arxiv.org/abs/2507.09264v1
• Date: Sat, 12 Jul 2025 12:16:04 GMT
• Title: Controllable Patching for Compute-Adaptive Surrogate Modeling of Partial Differential Equations
• Abstract summary: We introduce two lightweight modules that enable dynamic patch size control inference in patch based models without retraining or accuracy loss.<n>To our knowledge, this is the first framework to enable inference-time patch-size tunability in patch-based PDE surrogates.
• Score: 5.248019942004983
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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