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

2025-07-12

AI Summary

Patch-based PDE surrogate models suffer from high computational overhead, pronounced block artifacts, and unstable long-horizon predictions due to fixed patch sizes. Method: This paper proposes a dynamic patch-size adaptation method operating solely at inference time—requiring no retraining. It introduces a Convolutional Kernel Modulator (CKM) and a Convolutional Stride Modulator (CSM), integrated with a recurrent patch-unfolding strategy, enabling on-the-fly adjustment of patch dimensions during inference. Contribution/Results: The approach effectively suppresses boundary artifacts, improves rollout accuracy, and enhances long-term prediction stability, while maintaining plug-and-play compatibility and architectural generality. Evaluated on multiple 2D/3D PDE benchmark tasks, it achieves an average 12.7% improvement in prediction accuracy and 1.8–2.4× speedup in inference latency over fixed-patch baselines, demonstrating its effectiveness and practicality for complex spatiotemporal modeling.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Machine Learning: Large Multimodal Models (LMMs)
• Cognitive Modeling & Cognitive Systems: Adaptive Behavior

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Dynamic patch size control in patch-based PDE surrogates
• Mitigate patch artifacts in video-like prediction tasks
• Improve rollout fidelity and runtime efficiency in PDE benchmarks

Innovation

• Dynamic patch size control via CKM and CSM
• Cyclic patch-size rollout reduces artifacts
• Plug-and-play design for various architectures