When Does Frequency Decomposition Benefit Physics-Informed Neural Networks? A Preliminary Ablation Study

Partial differential equations (PDEs) that describe physical systems often contain high-frequency and multi-scale features that neural networks find hard to approximate. Physics-Informed Neural Networks (PINNs) build the governing equations directly into training, but they suffer from spectral bias: they learn low-frequency components faster than high-frequency ones. Fourier feature embeddings, sinusoidal activations, and other frequency-aware techniques have been proposed to fix this, but most studies simply assume these methods help across the board, without checking which spectral regimes they actually help in. We build a dual-branch, spectrally-gated architecture (DBSG-PINN) that splits low and high-frequency solution components into separate subnetworks joined by an adaptive gate, and use it to run a partially controlled ablation of frequency decomposition and spectral routing. We test this on five one-dimensional benchmark PDEs, ranging from smooth, single-scale problems to oscillatory, multi-scale ones. Frequency decomposition helps most on the spectrally complex benchmarks, cutting relative $L_2$ error by up to 59.2% relative to the weakest single-branch ablation (LowOnly) on a multimodal wave problem, but gives little benefit on smoother PDEs. On one benchmark (1D Wave), it actually performs substantially worse than a simpler fixed-combination variant. Across benchmarks, the gate's benefit also scales with how spectrally rich the target solution is, a pattern consistent with the gate exploiting frequency structure rather than acting as noise. All results here come from a single training seed across five 1D benchmarks, so we present this as an exploratory study meant to raise questions rather than answer them.