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

TL;DR

The paper tackles the data bottleneck in physics-guided photonic design by introducing a fast, physics-informed generator that maps five geometric design parameters to grating-coupler spectra, embedding key physical constraints while enabling on-demand data synthesis. Through a modular surrogate—encompassing effective-index estimation, grating modulation, resonant coupling, absorption, and normalization—the authors perform a systematic ablation to identify which physical components are essential. They show that explicit energy-conservation enforcement is mathematically redundant for physically consistent models, while Fabry-Perot oscillations drive substantial bandwidth variability under threshold definitions and critically shape spectral detail. The study demonstrates a clear physics–ML trade-off: removing Fabry-Perot effects improves envelope-level bandwidth learnability by substantial margins, while central-wavelength prediction remains unaffected, highlighting how ML performance can diagnose constraint relevance. Concrete guidance emerges for physics-informed dataset design, including when to include or omit certain physics for targeted learning tasks, and the work provides an open-source, high-throughput data generator to accelerate photonic inverse design.

Abstract

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.

Figures (5)

• Figure 1: Architecture of the physics-informed surrogate model for grating coupler spectra generation. The diagram illustrates the modular computational pipeline that maps geometric design parameters to physically consistent optical spectra through sequential analytical modeling and constraint enforcement stages.
• Figure 2: Example spectra generated by the Reference physics-informed generator for a representative parameter set, showing reflectance (R), transmittance (T), and absorbance (A). The spectra satisfy global energy conservation and exhibit physically realistic resonant structure.
• Figure 3: Distribution of maximum pointwise energy conservation error across all generated samples. All variants achieve errors near machine precision, demonstrating that energy conservation emerges intrinsically from the physical model formulation.
• Figure 4: Distribution of effective spectral bandwidth (second central moment of normalized transmission) for the Reference and No-Fabry–Perot generators. Removal of Fabry–Perot oscillations reduces effective bandwidth variability, indicating their role in fine spectral structuring.
• Figure 5: Distribution of minimum absorption values per sample for the Reference generator. While global energy conservation is satisfied, localized negative absorption values arise from noise addition followed by renormalization, revealing limitations of mean-based validation metrics.