PolyFKAN: Integrating Fourier-KAN layers into graph neural networks for polymer property prediction

Graph neural networks have become a central tool for polymer property prediction, but their fixed activation functions can impose a low-pass spectral bias that smooths over the sharp, multi-scale structure-property variations that distinguish chemically similar polymers. We address this limitation with PolyFKAN, a multitask graph-learning architecture that augments the prediction head of a polyGNN backbone with Fourier Kolmogorov-Arnold network layers. PolyFKAN represents edge-wise activations as truncated Fourier series and couples the resulting spectral branch to the standard multilayer perceptron (MLP) pathway through a bounded residual gate, thereby increasing functional expressivity without disrupting the learned graph embeddings. Across 17 polymer properties spanning electronic, thermodynamic, optical/dielectric, thermal, and gas-permeability domains, PolyFKAN achieves statistically significant improvement over a tightly controlled polyGNN baseline on 11 of 17 targets (one-sided t-test, p < 0.05), with one additional target showing marginal improvement. The gains are especially pronounced for multi-scale properties, including more than 15% average root mean squared error reduction for large-penetrant gas permeabilities and more than 15% improvement across optical and dielectric targets. Hierarchical ablation further reveals that optimal Fourier bandwidth is property-dependent: difficult, multi-scale targets require broader spectral capacity with stronger amplitude control, whereas high-fidelity targets benefit from lighter regularization. These results establish Fourier-KAN prediction heads as a minimally invasive and physically aligned inductive bias for polymer informatics.