# The Physics Constraint Paradox: When Removing Explicit Constraints Improves Physics-Informed Data for Machine Learning

arXiv: https://arxiv.org/abs/2512.22261 · HTML: https://mlsanity.com/paper/2512.22261/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 18 references that are in the map.
- First posted on arXiv 24 Dec 2025.

## Builds on (most cited first, 4 of 4)

- [Deep neural networks for the evaluation and design of photonic devices](https://mlsanity.com/paper/2007.00084/) (2020)
- [Training Generative Adversarial Networks for Optical Property Mapping using Synthetic Image Data](https://mlsanity.com/paper/2203.07793/) (2022)
- [Data driven approaches in nanophotonics: A review of AI-enabled metadevices](https://mlsanity.com/paper/2510.00283/) (2025)
- [Datasets and Benchmarks for Nanophotonic Structure and Parametric Design Simulations](https://mlsanity.com/paper/2310.19053/) (2023)

## Abstract (arXiv)

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.