arXiv:2601.20227cs.LGcs.AI2026-01被引 1

无需重训练,让生成模型采样结果严格符合物理规律。

ProFlow: Zero-Shot Physics-Consistent Sampling via Proximal Flow Guidance

  • 用两步交替优化保证物理方程与观测数据双重一致
  • 在泊松、亥姆霍兹等方程上优于现有扩散与流模型
  • 适合需要快速适配新物理场景的科研与工程应用

从稀疏观测中推断物理场并严格满足偏微分方程(PDE)是计算物理中的基础挑战。近年来,深度生成模型为这类反问题提供了强大的数据驱动先验,但现有方法难以在不进行代价高昂的重训练或破坏已学习生成先验的前提下强制执行硬性物理约束。因此,亟需一种采样机制,能在保持预训练先验统计结构的同时,实现严格的物理一致性与观测保真度。为此,我们提出 ProFlow,一种零样本物理一致性采样的近端引导框架,即在不进行任务特定重训练的情况下,利用固定生成先验从稀疏观测中推断解。该算法采用严格的两步方案:(Ⅰ)终端优化步骤,通过近端最小化将流预测投影到物理一致集与观测一致集的交集中;(Ⅱ)插值步骤,将修正后的状态映射回生成轨迹,以维持与学习到的流概率路径的一致性。该过程可解释为一系列局部最大后验(MAP)更新。在泊松、亥姆霍兹、达西及黏性布格尔斯方程上的综合基准测试表明,ProFlow 在物理一致性、观测保真度和分布统计准确性方面均优于当前最先进的扩散与流基模型。

原文摘要 · Abstract (English)

Inferring physical fields from sparse observations while strictly satisfying partial differential equations (PDEs) is a fundamental challenge in computational physics. Recently, deep generative models offer powerful data-driven priors for such inverse problems, yet existing methods struggle to enforce hard physical constraints without costly retraining or disrupting the learned generative prior. Consequently, there is a critical need for a sampling mechanism that can reconcile strict physical consistency and observational fidelity with the statistical structure of the pre-trained prior. To this end, we present ProFlow, a proximal guidance framework for zero-shot physics-consistent sampling, defined as inferring solutions from sparse observations using a fixed generative prior without task-specific retraining. The algorithm employs a rigorous two-step scheme that alternates between: (\romannumeral1) a terminal optimization step, which projects the flow prediction onto the intersection of the physically and observationally consistent sets via proximal minimization; and (\romannumeral2) an interpolation step, which maps the refined state back to the generative trajectory to maintain consistency with the learned flow probability path. This procedure admits a Bayesian interpretation as a sequence of local maximum a posteriori (MAP) updates. Comprehensive benchmarks on Poisson, Helmholtz, Darcy, and viscous Burgers' equations demonstrate that ProFlow achieves superior physical and observational consistency, as well as more accurate distributional statistics, compared to state-of-the-art diffusion- and flow-based baselines.

物理模型生成模型逆问题零样本

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