通过中间特征对齐提升物理扩散模型的泛化能力，防止捷径学习。
Learning to Think in Physics: Breaking Shortcut Learning in Scientific Diffusion via Representation Alignment
- 在中间层引入轻量投影头，用物理残差约束隐藏表示。
- 收敛速度最快提升2倍，物理残差降低66.4%，分布外性能提升49.3%。
- 无需教师模型，兼容多种架构，适合追求鲁棒性的科学建模者。
物理信息扩散模型通常仅在输出阶段施加偏微分方程（PDE）约束，导致中间表征未受约束，在边界条件偏移时易出现捷径学习。本文提出无教师、架构无关的REPA-P框架，通过一阶原理残差将中间特征与物理状态对齐。REPA-P在选定层附加轻量级1×1投影头，将隐层激活解码为物理量，并在训练中施加PDE残差损失；推理时丢弃这些头，实现零开销。在四个PDE任务（达西流、拓扑优化、静电势、湍流通道流）上，REPA-P使收敛速度加快最多2倍，物理残差减少最多66.4%，分布外鲁棒性提升最多49.3%，且在U-Net和Diffusion Transformer骨干网络上均表现一致提升。消融实验表明，仅监督少量中间层即可捕获大部分收益，并有效补充输出层物理损失。代码已公开于https://github.com/Hxxxz0/REPA-P。
原文摘要 · Abstract (English)
Physics-informed diffusion models typically enforce PDE constraints only on final outputs, leaving intermediate representations unconstrained and prone to shortcut learning under shifted boundary conditions. We introduce **REPA-P**, a teacher-free, architecture-agnostic framework that aligns intermediate features with physical states using first-principles residuals. REPA-P attaches lightweight $1{\times}1$ projection heads to selected layers, decodes hidden activations into physical quantities, and applies PDE residual losses during training. These heads are discarded at inference, introducing **zero overhead**. Across four PDE tasks, including Darcy flow, topology optimization, electrostatic potential, and turbulent channel flow, REPA-P accelerates convergence by up to $2{\times}$, reduces physics residuals by up to $66.4\%$, and improves out-of-distribution robustness by up to $49.3\%$, with consistent gains on both U-Net and Diffusion Transformer backbones. Ablations show that supervising a small set of intermediate layers captures most benefits and complements output-level physics losses. Code is available at [https://github.com/Hxxxz0/REPA-P](https://github.com/Hxxxz0/REPA-P).
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