删掉物理约束反而让机器学习数据更准，关键发现有三个。
The Physics Constraint Paradox: When Removing Explicit Constraints Improves Physics-Informed Data for Machine Learning
- 系统测试移除不同物理约束的效果，发现能量守恒可省略
- 去掉干涉条纹后带宽波动减少72%，预测精度提升超七成
- 噪声处理不当会引入虚假负吸收值，适合科研数据生成者看
在真实数据稀缺的科学领域，物理约束数据生成对机器学习至关重要。本文针对一个物理信息型光栅耦合器光谱生成器（映射5个几何参数到100点光谱响应）进行系统消融研究，逐步移除能量守恒、法布里-珀罗振荡、带宽变化和噪声等显式约束。结果揭示：当底层方程本身物理自洽时，显式能量守恒冗余，约束与无约束版本均实现约7×10⁻⁹的均值误差；而移除法布里-珀罗振荡使半高全宽展宽从132.3 nm降至37.4 nm，降幅达72%。标准加噪再归一化流程引入0.5%非物理解吸收值。生成速度达200样本/秒，远快于文献中典型全波求解器。下游机器学习评估显示，移除干涉振荡虽不影响中心波长预测，但使带宽预测的R²提升31.3%，RMSE下降73.8%。该发现为物理信息数据集设计提供实证指导，并表明机器学习性能可作为判断约束必要性的诊断工具。
原文摘要 · Abstract (English)
Physics-constrained data generation is essential for machine learning in scientific domains where real data are scarce; however, existing approaches often over-constrain models without identifying which physical components are necessary. We present a systematic ablation study of a physics-informed grating coupler spectrum generator that maps five geometric parameters to 100-point spectral responses. By selectively removing explicit energy conservation enforcement, Fabry-Perot oscillations, bandwidth variation, and noise, we uncover a physics constraint paradox: explicit energy conservation enforcement is mathematically redundant when the underlying equations are physically consistent, with constrained and unconstrained variants achieving identical conservation accuracy (mean error approximately 7 x 10^-9). In contrast, Fabry-Perot oscillations dominate threshold-based bandwidth variability, accounting for a 72 percent reduction in half-maximum bandwidth spread when removed (with bandwidth spread reduced from 132.3 nm to 37.4 nm). We further identify a subtle pitfall: standard noise-addition-plus-renormalization pipelines introduce 0.5 percent unphysical negative absorption values. The generator operates at 200 samples per second, enabling high-throughput data generation and remaining orders of magnitude faster than typical full-wave solvers reported in the literature. Finally, downstream machine learning evaluation reveals a clear physics-learnability trade-off: while central wavelength prediction remains unaffected, removing Fabry-Perot oscillations improves bandwidth prediction accuracy by 31.3 percent in R-squared and reduces RMSE by 73.8 percent. These findings provide actionable guidance for physics-informed dataset design and highlight machine learning performance as a diagnostic tool for assessing constraint relevance.
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