让深度学习重建物理场时遵守物理定律,精度与合规性双提升。
Physics-aligned Schrödinger bridge
- 用物理对齐的扩散桥模型,分两阶段训练兼顾局部映射与全局物理规律
- 在3个非线性系统中均实现更高精度和更强物理约束满足度
- 适合需要高保真物理场重建的流体、反应扩散等工程场景
从稀疏测量中重建物理场在科研与工程中至关重要。传统方法日益被深度学习模型补充,因其能有效提取数据特征,但常因无法满足守恒方程、边界条件等基本物理约束而精度受限。为此,本文提出一种新型数据驱动场重建框架——物理对齐的薛定谔桥(PalSB)。该框架采用专为物理约束对齐设计的扩散薛定谔桥机制,通过双阶段训练分别处理局部重建映射与全局物理原理,并引入边界感知采样技术以确保满足物理边界条件。我们在三个复杂非线性系统上验证了其有效性:基于粒子图像测速实验的圆柱绕流、二维湍流及反应-扩散系统。结果表明,相比现有方法,PalSB不仅显著提升重建精度,更大幅增强对物理约束的遵守程度,展现出生成复杂物理相互作用高质量表征的能力,具有推动场重建技术发展的潜力。
原文摘要 · Abstract (English)
The reconstruction of physical fields from sparse measurements is pivotal in both scientific research and engineering applications. Traditional methods are increasingly supplemented by deep learning models due to their efficacy in extracting features from data. However, except for the low accuracy on complex physical systems, these models often fail to comply with essential physical constraints, such as governing equations and boundary conditions. To overcome this limitation, we introduce a novel data-driven field reconstruction framework, termed the Physics-aligned Schrödinger Bridge (PalSB). This framework leverages a diffusion Schrödinger bridge mechanism that is specifically tailored to align with physical constraints. The PalSB approach incorporates a dual-stage training process designed to address both local reconstruction mapping and global physical principles. Additionally, a boundary-aware sampling technique is implemented to ensure adherence to physical boundary conditions. We demonstrate the effectiveness of PalSB through its application to three complex nonlinear systems: cylinder flow from Particle Image Velocimetry experiments, two-dimensional turbulence, and a reaction-diffusion system. The results reveal that PalSB not only achieves higher accuracy but also exhibits enhanced compliance with physical constraints compared to existing methods. This highlights PalSB's capability to generate high-quality representations of intricate physical interactions, showcasing its potential for advancing field reconstruction techniques.
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