CoupledFlow：一步预测多物理场耦合PDE的神经算子框架
CoupledFlow: One-Step Neural Operators for Coupled Multi-Physics PDEs
搞科学计算的朋友可以看看这篇：它把 flow matching 用到了多物理场耦合 PDE 上，一次前向就出解，不用跑传统数值模拟。还给了 Wasserstein-2 误差上界的理论保证，比单物理场的神经算子更贴近真实工程场景。
arXiv 论文提出 CoupledFlow，一个面向多物理场耦合 PDE 系统的神经算子学习框架，能在一步内完成快速预测，替代昂贵的数值模拟。与现有主要面向单物理场的神经算子不同，CoupledFlow 通过结构约束的 flow matching 算法，以完整多物理场状态为条件学习各过程专属的平均速度场，从而捕捉多个物理过程的共同演化与跨过程交互。
训练的核心难点在于采样能反映跨过程相关性的结构约束条件流插值。作者推导了多物理场 mean-flow 一致性恒等式来刻画跨过程交互并定义损失函数，并基于后验多输出高斯过程开发采样方法，比常用的端点条件线性插值捕捉更丰富的相关性。理论上，论文证明了预测与真解 PDE 解分布之间的 Wasserstein-2 距离可由损失值和学到流的光滑度上界约束。
在多个耦合 PDE 基准上的实验显示，CoupledFlow 持续优于现有 SOTA 神经算子与生成式 PDE 求解器。
CoupledFlow: One-Step Neural Operators for Coupled Multi-Physics PDEs
This paper introduces COUPLED FLOW, a new neural operator learning framework for multi-physics PDE systems that captures the co-evolution of multiple physical processes by modeling their cross-process interactions. Unlike existing neural operator methods that primarily target single-physics settings, COUPLED FLOW employs a novel structure-constrained flow matching algorithm to learn process- specific mean velocity fields conditioned on the full multi-physics state. This enables fast and accurate one-step prediction of coupled PDE systems that would otherwise require expensive numerical simulations. A key challenge in training COUPLED FLOW however lies in sampling structure-constrained conditional flow interpolants that capture cross-process correlations and serve as training examples for flow matching. To address this challenge, we derive a multi-physics mean-flow consistency identity that characterizes cross-process interactions and defines the structure-constrained mean-flow matching loss. To provide informative training samples for flow matching with this loss, we develop a principled method for sampling correlated conditional interpolants based on posterior multi-output Gaus- sian processes, which capture richer cross-process correlations than the commonly used endpoint-conditioned linear interpolants. We also establish a theoretical re- sult showing that the Wasserstein-2 distance between the predicted and oracle PDE solution distributions is upper-bounded in terms of the structure-constrained flow matching loss and the smoothness of the learned flow. Experiments across diverse coupled PDE benchmarks demonstrate that COUPLED FLOW consistently outperforms existing state-of-the-art neural operators and generative PDE solvers.
This report is categorized under AITOP's "Papers" desk. Within our cross-regional analytical framework, it directly maps to AI developer toolchains, coding agents, and engineering workflows. Key entities and technical topics under continuous tracking include 神经算子, PDE求解, flow matching, 科学计算.
Source attribution: curated from arXiv cs.LG (@Trong Khiem Tran, Minh Long Bui, Phi Le Nguyen, Mrinal Sen, Sanjay Srinivasan, Trong Nghia Hoang, Jana Doppa).