Tail‑error‑focused training objectives for HQ‑LP‑FNO

Design and evaluate training objectives that explicitly penalize tail errors for HQ‑LP‑FNO with a VQC spectral mixer, and ascertain their impact on geometry‑sensitive metrics such as the intersection‑over‑union (IoU) of the liquid‑fraction segmentation.

Background

In experiments, the VQC‑based HQ‑LP‑FNO improved mean temperature errors but sometimes exhibited elevated RMSE and lower IoU on melt‑related quantities, driven by localized deviations near steep gradients and interfaces.

The authors suggest that loss formulations emphasizing tail errors or interface sensitivity could improve these metrics, framing the development of such objectives as an open direction.

References

Several directions remain open. Training objectives that explicitly penalize tail errors could improve the VQC's performance on geometry-sensitive metrics like IoU.

— Hybrid Fourier Neural Operator for Surrogate Modeling of Laser Processing with a Quantum-Circuit Mixer  (2604.04828 - Papierz et al., 6 Apr 2026) in Conclusion (Section 6)