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

TL;DR

This study systematically analyzes the effects of explicit physical constraints on a physics-informed spectral generator, revealing when such constraints are redundant and how removing certain physical components can improve machine learning predictions.

Contribution

The paper provides a systematic ablation study demonstrating that some explicit physical constraints are redundant and shows how removing specific constraints enhances machine learning performance and data generation efficiency.

Findings

Explicit energy conservation enforcement is redundant with physically consistent equations.

Removing Fabry-Perot oscillations significantly reduces bandwidth variability.

Standard noise addition can introduce unphysical negative absorption values.

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.